import pandas as pd
import pandas_market_calendars as mcal
from datetime import date
import numpy as np
import matplotlib.pyplot as plt
import math
import time
import statsmodels.api as sm
import seaborn as sns
import datetime as dt
import pymc as pm
import arviz as az

C:\Users\isaxonov_rdy\AppData\Local\miniforge3\envs\sfr\Lib\site-packages\arviz\__init__.py:50: FutureWarning: 
ArviZ is undergoing a major refactor to improve flexibility and extensibility while maintaining a user-friendly interface.
Some upcoming changes may be backward incompatible.
For details and migration guidance, visit: https://python.arviz.org/en/latest/user_guide/migration_guide.html
  warn(

Read the CSV and convert dates to datetime

df = pd.read_csv("funding_liquidity_inputs.csv")
date_format = '%Y%m%d'
df["date"] = pd.to_datetime(df["date"], format=date_format, errors="coerce")

Create features and output

df["sofr_iorb_diff"] = df["sofr_rate"] - df["iorb"]
df["total_rrp"] =  df["rrp_total_bil"] # + df["rrp_foreign_bil"]
df["leverage_ratio"] = df["sofr_vol"] / (df["reserves"] + df["total_rrp"])
df = sm.add_constant(df)

Slice data to just this past year, and take differences of all the data

dfdiff = df

dfdiff["sofr_iorb_diff_diff"] = dfdiff["sofr_iorb_diff"].diff()
dfdiff["rrp_total_bil_diff"] = dfdiff["rrp_total_bil"].diff()
dfdiff["leverage_ratio_diff"] = dfdiff["leverage_ratio"].diff()
dfdiff["reserves_diff"] = dfdiff["reserves"].diff()

dfdiff = dfdiff.dropna()

start = dfdiff["date"].searchsorted(dt.datetime(2025,1,1))
dfdiff = dfdiff.iloc[start:]

Rolling mean to smooth our data

window = 30

dfdiff["rolling_sofr_iorb_diff_diff"] = dfdiff["sofr_iorb_diff_diff"].rolling(window=window).mean()
dfdiff["rolling_leverage_ratio_diff"] = dfdiff["leverage_ratio_diff"].rolling(window=window).mean()
dfdiff["rolling_rrp_total_bil_diff"] = dfdiff["rrp_total_bil_diff"].rolling(window=window).mean()
dfdiff["rolling_reserves_diff"] = dfdiff["reserves_diff"].rolling(window=window).mean()

dfdiff = dfdiff.dropna()

Normalize our data with z-scoring

def normalize(df, x):
    return [(df[x] - df[x].mean())/(df[x].std()), df[x].mean(), df[x].std()]

dfdiff["norm_leverage_ratio_diff"], leverage_mean, leverage_std = normalize(dfdiff, "leverage_ratio_diff")
dfdiff["norm_reserves_diff"], reserves_mean, reserves_std  = normalize(dfdiff, "reserves_diff")
dfdiff["norm_rrp_total_bil_diff"], rrp_mean, rrp_std = normalize(dfdiff, "rrp_total_bil_diff")
dfdiff["norm_sofr_iorb_diff_diff"], sofr_iorb_mean, sofr_iorb_std = normalize(dfdiff, "sofr_iorb_diff_diff")

input_df = dfdiff[['norm_leverage_ratio_diff', 'norm_reserves_diff', 'norm_rrp_total_bil_diff', 'const']]
model = sm.OLS(dfdiff["norm_sofr_iorb_diff_diff"], input_df)
results = model.fit()
print(results.summary())

                               OLS Regression Results                               
====================================================================================
Dep. Variable:     norm_sofr_iorb_diff_diff   R-squared:                       0.360
Model:                                  OLS   Adj. R-squared:                  0.352
Method:                       Least Squares   F-statistic:                     45.57
Date:                      Wed, 11 Feb 2026   Prob (F-statistic):           2.10e-23
Time:                              16:17:38   Log-Likelihood:                -294.85
No. Observations:                       247   AIC:                             597.7
Df Residuals:                           243   BIC:                             611.7
Df Model:                                 3                                         
Covariance Type:                  nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
norm_leverage_ratio_diff     0.5792      0.056     10.302      0.000       0.468       0.690
norm_reserves_diff           0.2707      0.056      4.871      0.000       0.161       0.380
norm_rrp_total_bil_diff      0.1999      0.052      3.844      0.000       0.097       0.302
const                    -1.388e-17      0.051  -2.71e-16      1.000      -0.101       0.101
==============================================================================
Omnibus:                       33.098   Durbin-Watson:                   2.154
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              138.310
Skew:                          -0.404   Prob(JB):                     9.26e-31
Kurtosis:                       6.576   Cond. No.                         1.55
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

az.plot_density(dfdiff["norm_sofr_iorb_diff_diff"])

array([[<Axes: title={'center': 'x'}>]], dtype=object)

dfdiff["end-of-month"] = 0

start_date = dfdiff["date"].min()
end_date = dfdiff["date"].max()
month_ends = pd.date_range(start=start_date, end=end_date, freq='ME')
month_ends

DatetimeIndex(['2025-02-28', '2025-03-31', '2025-04-30', '2025-05-31',
               '2025-06-30', '2025-07-31', '2025-08-31', '2025-09-30',
               '2025-10-31', '2025-11-30', '2025-12-31', '2026-01-31'],
              dtype='datetime64[ns]', freq='ME')

(dfdiff["date"].to_numpy()[31] in month_ends)

True

dfdiff.loc[dfdiff["date"].isin(month_ends), "end-of-month"] = 1
dfdiff.loc[dfdiff["date"].isin([date(2025,11,28), date(2025,8,29), date(2025,5,30)]), "end-of-month"] = 1

C:\Users\isaxonov_rdy\AppData\Local\Temp\ipykernel_7552\395586811.py:2: FutureWarning: The behavior of 'isin' with dtype=datetime64[ns] and castable values (e.g. strings) is deprecated. In a future version, these will not be considered matching by isin. Explicitly cast to the appropriate dtype before calling isin instead.
  dfdiff.loc[dfdiff["date"].isin([date(2025,11,28), date(2025,8,29), date(2025,5,30)]), "end-of-month"] = 1

dfdiff["date"].describe()

count                              247
mean     2025-08-10 04:10:41.295546624
min                2025-02-13 00:00:00
25%                2025-05-13 12:00:00
50%                2025-08-08 00:00:00
75%                2025-11-05 12:00:00
max                2026-02-06 00:00:00
Name: date, dtype: object

with pm.Model(coords={"day":dfdiff["date"]}) as model:
    leverage = pm.Data("leverage", dfdiff["norm_leverage_ratio_diff"], dims="day")
    reserves = pm.Data("reserves", dfdiff["norm_reserves_diff"], dims="day")
    rrp = pm.Data("rrp", dfdiff["norm_rrp_total_bil_diff"], dims="day")
    end_of_month = pm.Data("end_of_month", dfdiff["end-of-month"], dims="day")

    alpha = pm.Normal("alpha", 0, 0.05)
    
    beta_leverage = pm.Normal("beta_leverage", 1, 0.5)
    beta_reserves = pm.Normal("beta_reserves", -0.1, 0.5)
    beta_rrp = pm.Normal("beta_rrp", 0, 0.5)
    beta_end_of_month = pm.Normal("beta_end_of_month", 1, 1.5)

    sigma = pm.Exponential("sigma", lam=0.5)

    mu = alpha + (beta_leverage + beta_end_of_month * end_of_month) * leverage + beta_reserves * reserves + beta_rrp * rrp
    y_hat = pm.Normal("y_hat", mu=mu, sigma=sigma, observed=dfdiff["norm_sofr_iorb_diff_diff"], dims="day")

model.debug(verbose=True)

point={'alpha': array(0.), 'beta_leverage': array(1.), 'beta_reserves': array(-0.1), 'beta_rrp': array(0.), 'beta_end_of_month': array(1.), 'sigma_log__': array(0.69314718)}

No problems found

with model:
    idata=pm.sample(nuts_sampler="nutpie")

C:\Users\isaxonov_rdy\AppData\Local\miniforge3\envs\sfr\Lib\site-packages\threadpoolctl.py:1226: RuntimeWarning: 
Found Intel OpenMP ('libiomp') and LLVM OpenMP ('libomp') loaded at
the same time. Both libraries are known to be incompatible and this
can cause random crashes or deadlocks on Linux when loaded in the
same Python program.
Using threadpoolctl may cause crashes or deadlocks. For more
information and possible workarounds, please see
    https://github.com/joblib/threadpoolctl/blob/master/multiple_openmp.md

  warnings.warn(msg, RuntimeWarning)

Sampler Progress

Total Chains: 4

Active Chains: 0

Finished Chains: 4

Sampling for now

Estimated Time to Completion: now

Progress	Draws	Divergences	Step Size	Gradients/Draw
	2000	0	0.81	3
	2000	0	0.84	3
	2000	0	0.79	7
	2000	0	0.80	7

model.to_graphviz()

Sampling our prior distribution to see if it aligns with our data.

with model:
    prior = pm.sample_prior_predictive()

Sampling: [alpha, beta_end_of_month, beta_leverage, beta_reserves, beta_rrp, sigma, y_hat]

fig, ax = plt.subplots();

dfdiff["norm_sofr_iorb_diff_diff"].plot(ax=ax);
ax.plot(dfdiff.index,prior.prior_predictive.y_hat.sel(chain=0, draw=1), alpha = 0.25);

Not great but not terrible

pm.plot_trace(idata)
plt.tight_layout()
plt.show();

with model:
    idata=pm.sample_posterior_predictive(idata, extend_inferencedata=True)
    pm.compute_log_likelihood(idata)

Sampling ... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━   0% -:--:-- / 0:00:00

pm.plot_ppc(idata)

Perhaps we should use a generalized normal distribution here- it looks like we want our posterior predictive to be slightly less kurtotic…

pm.plot_ppc(idata)

C:\Users\isaxonov_rdy\AppData\Local\miniforge3\envs\sfr\Lib\site-packages\IPython\core\events.py:96: UserWarning: Creating legend with loc="best" can be slow with large amounts of data.
  func(*args, **kwargs)
C:\Users\isaxonov_rdy\AppData\Local\miniforge3\envs\sfr\Lib\site-packages\IPython\core\pylabtools.py:170: UserWarning: Creating legend with loc="best" can be slow with large amounts of data.
  fig.canvas.print_figure(bytes_io, **kw)

idata

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 200kB
  Dimensions:        (chain: 4, draw: 1000)
  Coordinates:
    * chain          (chain) int64 32B 0 1 2 3
    * draw           (draw) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
  Data variables:
      alpha          (chain, draw) float64 32kB -0.03466 0.03224 ... 0.01315
      beta_leverage  (chain, draw) float64 32kB 0.6218 0.7952 ... 0.6892 0.7543
      beta_reserves  (chain, draw) float64 32kB 0.0547 0.2745 ... 0.09361 0.09422
      beta_rrp       (chain, draw) float64 32kB 0.1009 0.1178 ... 0.0352 0.1103
      sigma_log__    (chain, draw) float64 32kB -0.2758 -0.2878 ... -0.3154
      sigma          (chain, draw) float64 32kB 0.7589 0.7499 ... 0.6958 0.7295
  Attributes:
      created_at:                 2026-02-10T18:34:29.476208+00:00
      arviz_version:              0.23.4
      inference_library:          nutpie
      inference_library_version:  0.16.5
      sampling_time:              0.16512465476989746
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

  • Data variables: (6)
    • alpha
      (chain, draw)
      float64
      -0.03466 0.03224 ... 0.01315

      array([[-0.03466254,  0.03224332,  0.05949509, ..., -0.01501405,
               0.01473414, -0.00107349],
             [ 0.04565191,  0.00110969, -0.0143784 , ..., -0.05070824,
               0.0415602 ,  0.04384447],
             [ 0.03682197,  0.00316912,  0.00316912, ..., -0.01426644,
               0.04071523, -0.00898986],
             [-0.03110014,  0.03839895,  0.00491066, ..., -0.05404182,
               0.03384539,  0.01315091]], shape=(4, 1000))

    • beta_leverage
      (chain, draw)
      float64
      0.6218 0.7952 ... 0.6892 0.7543

      array([[0.62178427, 0.79520919, 0.85059116, ..., 0.80645795, 0.78715207,
              0.89397464],
             [0.80330896, 0.74588021, 0.90275946, ..., 0.71145335, 0.69735964,
              0.73286383],
             [0.91948165, 0.84147814, 0.84147814, ..., 0.74403354, 0.91426471,
              0.77777509],
             [0.80666713, 0.84471657, 0.80507357, ..., 0.85020105, 0.68924423,
              0.75431369]], shape=(4, 1000))

    • beta_reserves
      (chain, draw)
      float64
      0.0547 0.2745 ... 0.09361 0.09422

      array([[0.054698  , 0.27447922, 0.2449931 , ..., 0.2412452 , 0.21035166,
              0.331458  ],
             [0.18502112, 0.19520464, 0.35319685, ..., 0.08814353, 0.11384295,
              0.08980776],
             [0.27106164, 0.29186521, 0.29186521, ..., 0.1743827 , 0.36860203,
              0.21119182],
             [0.26064828, 0.26836197, 0.26315497, ..., 0.2338219 , 0.09361395,
              0.09421615]], shape=(4, 1000))

    • beta_rrp
      (chain, draw)
      float64
      0.1009 0.1178 ... 0.0352 0.1103

      array([[ 0.10089523,  0.1177578 ,  0.05479198, ...,  0.07650557,
               0.07258149,  0.02620598],
             [ 0.08273127,  0.07488428,  0.03359865, ...,  0.1251008 ,
               0.18354456,  0.15243728],
             [ 0.00739561,  0.06165879,  0.06165879, ...,  0.0872317 ,
               0.04126558,  0.04372554],
             [-0.03434605,  0.0784648 ,  0.13797706, ...,  0.09184013,
               0.03519808,  0.11025619]], shape=(4, 1000))

    • sigma_log__
      (chain, draw)
      float64
      -0.2758 -0.2878 ... -0.3627 -0.3154

      array([[-0.27582085, -0.28779875, -0.23571403, ..., -0.29507555,
              -0.29287327, -0.29261385],
             [-0.36940104, -0.29942321, -0.33630395, ..., -0.26033073,
              -0.32606206, -0.33161492],
             [-0.24392927, -0.28942893, -0.28942893, ..., -0.29514194,
              -0.22834191, -0.31836887],
             [-0.30539877, -0.28070581, -0.23686053, ..., -0.24977363,
              -0.3626798 , -0.3153832 ]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      0.7589 0.7499 ... 0.6958 0.7295

      array([[0.75894888, 0.7499125 , 0.79000656, ..., 0.74447534, 0.74611669,
              0.74631027],
             [0.69114818, 0.74124564, 0.71440593, ..., 0.77079661, 0.72176039,
              0.71776366],
             [0.78354305, 0.748691  , 0.748691  , ..., 0.74442592, 0.7958521 ,
              0.72733445],
             [0.73682949, 0.75525049, 0.78910134, ..., 0.7789771 , 0.6958092 ,
              0.72950927]], shape=(4, 1000))

  • Attributes: (6)

    created_at :

    2026-02-10T18:34:29.476208+00:00

    arviz_version :

    0.23.4

    inference_library :

    nutpie

    inference_library_version :

    0.16.5

    sampling_time :

    0.16512465476989746

    tuning_steps :

    1000

  
  
• posterior_predictive

  <xarray.Dataset> Size: 8MB
  Dimensions:  (chain: 4, draw: 1000, day: 247)
  Coordinates:
    * chain    (chain) int64 32B 0 1 2 3
    * draw     (draw) int64 8kB 0 1 2 3 4 5 6 7 ... 993 994 995 996 997 998 999
    * day      (day) datetime64[ns] 2kB 2025-02-13 2025-02-14 ... 2026-02-06
  Data variables:
      y_hat    (chain, draw, day) float64 8MB -1.904 0.07099 ... -0.5723 -0.3517
  Attributes:
      created_at:                 2026-02-10T18:34:55.625717+00:00
      arviz_version:              0.23.4
      inference_library:          pymc
      inference_library_version:  5.27.1

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
    • day: 247
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

    • day
      (day)
      datetime64[ns]
      2025-02-13 ... 2026-02-06

      array(['2025-02-13T00:00:00.000000000', '2025-02-14T00:00:00.000000000',
             '2025-02-18T00:00:00.000000000', ..., '2026-02-04T00:00:00.000000000',
             '2026-02-05T00:00:00.000000000', '2026-02-06T00:00:00.000000000'],
            shape=(247,), dtype='datetime64[ns]')

  • Data variables: (1)
    • y_hat
      (chain, draw, day)
      float64
      -1.904 0.07099 ... -0.5723 -0.3517

      array([[[-1.90416882,  0.07099217,  0.41904727, ...,  0.13913182,
               -0.38478951, -0.24245714],
              [-1.63977236,  0.72634462, -0.37117126, ...,  0.97094873,
               -0.84068839, -0.65960128],
              [ 0.22431856, -1.49165512, -0.18464834, ...,  1.15820306,
               -0.16760821, -0.86808953],
              ...,
              [-0.71413342,  0.13940753, -2.7206446 , ..., -0.53392273,
               -0.68258459, -0.76071442],
              [-1.28186346, -0.01245861, -0.56986599, ...,  0.40214121,
               -0.59861232, -0.47054017],
              [-0.48629545, -0.45540245, -0.96036075, ...,  0.45805489,
               -0.65869955, -1.47087242]],
      
             [[-1.9400545 ,  0.54995361, -0.53291126, ..., -0.04522179,
               -0.5052763 , -0.38053821],
              [-1.29636788,  0.34196826,  0.01627429, ...,  0.02806891,
               -0.1814334 ,  0.09488244],
              [-0.3113117 , -0.84941529, -0.23181985, ..., -0.44533159,
               -0.51805723, -2.21424024],
      ...
              [-0.80955018, -1.29041445, -0.96530087, ...,  0.51687706,
               -0.39722288,  0.66080158],
              [-2.51429692, -1.52726527,  0.50100647, ..., -0.57817733,
               -1.32046923,  0.2436026 ],
              [-0.41401589, -1.6404627 ,  0.28739179, ...,  0.48835921,
                0.18583158, -0.17127583]],
      
             [[ 0.76559541, -2.07101303,  0.0945924 , ..., -1.09026009,
               -1.49632272,  0.49643531],
              [-1.24095326, -0.02235352,  0.52668601, ...,  0.71662282,
                0.15534177,  0.29826691],
              [-1.49440481, -0.92494224,  0.8207083 , ...,  0.07856881,
                1.17509887, -2.42307619],
              ...,
              [-0.43449441, -0.78317785, -0.13075383, ..., -0.64355622,
               -0.61455181, -1.83552853],
              [-2.29879597, -0.9538823 , -1.30568459, ..., -0.75144643,
               -0.04215143,  0.23337555],
              [-0.97525281, -0.72628896, -0.67556599, ..., -0.17632972,
               -0.57226822, -0.35166594]]], shape=(4, 1000, 247))

  • Attributes: (4)

    created_at :

    2026-02-10T18:34:55.625717+00:00

    arviz_version :

    0.23.4

    inference_library :

    pymc

    inference_library_version :

    5.27.1

  
  
• log_likelihood

  <xarray.Dataset> Size: 8MB
  Dimensions:  (chain: 4, draw: 1000, day: 247)
  Coordinates:
    * chain    (chain) int64 32B 0 1 2 3
    * draw     (draw) int64 8kB 0 1 2 3 4 5 6 7 ... 993 994 995 996 997 998 999
    * day      (day) datetime64[ns] 2kB 2025-02-13 2025-02-14 ... 2026-02-06
  Data variables:
      y_hat    (chain, draw, day) float64 8MB -1.778 -0.6509 ... -0.6227 -0.6189
  Attributes:
      created_at:                 2026-02-10T18:34:55.856763+00:00
      arviz_version:              0.23.4
      inference_library:          pymc
      inference_library_version:  5.27.1

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
    • day: 247
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

    • day
      (day)
      datetime64[ns]
      2025-02-13 ... 2026-02-06

      array(['2025-02-13T00:00:00.000000000', '2025-02-14T00:00:00.000000000',
             '2025-02-18T00:00:00.000000000', ..., '2026-02-04T00:00:00.000000000',
             '2026-02-05T00:00:00.000000000', '2026-02-06T00:00:00.000000000'],
            shape=(247,), dtype='datetime64[ns]')

  • Data variables: (1)
    • y_hat
      (chain, draw, day)
      float64
      -1.778 -0.6509 ... -0.6227 -0.6189

      array([[[-1.77819776, -0.65093937, -1.41596001, ..., -0.67638269,
               -0.66802998, -0.65170011],
              [-1.39319786, -0.64259428, -1.47214219, ..., -0.68632727,
               -0.64927497, -0.6457406 ],
              [-1.71703775, -0.68519905, -1.28367366, ..., -0.73457852,
               -0.6949058 , -0.700986  ],
              ...,
              [-1.57611011, -0.63357997, -1.45541433, ..., -0.65627656,
               -0.62930793, -0.65718078],
              [-1.7080926 , -0.62743816, -1.37934696, ..., -0.66960753,
               -0.63840283, -0.6469172 ],
              [-1.75788751, -0.64201559, -1.37016842, ..., -0.65591445,
               -0.62707153, -0.67819473]],
      
             [[-1.76388095, -0.55121116, -1.3939468 , ..., -0.61557952,
               -0.57029717, -0.56700703],
              [-1.76482527, -0.6195249 , -1.39196336, ..., -0.6604183 ,
               -0.63445202, -0.63764142],
              [-1.70140506, -0.61146474, -1.44672874, ..., -0.61074418,
               -0.58279218, -0.64725831],
      ...
              [-1.64773458, -0.62475207, -1.43792113, ..., -0.65974071,
               -0.63607552, -0.64489933],
              [-1.61143141, -0.70724748, -1.3294177 , ..., -0.73064725,
               -0.69375833, -0.72428054],
              [-1.94465115, -0.60060045, -1.36267806, ..., -0.63483359,
               -0.60848512, -0.6302221 ]],
      
             [[-2.48556812, -0.6160714 , -1.24320232, ..., -0.63316369,
               -0.61454812, -0.66376842],
              [-1.56482327, -0.64786926, -1.38329364, ..., -0.68837285,
               -0.64877109, -0.66085258],
              [-1.21355917, -0.7090151 , -1.53064047, ..., -0.72289275,
               -0.69264998, -0.70184775],
              ...,
              [-1.31457941, -0.70890582, -1.54051678, ..., -0.68740701,
               -0.66939884, -0.72227428],
              [-2.52644234, -0.58913816, -1.22616118, ..., -0.61577654,
               -0.5904684 , -0.56381752],
              [-1.55813214, -0.6051515 , -1.43962555, ..., -0.65330038,
               -0.62266269, -0.61888956]]], shape=(4, 1000, 247))

  • Attributes: (4)

    created_at :

    2026-02-10T18:34:55.856763+00:00

    arviz_version :

    0.23.4

    inference_library :

    pymc

    inference_library_version :

    5.27.1

  
  
• sample_stats

  <xarray.Dataset> Size: 340kB
  Dimensions:               (chain: 4, draw: 1000)
  Coordinates:
    * chain                 (chain) int64 32B 0 1 2 3
    * draw                  (draw) int64 8kB 0 1 2 3 4 5 ... 995 996 997 998 999
  Data variables: (12/13)
      depth                 (chain, draw) uint64 32kB 3 3 2 3 2 2 ... 2 3 3 3 3 2
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      index_in_trajectory   (chain, draw) int64 32kB 3 4 -2 -2 -2 ... 4 -5 6 5 -1
      logp                  (chain, draw) float64 32kB -281.1 -279.2 ... -279.7
      energy                (chain, draw) float64 32kB 282.5 283.4 ... 284.6 284.0
      energy_error          (chain, draw) float64 32kB 0.01677 0.1483 ... -0.2772
      ...                    ...
      step_size_bar         (chain, draw) float64 32kB 0.7936 0.7936 ... 0.8091
      mean_tree_accept      (chain, draw) float64 32kB 0.9377 0.7526 ... 0.8853
      mean_tree_accept_sym  (chain, draw) float64 32kB 0.9668 0.8437 ... 0.8585
      n_steps               (chain, draw) uint64 32kB 7 7 7 7 3 7 ... 7 7 7 7 7 7
      tuning                (chain, draw) bool 4kB False False ... False False
      diverging             (chain, draw) bool 4kB False False ... False False
  Attributes:
      created_at:     2026-02-10T18:34:29.450563+00:00
      arviz_version:  0.23.4

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

  • Data variables: (13)
    • depth
      (chain, draw)
      uint64
      3 3 2 3 2 2 2 2 ... 2 2 2 3 3 3 3 2

      array([[3, 3, 2, ..., 2, 3, 3],
             [2, 2, 3, ..., 2, 3, 2],
             [3, 2, 2, ..., 2, 3, 3],
             [2, 3, 2, ..., 3, 3, 2]], shape=(4, 1000), dtype=uint64)

    • maxdepth_reached
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]], shape=(4, 1000))

    • index_in_trajectory
      (chain, draw)
      int64
      3 4 -2 -2 -2 -2 ... 2 4 -5 6 5 -1

      array([[ 3,  4, -2, ..., -1,  4,  4],
             [ 2,  2, -5, ..., -3,  2,  1],
             [ 7, -3,  0, ...,  2,  3,  2],
             [ 3, -3,  2, ...,  6,  5, -1]], shape=(4, 1000))

    • logp
      (chain, draw)
      float64
      -281.1 -279.2 ... -282.6 -279.7

      array([[-281.08701956, -279.21847761, -279.9869969 , ..., -277.61133626,
              -277.61564691, -278.38284659],
             [-280.26884964, -277.87293002, -279.30394513, ..., -280.25395775,
              -280.82419811, -280.77437303],
             [-280.61095439, -277.84952151, -277.84952151, ..., -277.88647777,
              -280.57317346, -278.05636042],
             [-280.44773059, -278.34166259, -279.58319611, ..., -279.56639896,
              -282.60135996, -279.68238121]], shape=(4, 1000))

    • energy
      (chain, draw)
      float64
      282.5 283.4 281.2 ... 284.6 284.0

      array([[282.53470675, 283.43685201, 281.20125298, ..., 280.75279462,
              277.87884352, 279.52294525],
             [282.68039787, 280.61390272, 280.08525467, ..., 284.37667669,
              286.00607381, 281.6603627 ],
             [281.31477763, 282.38390877, 281.03838035, ..., 283.02692721,
              282.14465005, 282.82259901],
             [283.05461158, 282.30697228, 281.11426535, ..., 281.25361685,
              284.62410218, 283.97862742]], shape=(4, 1000))

    • energy_error
      (chain, draw)
      float64
      0.01677 0.1483 ... 0.3218 -0.2772

      array([[ 0.01677489,  0.14833495, -0.08174199, ..., -0.50453776,
              -0.00769044,  0.03272847],
             [-0.29552323, -0.35256152,  0.12198502, ...,  0.01834631,
              -0.73965546,  0.15601304],
             [ 0.40206765, -0.85099647,  0.        , ..., -0.41385729,
               0.37916202, -0.37831678],
             [ 0.32046333, -0.2797122 ,  0.32171126, ...,  0.05354666,
               0.32179511, -0.27717717]], shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      0.7729 0.7286 ... 0.83 0.7929

      array([[0.77289735, 0.72860186, 0.79765898, ..., 0.77264268, 0.83545353,
              0.86652885],
             [0.73984669, 0.77571968, 0.78320031, ..., 0.8424737 , 0.73089857,
              0.81126291],
             [0.86551986, 0.79904685, 0.84704494, ..., 0.78711417, 0.75564056,
              0.76532297],
             [0.76209984, 0.78950757, 0.73792085, ..., 0.76324978, 0.83000849,
              0.79293687]], shape=(4, 1000))

    • step_size_bar
      (chain, draw)
      float64
      0.7936 0.7936 ... 0.8091 0.8091

      array([[0.79364025, 0.79364025, 0.79364025, ..., 0.79364025, 0.79364025,
              0.79364025],
             [0.78896287, 0.78896287, 0.78896287, ..., 0.78896287, 0.78896287,
              0.78896287],
             [0.7899729 , 0.7899729 , 0.7899729 , ..., 0.7899729 , 0.7899729 ,
              0.7899729 ],
             [0.8090789 , 0.8090789 , 0.8090789 , ..., 0.8090789 , 0.8090789 ,
              0.8090789 ]], shape=(4, 1000))

    • mean_tree_accept
      (chain, draw)
      float64
      0.9377 0.7526 ... 0.803 0.8853

      array([[0.93766164, 0.75258973, 0.97566921, ..., 0.97222822, 0.97402933,
              0.8184226 ],
             [0.86660974, 0.94224478, 0.89714478, ..., 0.79522369, 0.39583356,
              0.94187224],
             [0.77540712, 0.95031054, 0.7713154 , ..., 0.44820378, 0.69648875,
              0.82868364],
             [0.69183303, 0.90223216, 0.6842297 , ..., 0.94128457, 0.80302461,
              0.88530046]], shape=(4, 1000))

    • mean_tree_accept_sym
      (chain, draw)
      float64
      0.9668 0.8437 ... 0.8585 0.8585

      array([[0.96682646, 0.84369611, 0.94768671, ..., 0.88524243, 0.98623131,
              0.89855393],
             [0.8729053 , 0.91165557, 0.94480997, ..., 0.86405029, 0.36176932,
              0.93497423],
             [0.82906872, 0.83521794, 0.86994323, ..., 0.46064479, 0.81935884,
              0.84418509],
             [0.81140357, 0.89550278, 0.80556091, ..., 0.96583275, 0.85852251,
              0.85845694]], shape=(4, 1000))

    • n_steps
      (chain, draw)
      uint64
      7 7 7 7 3 7 3 3 ... 7 3 7 7 7 7 7 7

      array([[7, 7, 7, ..., 3, 7, 7],
             [3, 3, 7, ..., 7, 7, 3],
             [7, 3, 7, ..., 3, 7, 7],
             [3, 7, 7, ..., 7, 7, 7]], shape=(4, 1000), dtype=uint64)

    • tuning
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]], shape=(4, 1000))

    • diverging
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]], shape=(4, 1000))

  • Attributes: (2)

    created_at :

    2026-02-10T18:34:29.450563+00:00

    arviz_version :

    0.23.4

  
  
• observed_data

  <xarray.Dataset> Size: 4kB
  Dimensions:  (day: 247)
  Coordinates:
    * day      (day) datetime64[ns] 2kB 2025-02-13 2025-02-14 ... 2026-02-06
  Data variables:
      y_hat    (day) float64 2kB -2.232 -1.062 0.6285 ... -0.2816 -0.5417 -0.2816
  Attributes:
      created_at:                 2026-02-10T18:34:29.475204+00:00
      arviz_version:              0.23.4
      inference_library:          pymc
      inference_library_version:  5.27.1

  xarray.Dataset

  • Dimensions:
    • day: 247
  • Coordinates: (1)
    • day
      (day)
      datetime64[ns]
      2025-02-13 ... 2026-02-06

      array(['2025-02-13T00:00:00.000000000', '2025-02-14T00:00:00.000000000',
             '2025-02-18T00:00:00.000000000', ..., '2026-02-04T00:00:00.000000000',
             '2026-02-05T00:00:00.000000000', '2026-02-06T00:00:00.000000000'],
            shape=(247,), dtype='datetime64[ns]')

  • Data variables: (1)
    • y_hat
      (day)
      float64
      -2.232 -1.062 ... -0.5417 -0.2816

      array([-2.23188706, -1.06172552,  0.62850782,  0.88854372,  0.62850782,
              0.49848987,  0.36847192,  0.23845397,  0.36847192,  0.88854372,
              1.27859756,  0.36847192,  0.36847192,  0.49848987,  0.49848987,
             -0.28161782, -0.28161782, -0.41163577, -0.67167167, -0.80168962,
             -0.93170757, -0.93170757, -0.67167167, -0.67167167, -0.67167167,
             -0.93170757, -0.67167167, -0.41163577, -0.02158193,  0.36847192,
             -0.02158193,  0.88854372,  0.10843602,  0.10843602,  0.62850782,
             -0.02158193, -0.28161782,  0.75852577,  1.01856166, -0.02158193,
             -0.93170757, -0.15159988,  0.23845397, -0.54165372, -0.54165372,
             -0.41163577, -0.54165372, -0.67167167, -0.41163577,  0.23845397,
              0.62850782,  0.36847192,  1.14857961,  1.14857961,  0.75852577,
              0.23845397, -0.02158193, -0.54165372, -0.93170757, -1.19174347,
             -0.93170757, -1.58179731, -1.45177937, -0.93170757, -1.32176142,
             -0.93170757, -0.93170757, -1.97185116, -2.23188706, -1.58179731,
             -0.41163577, -0.15159988, -0.54165372,  0.36847192,  0.23845397,
             -0.15159988, -0.41163577, -0.02158193, -0.15159988, -0.67167167,
             -1.19174347, -1.19174347, -1.84183321, -1.58179731, -0.67167167,
             -0.41163577, -0.67167167, -0.41163577, -0.15159988, -0.02158193,
              0.10843602,  0.62850782,  1.27859756,  0.88854372,  1.79866936,
              1.79866936,  1.53863346,  1.01856166,  1.01856166,  0.75852577,
      ...
              0.36847192,  0.49848987,  0.36847192,  0.36847192,  0.23845397,
              0.10843602,  1.14857961,  0.75852577,  0.10843602,  1.79866936,
              1.40861551,  1.66865141,  1.27859756,  0.36847192,  0.10843602,
             -0.28161782,  0.10843602,  0.62850782,  1.14857961,  1.79866936,
              1.92868731,  0.10843602, -0.28161782,  0.88854372,  0.62850782,
              1.14857961,  0.88854372,  1.14857961,  0.49848987,  1.53863346,
              1.92868731,  4.13899244,  2.9688309 ,  1.27859756,  0.36847192,
              0.36847192, -0.15159988,  0.36847192,  1.14857961, -0.02158193,
             -0.15159988,  0.49848987, -0.02158193, -0.02158193,  0.10843602,
              0.62850782,  0.88854372,  1.27859756,  1.27859756,  0.88854372,
              0.75852577,  0.88854372,  0.36847192, -0.93170757, -0.54165372,
             -0.67167167, -0.93170757, -1.71181526, -2.10186911, -1.45177937,
             -0.67167167, -3.79210245, -2.62194091, -1.32176142, -0.15159988,
             -0.02158193, -0.41163577, -0.67167167,  0.23845397,  0.10843602,
             -0.02158193,  1.40861551,  0.62850782,  0.36847192, -0.15159988,
             -0.54165372, -1.06172552, -1.71181526, -2.23188706, -3.01199475,
             -3.1420127 , -1.45177937, -0.80168962, -0.54165372, -0.80168962,
             -0.93170757, -0.54165372, -0.02158193, -0.15159988, -0.54165372,
             -1.45177937, -0.28161782, -0.15159988,  0.23845397, -0.28161782,
             -0.54165372, -0.28161782])

  • Attributes: (4)

    created_at :

    2026-02-10T18:34:29.475204+00:00

    arviz_version :

    0.23.4

    inference_library :

    pymc

    inference_library_version :

    5.27.1

  
  
• constant_data

  <xarray.Dataset> Size: 8kB
  Dimensions:   (day: 247)
  Coordinates:
    * day       (day) datetime64[ns] 2kB 2025-02-13 2025-02-14 ... 2026-02-06
  Data variables:
      leverage  (day) float64 2kB -1.069 -1.228 -0.2134 ... -0.5865 -0.5959
      reserves  (day) float64 2kB -0.1624 -0.1624 -0.1624 ... 0.01753 0.01753
      rrp       (day) float64 2kB -3.769 -1.585 -1.376 ... 0.2508 0.2592 0.2299
  Attributes:
      created_at:                 2026-02-10T18:34:29.471195+00:00
      arviz_version:              0.23.4
      inference_library:          pymc
      inference_library_version:  5.27.1

  xarray.Dataset

  • Dimensions:
    • day: 247
  • Coordinates: (1)
    • day
      (day)
      datetime64[ns]
      2025-02-13 ... 2026-02-06

      array(['2025-02-13T00:00:00.000000000', '2025-02-14T00:00:00.000000000',
             '2025-02-18T00:00:00.000000000', ..., '2026-02-04T00:00:00.000000000',
             '2026-02-05T00:00:00.000000000', '2026-02-06T00:00:00.000000000'],
            shape=(247,), dtype='datetime64[ns]')

  • Data variables: (3)
    • leverage
      (day)
      float64
      -1.069 -1.228 ... -0.5865 -0.5959

      array([-1.06879262e+00, -1.22763679e+00, -2.13430993e-01, -4.15265515e-01,
             -2.62111693e-01,  1.08953639e-01,  2.24138808e-01,  4.33348904e-01,
              3.06292504e-01,  7.36819914e-01,  1.08793589e+00,  7.28211268e-01,
              3.84458383e-01,  1.29731362e-01,  6.28883729e-01,  2.87671723e-01,
              3.21813403e-01,  1.03917402e-01,  9.44523762e-03, -5.93060651e-01,
             -8.78323331e-01, -1.45634573e+00, -9.70387437e-01, -1.22710365e+00,
             -1.12556814e+00, -1.19807430e+00, -1.01832428e+00, -9.18444585e-01,
             -8.43717649e-01, -6.89372092e-01, -8.71914525e-01, -3.64235472e-02,
             -8.02272630e-01, -3.10796768e-01, -2.58274220e-01, -2.04124020e-01,
             -1.33107495e-01, -1.96682459e-01, -3.80627891e-01, -6.98006781e-01,
             -1.52353998e+00, -1.41499828e+00, -1.24511579e+00, -1.12251559e+00,
             -1.29391259e+00, -1.09836941e+00, -9.81949571e-01, -5.79774016e-01,
              3.22973364e-02,  2.41724451e-01,  3.36331417e-01,  4.44811484e-01,
              1.50568827e+00,  1.88358254e+00,  1.22233181e+00,  9.29541626e-01,
              8.25182625e-01,  4.46638697e-01,  3.93282550e-01,  1.23450559e-01,
              4.79424554e-01, -1.82681159e-01, -1.46765770e-01,  3.88795081e-01,
              1.64457228e-04, -2.44009130e-01, -4.90535724e-01, -9.43169166e-01,
             -5.64628937e-01, -5.32106009e-01,  2.40394824e-01,  1.84090482e-01,
              5.25167785e-01,  4.63585878e-01,  1.05120986e+00,  9.40846626e-01,
              2.58836676e-01,  1.23528574e-01, -2.39922564e-01, -4.40356385e-01,
      ...
              5.38706825e-01,  7.42729810e-01,  7.98441499e-01,  8.93906301e-01,
              4.80961397e-01,  4.26778485e-01,  8.62154961e-01,  1.27605704e+00,
              1.14293223e+00,  1.22442336e+00,  1.24527324e+00,  1.73970447e+00,
              1.58041345e+00,  1.94774810e+00,  2.13431653e+00,  1.57986509e+00,
              1.62339853e+00,  1.48390696e+00,  5.34560841e-01,  1.07950870e+00,
              1.59328323e+00,  3.49340244e-01,  5.04623752e-01,  1.15965219e+00,
              8.95069285e-01,  6.87990721e-01,  8.09069678e-01,  1.22043851e+00,
              1.36519608e+00,  1.90613618e+00,  1.59362009e+00,  1.40776314e+00,
              1.92055810e+00,  1.80041126e+00,  2.14682012e+00,  1.79840952e+00,
              1.01682304e+00,  7.39387326e-01,  9.19753465e-01,  3.25950416e-01,
              4.64075826e-01, -1.22892917e-01, -2.61363477e-01, -5.81648959e-01,
             -9.94460217e-01, -6.28976647e-01, -7.05848844e-01, -6.88734340e-01,
             -2.55236224e-01, -8.46972329e-01, -1.09342240e+00, -4.72858075e-01,
             -5.81145486e-01, -2.23399630e-01,  1.69169889e-01,  2.34154565e-01,
              3.70331340e-02, -9.03112885e-01, -1.12704403e+00, -1.92423194e+00,
             -1.96089690e+00, -2.04099364e+00, -2.88006716e+00, -2.41108415e+00,
             -2.57544831e+00, -2.28709845e+00, -1.79182619e+00, -1.57265921e+00,
             -1.66796273e+00, -1.13618532e+00, -1.49322328e+00, -1.03477770e+00,
             -9.81423325e-01, -6.90447571e-01, -2.51289340e-01, -3.63345859e-01,
             -1.24583700e-01, -5.86525956e-01, -5.95942639e-01])

    • reserves
      (day)
      float64
      -0.1624 -0.1624 ... 0.01753 0.01753

      array([-1.62449903e-01, -1.62449903e-01, -1.62449903e-01,  1.55570991e-01,
              1.55570991e-01,  3.30201344e-01,  3.30201344e-01,  3.30201344e-01,
              6.93407825e-01,  6.93407825e-01,  1.46549122e-01,  1.46549122e-01,
              1.46549122e-01,  5.36365745e-02,  1.07882152e-01,  1.07882152e-01,
              1.07882152e-01,  1.07882152e-01,  6.64506076e-01,  1.34745523e+00,
              1.34745523e+00,  1.34745523e+00,  1.34745523e+00,  1.77665478e+00,
              2.07984042e+00,  2.07984042e+00,  2.07984042e+00,  2.07984042e+00,
              1.97274702e+00,  1.69979100e+00,  1.69979100e+00,  1.69979100e+00,
              1.69979100e+00,  9.26902698e-01,  9.26902698e-01,  9.26902698e-01,
              9.26902698e-01,  9.26902698e-01,  1.16945121e+00,  1.16945121e+00,
              1.16945121e+00,  1.16945121e+00,  1.16945121e+00,  1.11844588e+00,
              1.11844588e+00,  1.11844588e+00,  1.11844588e+00, -1.22353412e-01,
             -6.78977336e-01, -6.78977336e-01, -6.78977336e-01, -6.78977336e-01,
             -9.17357996e-01, -1.34655755e+00, -1.34655755e+00, -1.34655755e+00,
             -1.34655755e+00, -1.35022983e+00, -1.24313643e+00, -1.24313643e+00,
             -1.24313643e+00, -1.24313643e+00, -1.13457538e+00, -6.79707980e-01,
             -6.79707980e-01, -6.79707980e-01, -6.79707980e-01, -3.38236579e-01,
             -9.43991571e-01, -9.43991571e-01, -9.43991571e-01, -1.06348687e+00,
             -1.06348687e+00, -9.19568989e-01, -9.19568989e-01, -9.19568989e-01,
             -7.68865651e-01,  4.71933640e-01,  4.71933640e-01,  4.71933640e-01,
      ...
             -1.20628018e+00, -1.07567274e+00, -8.00785279e-01, -8.00785279e-01,
             -8.00785279e-01, -8.00785279e-01, -1.34712300e+00, -1.21416479e+00,
             -1.21416479e+00, -1.21416479e+00, -1.21416479e+00, -1.75430792e+00,
             -1.19889750e+00, -1.19889750e+00, -1.19889750e+00, -1.19889750e+00,
             -1.10646781e+00, -6.54503927e-01, -6.54503927e-01, -6.54503927e-01,
             -7.02402429e-01, -7.02402429e-01, -4.72891156e-01, -4.72891156e-01,
             -4.72891156e-01, -2.59333343e-01, -2.59333343e-01, -4.65038317e-01,
             -4.65038317e-01, -4.65038317e-01, -4.14573030e-01, -5.45180472e-01,
             -5.45180472e-01, -5.45180472e-01, -7.88529514e-01, -7.88529514e-01,
             -2.42191792e-01, -2.42191792e-01, -2.42191792e-01,  2.26869173e-01,
              2.26869173e-01,  7.67012302e-01,  7.67012302e-01,  7.67012302e-01,
              9.38122854e-01,  9.38122854e-01,  8.45693168e-01,  8.45693168e-01,
              8.45693168e-01,  8.23691243e-01,  8.71589745e-01,  8.71589745e-01,
              8.71589745e-01,  8.83210166e-01,  8.83210166e-01,  6.69652354e-01,
              6.69652354e-01,  9.17239133e-01,  9.17239133e-01,  9.17239133e-01,
              8.66773845e-01,  8.66773845e-01,  1.20510030e+00,  1.20510030e+00,
              1.44844934e+00,  1.44844934e+00,  8.46608061e-01,  8.46608061e-01,
              8.46608061e-01,  3.77547097e-01,  3.77547097e-01,  3.88902656e-02,
              3.88902656e-02,  3.88902656e-02, -1.32220287e-01, -1.32220287e-01,
              1.75300369e-02,  1.75300369e-02,  1.75300369e-02])

    • rrp
      (day)
      float64
      -3.769 -1.585 ... 0.2592 0.2299

      array([-3.76894205, -1.58508657, -1.3757184 , -1.33812005, -1.20545602,
             -0.8834484 , -0.64270613, -0.55899971, -0.33451829,  0.43802769,
              1.35544305,  0.49039891,  0.40707177,  0.72040435,  0.27309482,
              0.26323328,  0.45679769,  0.65393132,  0.39667533,  0.31129615,
              0.39567362, -0.56408609,  0.89607404,  1.31431438,  1.35368276,
              1.42190636,  1.23177501,  1.36614098,  1.93928731,  2.43545719,
              2.38332911,  3.56634484,  1.73650323,  1.80005865,  1.53519741,
              1.36459464,  0.93484917,  0.83353979,  0.45061234, -0.46504273,
             -1.28000113, -0.12518902, -0.40946213, -0.91998669, -0.78332553,
             -0.31185813, -0.00951525,  0.39046081,  0.0479229 , -0.13066442,
              0.27613887,  0.71986945,  1.12218933, -0.08498427, -0.16991609,
             -0.47531274, -0.38337864, -0.43245295, -0.92666803, -1.3926114 ,
             -1.29104917, -2.41805638, -0.72187079, -1.31062637, -0.68250242,
             -0.14387149, -0.22197609,  0.11992967,  0.33037736,  0.52476843,
              0.66718702,  0.96280966,  1.02095776,  2.89392174,  1.10791246,
              0.73661657,  0.70202336,  0.06464084,  0.43744416,  1.07945597,
              0.58134101,  0.67277912, -0.53883898,  0.2438214 ,  0.06472837,
              0.56434104,  0.87212041,  0.74398842,  0.24141923,  0.48000246,
              0.64353488,  0.91425079,  1.26678641,  2.13135401,  3.56707424,
              1.04995887,  1.60255545,  0.95520441,  0.85584984,  1.06535416,
      ...
             -0.5749688 , -0.4930324 , -0.37962464, -0.37507316, -0.39143126,
              0.21167899,  0.26416691,  0.76101757,  0.79221662,  0.6790909 ,
              0.40159638,  0.07612652,  0.33479269,  0.19345361, -0.08319479,
             -0.12582117, -0.13796818, -0.1145689 , -0.56718849, -0.07499629,
              0.04386741, -0.00537223,  0.00396414,  0.0073583 ,  0.04440231,
             -0.01683847, -0.03631842,  0.13653091,  0.17378888,  0.18385465,
              0.18836723,  0.50825472,  0.25864289,  0.16509438,  0.23556455,
             -0.14604026, -0.16595785, -0.36489068, -0.68205505, -0.6331947 ,
             -0.22252071, -0.18988231, -0.37683345, -0.44003876, -0.22077987,
             -0.03250607, -0.03922631, -0.02357816,  0.02080851,  0.13330208,
              0.07692401,  0.12786559,  0.07863567,  0.08788452,  0.00953679,
             -0.01689682,  0.04159167, -0.05482584, -0.10953115, -0.15751621,
             -0.13708317, -0.46466344, -0.15163235, -0.07231208, -0.22924096,
             -0.22513684, -0.12573364, -0.20827302,  0.18075225,  0.1062266 ,
              0.14761786,  1.42401677,  0.47035488,  0.57668255,  0.48629479,
              0.22886375,  0.2281538 ,  0.2180394 ,  0.18075225,  0.1275641 ,
              0.07968602,  0.04467462,  0.06852127,  0.09346689,  0.15281121,
              0.13818423,  0.11251893,  0.13458583,  0.15340446,  0.23013778,
              0.23000162,  0.30609306,  0.27311427,  0.17608407,  0.25084313,
              0.25918751,  0.22994327])

  • Attributes: (4)

    created_at :

    2026-02-10T18:34:29.471195+00:00

    arviz_version :

    0.23.4

    inference_library :

    pymc

    inference_library_version :

    5.27.1

  
  
• warmup_posterior

  <xarray.Dataset> Size: 200kB
  Dimensions:        (chain: 4, draw: 1000)
  Coordinates:
    * chain          (chain) int64 32B 0 1 2 3
    * draw           (draw) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
  Data variables:
      alpha          (chain, draw) float64 32kB -0.101 -0.101 ... 0.007163
      beta_leverage  (chain, draw) float64 32kB 0.3314 0.3314 ... 0.8766 0.9102
      beta_reserves  (chain, draw) float64 32kB -0.06851 -0.06851 ... 0.3301
      beta_rrp       (chain, draw) float64 32kB 0.03469 0.03469 ... 0.0375 0.04218
      sigma_log__    (chain, draw) float64 32kB 0.3867 0.3867 ... -0.296 -0.2535
      sigma          (chain, draw) float64 32kB 1.472 1.472 ... 0.7438 0.7761
  Attributes:
      created_at:     2026-02-10T18:34:29.443305+00:00
      arviz_version:  0.23.4

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

  • Data variables: (6)
    • alpha
      (chain, draw)
      float64
      -0.101 -0.101 ... -0.00299 0.007163

      array([[-0.10104816, -0.10104816,  0.00715991, ..., -0.01151505,
               0.05980851,  0.04652121],
             [ 0.26930846,  0.26930846, -0.06191775, ...,  0.03647561,
              -0.03678966, -0.03972718],
             [-0.49698651, -0.49698651, -0.31348569, ..., -0.01714374,
              -0.03960741,  0.04124205],
             [-0.22347657, -0.22347657, -0.17782745, ..., -0.00299042,
              -0.00299042,  0.00716271]], shape=(4, 1000))

    • beta_leverage
      (chain, draw)
      float64
      0.3314 0.3314 ... 0.8766 0.9102

      array([[0.33137547, 0.33137547, 0.88001561, ..., 0.76945271, 0.79236996,
              0.77351751],
             [0.15808737, 0.15808737, 0.22363533, ..., 0.82448198, 0.8332028 ,
              0.80565367],
             [1.76139553, 1.76139553, 1.47418958, ..., 0.78857545, 0.89101266,
              0.72727506],
             [1.23514361, 1.23514361, 1.18541446, ..., 0.87656076, 0.87656076,
              0.91020923]], shape=(4, 1000))

    • beta_reserves
      (chain, draw)
      float64
      -0.06851 -0.06851 ... 0.3613 0.3301

      array([[-0.06850548, -0.06850548,  0.33211899, ...,  0.22786602,
               0.13475491,  0.22159217],
             [-0.07584318, -0.07584318, -0.11609089, ...,  0.21357906,
               0.22482491,  0.24027884],
             [-0.85189   , -0.85189   , -0.52310312, ...,  0.317567  ,
               0.21080498,  0.1185508 ],
             [-0.0118584 , -0.0118584 ,  0.08605253, ...,  0.36126222,
               0.36126222,  0.33014817]], shape=(4, 1000))

    • beta_rrp
      (chain, draw)
      float64
      0.03469 0.03469 ... 0.0375 0.04218

      array([[ 0.0346857 ,  0.0346857 , -0.04103783, ...,  0.10745798,
               0.08407994,  0.11980674],
             [ 0.46898168,  0.46898168,  0.31860693, ...,  0.08550049,
               0.08824734,  0.15185885],
             [ 0.74303351,  0.74303351,  0.31423995, ...,  0.07567406,
               0.13688848,  0.08284815],
             [-0.08377984, -0.08377984, -0.1977432 , ...,  0.0375002 ,
               0.0375002 ,  0.04218373]], shape=(4, 1000))

    • sigma_log__
      (chain, draw)
      float64
      0.3867 0.3867 ... -0.296 -0.2535

      array([[ 0.38674084,  0.38674084, -0.16653368, ..., -0.31355644,
              -0.26350762, -0.26219445],
             [-0.12561497, -0.12561497, -0.10735272, ..., -0.28835177,
              -0.27809665, -0.21352208],
             [ 0.0337192 ,  0.0337192 ,  0.29126711, ..., -0.31467463,
              -0.31270618, -0.25507331],
             [ 1.15803809,  1.15803809,  1.13535285, ..., -0.29598678,
              -0.29598678, -0.25346331]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      1.472 1.472 ... 0.7438 0.7761

      array([[1.47217492, 1.47217492, 0.8465943 , ..., 0.73084313, 0.76835177,
              0.7693614 ],
             [0.88195436, 0.88195436, 0.8982088 , ..., 0.74949789, 0.75722363,
              0.80773432],
             [1.03429414, 1.03429414, 1.33812196, ..., 0.73002636, 0.7314648 ,
              0.77485969],
             [3.18368105, 3.18368105, 3.11227152, ..., 0.74379726, 0.74379726,
              0.77610822]], shape=(4, 1000))

  • Attributes: (2)

    created_at :

    2026-02-10T18:34:29.443305+00:00

    arviz_version :

    0.23.4

  
  
• warmup_sample_stats

  <xarray.Dataset> Size: 340kB
  Dimensions:               (chain: 4, draw: 1000)
  Coordinates:
    * chain                 (chain) int64 32B 0 1 2 3
    * draw                  (draw) int64 8kB 0 1 2 3 4 5 ... 995 996 997 998 999
  Data variables: (12/13)
      depth                 (chain, draw) uint64 32kB 4 0 3 3 0 1 ... 2 3 2 2 1 2
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      index_in_trajectory   (chain, draw) int64 32kB 12 0 7 -7 0 0 ... -3 1 -3 0 3
      logp                  (chain, draw) float64 32kB -363.5 -363.5 ... -278.8
      energy                (chain, draw) float64 32kB 578.6 364.3 ... 284.3 280.3
      energy_error          (chain, draw) float64 32kB -0.9422 0.0 ... 0.0 -0.1128
      ...                    ...
      step_size_bar         (chain, draw) float64 32kB 1.179 0.3955 ... 0.8091
      mean_tree_accept      (chain, draw) float64 32kB 0.8905 0.0 ... 0.541 0.8791
      mean_tree_accept_sym  (chain, draw) float64 32kB 0.522 0.0 ... 0.701 0.9106
      n_steps               (chain, draw) uint64 32kB 31 1 7 7 1 3 ... 7 7 7 7 3 3
      tuning                (chain, draw) bool 4kB True True True ... True True
      diverging             (chain, draw) bool 4kB False True ... False False
  Attributes:
      created_at:     2026-02-10T18:34:29.459145+00:00
      arviz_version:  0.23.4

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

  • Data variables: (13)
    • depth
      (chain, draw)
      uint64
      4 0 3 3 0 1 4 4 ... 2 3 2 3 2 2 1 2

      array([[4, 0, 3, ..., 2, 2, 2],
             [2, 0, 2, ..., 3, 3, 2],
             [1, 0, 2, ..., 3, 2, 3],
             [5, 0, 2, ..., 2, 1, 2]], shape=(4, 1000), dtype=uint64)

    • maxdepth_reached
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]], shape=(4, 1000))

    • index_in_trajectory
      (chain, draw)
      int64
      12 0 7 -7 0 0 6 ... 4 2 -3 1 -3 0 3

      array([[12,  0,  7, ...,  2,  3, -1],
             [ 3,  0,  2, ...,  2,  5, -1],
             [ 0,  0,  2, ..., -6, -2,  5],
             [-4,  0,  1, ..., -3,  0,  3]], shape=(4, 1000))

    • logp
      (chain, draw)
      float64
      -363.5 -363.5 ... -279.1 -278.8

      array([[-363.50672881, -363.50672881, -283.14777069, ..., -278.12771568,
              -280.56956641, -279.13739439],
             [-354.96466799, -354.96466799, -310.93603124, ..., -278.2688052 ,
              -278.34410734, -280.90280716],
             [-811.30567731, -811.30567731, -484.07092142, ..., -280.16797442,
              -281.36198696, -279.55513596],
             [-535.54282911, -535.54282911, -525.34484144, ..., -279.07160004,
              -279.07160004, -278.81781046]], shape=(4, 1000))

    • energy
      (chain, draw)
      float64
      578.6 364.3 362.7 ... 284.3 280.3

      array([[578.6149497 , 364.33691369, 362.71756434, ..., 283.29382843,
              281.25305468, 281.24373404],
             [469.29626211, 356.12144614, 351.97930538, ..., 279.5219819 ,
              279.73803432, 282.15642944],
             [811.97514796, 814.583989  , 791.43546223, ..., 282.37592699,
              283.78005705, 281.64077688],
             [558.09299188, 539.70990811, 537.88409118, ..., 281.86034033,
              284.29883037, 280.33541959]], shape=(4, 1000))

    • energy_error
      (chain, draw)
      float64
      -0.9422 0.0 -2.357 ... 0.0 -0.1128

      array([[-9.42224859e-01,  0.00000000e+00, -2.35681194e+00, ...,
              -1.06924440e+00,  5.27260400e-01, -3.72058668e-01],
             [-1.87686012e+01,  0.00000000e+00, -5.39737945e+00, ...,
              -9.23212292e-02,  1.51825270e-02,  4.51810951e-01],
             [ 0.00000000e+00,  0.00000000e+00, -2.65707755e+01, ...,
               5.23833711e-01,  1.25106326e-01, -8.01020966e-01],
             [-6.06025118e-02,  0.00000000e+00, -1.68903213e-01, ...,
              -8.91648453e-01,  0.00000000e+00, -1.12804603e-01]],
            shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      1.14 0.1753 0.4 ... 0.7674 0.7684

      array([[1.14001962, 0.17533344, 0.4       , ..., 0.75505491, 0.74661017,
              0.83908668],
             [1.36777169, 0.14502174, 0.17919655, ..., 0.65864294, 0.81828023,
              0.86568849],
             [3.76318712, 0.4045302 , 0.41015079, ..., 0.75371129, 0.79388745,
              0.80171667],
             [1.46100723, 0.23216249, 0.1       , ..., 0.89813494, 0.76741406,
              0.76844404]], shape=(4, 1000))

    • step_size_bar
      (chain, draw)
      float64
      1.179 0.3955 0.4 ... 0.8089 0.8091

      array([[1.17893025, 0.39550932, 0.4       , ..., 0.79412045, 0.79371899,
              0.79364025],
             [1.34510416, 0.36176142, 0.25547214, ..., 0.78929622, 0.78909933,
              0.78896287],
             [3.73610367, 0.94226449, 0.63531196, ..., 0.79032664, 0.79026565,
              0.7899729 ],
             [1.43855101, 0.49983385, 0.42449831, ..., 0.8090886 , 0.80892535,
              0.8090789 ]], shape=(4, 1000))

    • mean_tree_accept
      (chain, draw)
      float64
      0.8905 0.0 1.0 ... 0.541 0.8791

      array([[8.90534103e-001, 0.00000000e+000, 1.00000000e+000, ...,
              1.00000000e+000, 7.04241617e-001, 9.58500227e-001],
             [2.00597400e-001, 0.00000000e+000, 1.00000000e+000, ...,
              1.00000000e+000, 9.36929053e-001, 7.01882301e-001],
             [2.41497505e-114, 0.00000000e+000, 1.00000000e+000, ...,
              7.82101667e-001, 8.06830831e-001, 1.00000000e+000],
             [1.00000000e+000, 0.00000000e+000, 1.00000000e+000, ...,
              8.98106422e-001, 5.41029401e-001, 8.79092024e-001]],
            shape=(4, 1000))

    • mean_tree_accept_sym
      (chain, draw)
      float64
      0.522 0.0 0.7383 ... 0.701 0.9106

      array([[5.22033767e-001, 0.00000000e+000, 7.38258776e-001, ...,
              6.86864505e-001, 8.21962887e-001, 9.12743317e-001],
             [1.19244305e-003, 0.00000000e+000, 5.97284374e-002, ...,
              9.50313318e-001, 9.64237643e-001, 8.19325244e-001],
             [4.82995010e-114, 0.00000000e+000, 2.20067286e-008, ...,
              8.37618537e-001, 8.80654800e-001, 7.14055234e-001],
             [8.83610241e-001, 0.00000000e+000, 8.94830221e-001, ...,
              7.38527644e-001, 7.00961248e-001, 9.10647687e-001]],
            shape=(4, 1000))

    • n_steps
      (chain, draw)
      uint64
      31 1 7 7 1 3 15 ... 7 7 7 7 7 3 3

      array([[31,  1,  7, ...,  3,  3,  3],
             [ 5,  1,  3, ...,  7,  7,  3],
             [ 1,  1,  3, ...,  7,  3,  7],
             [31,  1,  3, ...,  7,  3,  3]], shape=(4, 1000), dtype=uint64)

    • tuning
      (chain, draw)
      bool
      True True True ... True True True

      array([[ True,  True,  True, ...,  True,  True,  True],
             [ True,  True,  True, ...,  True,  True,  True],
             [ True,  True,  True, ...,  True,  True,  True],
             [ True,  True,  True, ...,  True,  True,  True]], shape=(4, 1000))

    • diverging
      (chain, draw)
      bool
      False True False ... False False

      array([[False,  True, False, ..., False, False, False],
             [ True,  True, False, ..., False, False, False],
             [False,  True, False, ..., False, False, False],
             [False,  True, False, ..., False, False, False]], shape=(4, 1000))

  • Attributes: (2)

    created_at :

    2026-02-10T18:34:29.459145+00:00

    arviz_version :

    0.23.4

  
  

pred_mean = idata.posterior_predictive.y_hat.mean(dim=["draw", "chain"]).to_numpy()

r2_data = az.r2_score(dfdiff["norm_sofr_iorb_diff_diff"].to_numpy(), pred_mean)
print(r2_data)

r2        0.365583
r2_std    0.000000
dtype: float64

r2_data = az.r2_score(dfdiff["norm_sofr_iorb_diff_diff"].to_numpy(), pred_mean)
print(r2_data)

r2        0.365583
r2_std    0.000000
dtype: float64

# 1. Get your observed data
y_obs = dfdiff["norm_sofr_iorb_diff_diff"].to_numpy()

# 2. Extract y_hat and flatten the chain/draw dimensions
# .stack(sample=("chain", "draw")) merges the first two dimensions
# .transpose("sample", ...) ensures the samples are the first dimension
y_pred = idata.posterior_predictive.y_hat.stack(sample=("chain", "draw")).transpose("sample", ...)

# 3. Pass to r2_score
r2_results = az.r2_score(y_obs, y_pred.values)

print(r2_results)

r2        0.441476
r2_std    0.026424
dtype: float64

# 1. Get your observed data
y_obs = dfdiff["norm_sofr_iorb_diff_diff"].to_numpy()

# 2. Extract y_hat and flatten the chain/draw dimensions
# .stack(sample=("chain", "draw")) merges the first two dimensions
# .transpose("sample", ...) ensures the samples are the first dimension
y_pred = idata.posterior_predictive.y_hat.stack(sample=("chain", "draw")).transpose("sample", ...)

# 3. Pass to r2_score
r2_results = az.r2_score(y_obs, y_pred.values)

print(r2_results)

r2        0.439907
r2_std    0.026064
dtype: float64

dfdiff.loc[1350]

const                                               1.0
date                                2025-05-27 00:00:00
sofr_rate                                          4.31
iorb                                                4.4
reserves                                      3289469.0
rrp_on_bil                                      138.066
rrp_foreign_mm                                 371341.0
sofr_vol                                         2655.0
tgcr_vol                                         1025.0
rrp_foreign_bil                                 371.341
rrp_total_bil                                   509.407
repo_vol_total                                   3680.0
sofr_iorb_diff                                    -0.09
total_rrp                                       509.407
leverage_ratio                                 0.000807
sofr_iorb_diff_diff                                0.05
rrp_total_bil_diff                              -16.775
leverage_ratio_diff                            0.000034
reserves_diff                                       0.0
rolling_sofr_iorb_diff_diff                   -0.000667
rolling_leverage_ratio_diff                    0.000002
rolling_rrp_total_bil_diff                     1.491267
rolling_reserves_diff                      -6173.766667
norm_rolling_leverage_ratio_diff               0.240395
norm_rolling_reserves_diff                    -0.943992
norm_rolling_rrp_total_bil_diff                0.667187
norm_rolling_sofr_iorb_diff_diff              -0.411636
Name: 1350, dtype: object

Inference

input_leverage = 0.000002
norm_leverage = (input_leverage - leverage_mean)/(leverage_std)

input_reserves = 1.491267
norm_reserves = (input_reserves - reserves_mean)/(reserves_std)

input_rrp = -6173.766667
norm_rrp = (input_rrp - rrp_mean)/(rrp_std)

target_sofr_iorb = -0.000667
norm_target_sofr_iorb = (target_sofr_iorb - sofr_iorb_mean)/(sofr_iorb_std)

input_data = [norm_leverage, norm_reserves, norm_rrp, 1]

input_data = [0.240395, -0.943992, 0.667187, 1]

input_matrix = np.stack(input_data)
input_matrix.shape

(4,)

beta_leverage = idata.posterior["beta_leverage"].values.ravel()
beta_reserves = idata.posterior["beta_reserves"].values.ravel()
beta_rrp = idata.posterior["beta_rrp"].values.ravel()
alpha = idata.posterior["alpha"].values.ravel()

beta_leverage

array([0.62178427, 0.79520919, 0.85059116, ..., 0.85020105, 0.68924423,
       0.75431369], shape=(4000,))

arrays = [beta_leverage, beta_reserves, beta_rrp, alpha]
matrix = np.stack(arrays)

matrix.shape

(4, 4000)

mult_matrix = input_matrix[:, None] * matrix

matrix

array([[ 0.62178427,  0.79520919,  0.85059116, ...,  0.85020105,
         0.68924423,  0.75431369],
       [ 0.054698  ,  0.27447922,  0.2449931 , ...,  0.2338219 ,
         0.09361395,  0.09421615],
       [ 0.10089523,  0.1177578 ,  0.05479198, ...,  0.09184013,
         0.03519808,  0.11025619],
       [-0.03466254,  0.03224332,  0.05949509, ..., -0.05404182,
         0.03384539,  0.01315091]], shape=(4, 4000))

outputs = mult_matrix.sum(axis=0)

az.plot_density(outputs)

array([[<Axes: title={'center': 'x'}>]], dtype=object)

norm_target_sofr_iorb

np.float64(-0.41176579153356735)

ols test

dfdiff

	const	date	sofr_rate	iorb	reserves	rrp_on_bil	rrp_foreign_mm	sofr_vol	tgcr_vol	rrp_foreign_bil	...	leverage_ratio_diff	reserves_diff	rolling_sofr_iorb_diff_diff	rolling_leverage_ratio_diff	rolling_rrp_total_bil_diff	rolling_reserves_diff	norm_rolling_leverage_ratio_diff	norm_rolling_reserves_diff	norm_rolling_rrp_total_bil_diff	norm_rolling_sofr_iorb_diff_diff
1280	1.0	2025-02-13	4.33	4.40	3220027.0	67.820	384797.0	2329.0	907.0	384.797	...	4.968171e-06	0.0	-0.005333	-1.012450e-06	-13.713367	-2073.400000	-1.068793	-0.162450	-3.768942	-2.231887
1281	1.0	2025-02-14	4.33	4.40	3220027.0	58.770	384797.0	2319.0	913.0	384.797	...	-3.103104e-06	0.0	-0.002333	-1.391825e-06	-6.228300	-2073.400000	-1.227637	-0.162450	-1.585087	-1.061726
1282	1.0	2025-02-18	4.37	4.40	3220027.0	77.817	384797.0	2452.0	913.0	384.797	...	4.129381e-05	0.0	0.002000	1.030453e-06	-5.510700	-2073.400000	-0.213431	-0.162450	-1.375718	0.628508
1283	1.0	2025-02-19	4.35	4.40	3270082.0	73.196	387833.0	2394.0	914.0	387.833	...	-2.938638e-05	50055.0	0.002667	5.484018e-07	-5.381833	-404.900000	-0.415266	0.155571	-1.338120	0.888544
1284	1.0	2025-02-20	4.33	4.40	3270082.0	63.207	387833.0	2403.0	914.0	387.833	...	2.754081e-06	0.0	0.002000	9.141867e-07	-4.927133	-404.900000	-0.262112	0.155571	-1.205456	0.628508
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1522	1.0	2026-02-02	3.69	3.65	2901600.0	10.415	326048.0	3307.0	1299.0	326.048	...	1.102681e-05	0.0	0.000000	9.400342e-07	0.140600	-1914.800000	-0.251289	-0.132220	0.273114	-0.151600
1523	1.0	2026-02-03	3.69	3.65	2901600.0	1.785	326048.0	3268.0	1297.0	326.048	...	-1.343595e-05	0.0	0.001000	6.724041e-07	-0.191967	-1914.800000	-0.363346	-0.132220	0.176084	0.238454
1524	1.0	2026-02-04	3.65	3.65	2925170.0	2.414	324445.0	3310.0	1306.0	324.445	...	5.283817e-06	23570.0	-0.000333	1.242652e-06	0.064267	-1129.133333	-0.124584	0.017530	0.250843	-0.281618
1525	1.0	2026-02-05	3.65	3.65	2925170.0	1.748	324445.0	3228.0	1290.0	324.445	...	-2.802918e-05	0.0	-0.001000	1.393720e-07	0.092867	-1129.133333	-0.586526	0.017530	0.259188	-0.541654
1526	1.0	2026-02-06	3.65	3.65	2925170.0	3.111	324445.0	3228.0	1290.0	324.445	...	-5.140793e-10	0.0	-0.000333	1.168816e-07	-0.007367	-1129.133333	-0.595943	0.017530	0.229943	-0.281618

247 rows × 27 columns

inputdf = dfdiff[["norm_rolling_leverage_ratio_diff", "norm_rolling_reserves_diff", "norm_rolling_rrp_total_bil_diff", "const"]]
dfmatrix = inputdf.to_numpy()

dfmatrix.shape

(247, 4)

dfmatrix

array([[-1.06879262e+00, -1.62449903e-01, -3.76894205e+00,
         1.00000000e+00],
       [-1.22763679e+00, -1.62449903e-01, -1.58508657e+00,
         1.00000000e+00],
       [-2.13430993e-01, -1.62449903e-01, -1.37571840e+00,
         1.00000000e+00],
       [-4.15265515e-01,  1.55570991e-01, -1.33812005e+00,
         1.00000000e+00],
       [-2.62111693e-01,  1.55570991e-01, -1.20545602e+00,
         1.00000000e+00],
       [ 1.08953639e-01,  3.30201344e-01, -8.83448402e-01,
         1.00000000e+00],
       [ 2.24138808e-01,  3.30201344e-01, -6.42706131e-01,
         1.00000000e+00],
       [ 4.33348904e-01,  3.30201344e-01, -5.58999710e-01,
         1.00000000e+00],
       [ 3.06292504e-01,  6.93407825e-01, -3.34518289e-01,
         1.00000000e+00],
       [ 7.36819914e-01,  6.93407825e-01,  4.38027687e-01,
         1.00000000e+00],
       [ 1.08793589e+00,  1.46549122e-01,  1.35544305e+00,
         1.00000000e+00],
       [ 7.28211268e-01,  1.46549122e-01,  4.90398905e-01,
         1.00000000e+00],
       [ 3.84458383e-01,  1.46549122e-01,  4.07071775e-01,
         1.00000000e+00],
       [ 1.29731362e-01,  5.36365745e-02,  7.20404348e-01,
         1.00000000e+00],
       [ 6.28883729e-01,  1.07882152e-01,  2.73094820e-01,
         1.00000000e+00],
       [ 2.87671723e-01,  1.07882152e-01,  2.63233276e-01,
         1.00000000e+00],
       [ 3.21813403e-01,  1.07882152e-01,  4.56797687e-01,
         1.00000000e+00],
       [ 1.03917402e-01,  1.07882152e-01,  6.53931316e-01,
         1.00000000e+00],
       [ 9.44523762e-03,  6.64506076e-01,  3.96675334e-01,
         1.00000000e+00],
       [-5.93060651e-01,  1.34745523e+00,  3.11296147e-01,
         1.00000000e+00],
       [-8.78323331e-01,  1.34745523e+00,  3.95673619e-01,
         1.00000000e+00],
       [-1.45634573e+00,  1.34745523e+00, -5.64086088e-01,
         1.00000000e+00],
       [-9.70387437e-01,  1.34745523e+00,  8.96074044e-01,
         1.00000000e+00],
       [-1.22710365e+00,  1.77665478e+00,  1.31431438e+00,
         1.00000000e+00],
       [-1.12556814e+00,  2.07984042e+00,  1.35368276e+00,
         1.00000000e+00],
       [-1.19807430e+00,  2.07984042e+00,  1.42190636e+00,
         1.00000000e+00],
       [-1.01832428e+00,  2.07984042e+00,  1.23177501e+00,
         1.00000000e+00],
       [-9.18444585e-01,  2.07984042e+00,  1.36614098e+00,
         1.00000000e+00],
       [-8.43717649e-01,  1.97274702e+00,  1.93928731e+00,
         1.00000000e+00],
       [-6.89372092e-01,  1.69979100e+00,  2.43545719e+00,
         1.00000000e+00],
       [-8.71914525e-01,  1.69979100e+00,  2.38332911e+00,
         1.00000000e+00],
       [-3.64235472e-02,  1.69979100e+00,  3.56634484e+00,
         1.00000000e+00],
       [-8.02272630e-01,  1.69979100e+00,  1.73650323e+00,
         1.00000000e+00],
       [-3.10796768e-01,  9.26902698e-01,  1.80005865e+00,
         1.00000000e+00],
       [-2.58274220e-01,  9.26902698e-01,  1.53519741e+00,
         1.00000000e+00],
       [-2.04124020e-01,  9.26902698e-01,  1.36459464e+00,
         1.00000000e+00],
       [-1.33107495e-01,  9.26902698e-01,  9.34849168e-01,
         1.00000000e+00],
       [-1.96682459e-01,  9.26902698e-01,  8.33539794e-01,
         1.00000000e+00],
       [-3.80627891e-01,  1.16945121e+00,  4.50612340e-01,
         1.00000000e+00],
       [-6.98006781e-01,  1.16945121e+00, -4.65042730e-01,
         1.00000000e+00],
       [-1.52353998e+00,  1.16945121e+00, -1.28000113e+00,
         1.00000000e+00],
       [-1.41499828e+00,  1.16945121e+00, -1.25189022e-01,
         1.00000000e+00],
       [-1.24511579e+00,  1.16945121e+00, -4.09462134e-01,
         1.00000000e+00],
       [-1.12251559e+00,  1.11844588e+00, -9.19986687e-01,
         1.00000000e+00],
       [-1.29391259e+00,  1.11844588e+00, -7.83325526e-01,
         1.00000000e+00],
       [-1.09836941e+00,  1.11844588e+00, -3.11858133e-01,
         1.00000000e+00],
       [-9.81949571e-01,  1.11844588e+00, -9.51524942e-03,
         1.00000000e+00],
       [-5.79774016e-01, -1.22353412e-01,  3.90460811e-01,
         1.00000000e+00],
       [ 3.22973364e-02, -6.78977336e-01,  4.79228962e-02,
         1.00000000e+00],
       [ 2.41724451e-01, -6.78977336e-01, -1.30664416e-01,
         1.00000000e+00],
       [ 3.36331417e-01, -6.78977336e-01,  2.76138867e-01,
         1.00000000e+00],
       [ 4.44811484e-01, -6.78977336e-01,  7.19869451e-01,
         1.00000000e+00],
       [ 1.50568827e+00, -9.17357996e-01,  1.12218933e+00,
         1.00000000e+00],
       [ 1.88358254e+00, -1.34655755e+00, -8.49842656e-02,
         1.00000000e+00],
       [ 1.22233181e+00, -1.34655755e+00, -1.69916085e-01,
         1.00000000e+00],
       [ 9.29541626e-01, -1.34655755e+00, -4.75312741e-01,
         1.00000000e+00],
       [ 8.25182625e-01, -1.34655755e+00, -3.83378641e-01,
         1.00000000e+00],
       [ 4.46638697e-01, -1.35022983e+00, -4.32452953e-01,
         1.00000000e+00],
       [ 3.93282550e-01, -1.24313643e+00, -9.26668030e-01,
         1.00000000e+00],
       [ 1.23450559e-01, -1.24313643e+00, -1.39261140e+00,
         1.00000000e+00],
       [ 4.79424554e-01, -1.24313643e+00, -1.29104917e+00,
         1.00000000e+00],
       [-1.82681159e-01, -1.24313643e+00, -2.41805638e+00,
         1.00000000e+00],
       [-1.46765770e-01, -1.13457538e+00, -7.21870795e-01,
         1.00000000e+00],
       [ 3.88795081e-01, -6.79707980e-01, -1.31062637e+00,
         1.00000000e+00],
       [ 1.64457228e-04, -6.79707980e-01, -6.82502421e-01,
         1.00000000e+00],
       [-2.44009130e-01, -6.79707980e-01, -1.43871494e-01,
         1.00000000e+00],
       [-4.90535724e-01, -6.79707980e-01, -2.21976091e-01,
         1.00000000e+00],
       [-9.43169166e-01, -3.38236579e-01,  1.19929674e-01,
         1.00000000e+00],
       [-5.64628937e-01, -9.43991571e-01,  3.30377360e-01,
         1.00000000e+00],
       [-5.32106009e-01, -9.43991571e-01,  5.24768429e-01,
         1.00000000e+00],
       [ 2.40394824e-01, -9.43991571e-01,  6.67187021e-01,
         1.00000000e+00],
       [ 1.84090482e-01, -1.06348687e+00,  9.62809661e-01,
         1.00000000e+00],
       [ 5.25167785e-01, -1.06348687e+00,  1.02095776e+00,
         1.00000000e+00],
       [ 4.63585878e-01, -9.19568989e-01,  2.89392174e+00,
         1.00000000e+00],
       [ 1.05120986e+00, -9.19568989e-01,  1.10791246e+00,
         1.00000000e+00],
       [ 9.40846626e-01, -9.19568989e-01,  7.36616571e-01,
         1.00000000e+00],
       [ 2.58836676e-01, -7.68865651e-01,  7.02023363e-01,
         1.00000000e+00],
       [ 1.23528574e-01,  4.71933640e-01,  6.46408393e-02,
         1.00000000e+00],
       [-2.39922564e-01,  4.71933640e-01,  4.37444164e-01,
         1.00000000e+00],
       [-4.40356385e-01,  4.71933640e-01,  1.07945597e+00,
         1.00000000e+00],
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         1.00000000e+00],
       [-1.23518180e+00,  1.18813664e+00,  6.72779119e-01,
         1.00000000e+00],
       [-2.00494840e+00,  1.42651730e+00, -5.38838979e-01,
         1.00000000e+00],
       [-1.90535833e+00,  1.42651730e+00,  2.43821400e-01,
         1.00000000e+00],
       [-1.27643543e+00,  1.42651730e+00,  6.47283678e-02,
         1.00000000e+00],
       [-1.02833564e+00,  1.42651730e+00,  5.64341035e-01,
         1.00000000e+00],
       [-1.19113444e+00,  1.42180306e+00,  8.72120411e-01,
         1.00000000e+00],
       [-8.24610458e-01,  1.42547534e+00,  7.43988415e-01,
         1.00000000e+00],
       [-6.17912110e-01,  1.42547534e+00,  2.41419229e-01,
         1.00000000e+00],
       [-1.67984813e-01,  1.42547534e+00,  4.80002465e-01,
         1.00000000e+00],
       [-4.39503820e-01,  1.42547534e+00,  6.43534876e-01,
         1.00000000e+00],
       [-2.85090062e-01,  1.19015703e+00,  9.14250795e-01,
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       [-7.37590670e-03,  1.08159599e+00,  1.26678641e+00,
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         1.00000000e+00],
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         1.00000000e+00],
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         1.00000000e+00],
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         1.00000000e+00],
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         1.00000000e+00],
       [-1.66796273e+00,  8.46608061e-01,  1.12518928e-01,
         1.00000000e+00],
       [-1.13618532e+00,  3.77547097e-01,  1.34585835e-01,
         1.00000000e+00],
       [-1.49322328e+00,  3.77547097e-01,  1.53404462e-01,
         1.00000000e+00],
       [-1.03477770e+00,  3.88902656e-02,  2.30137779e-01,
         1.00000000e+00],
       [-9.81423325e-01,  3.88902656e-02,  2.30001623e-01,
         1.00000000e+00],
       [-6.90447571e-01,  3.88902656e-02,  3.06093064e-01,
         1.00000000e+00],
       [-2.51289340e-01, -1.32220287e-01,  2.73114271e-01,
         1.00000000e+00],
       [-3.63345859e-01, -1.32220287e-01,  1.76084068e-01,
         1.00000000e+00],
       [-1.24583700e-01,  1.75300369e-02,  2.50843131e-01,
         1.00000000e+00],
       [-5.86525956e-01,  1.75300369e-02,  2.59187515e-01,
         1.00000000e+00],
       [-5.95942639e-01,  1.75300369e-02,  2.29943271e-01,
         1.00000000e+00]])

np.array([0.8067, 0.2317, 0.0750, -4.163e-17])[None, :]

array([[ 8.067e-01,  2.317e-01,  7.500e-02, -4.163e-17]])

inference_output = (dfmatrix * np.array([0.8067, 0.2317, 0.0750, -4.163e-17])[None, :]).sum(axis=1)

pred_mean = idata.posterior_predictive.y_hat.mean(dim=["draw", "chain"]).to_numpy()

pred_mean.shape

(247,)

fig, ax = plt.subplots(figsize=(12, 6)) # Added figsize for better visibility

# Your existing plots
#ax.plot(dfdiff["date"], inference_output, label="Inference Output")
#ax.plot(dfdiff["date"], pred_mean, label="Pred Mean")
ax.plot(dfdiff["date"], dfdiff["sofr_iorb_diff_diff"], label="Actual", alpha=0.7)

# --- 1. Get the boundaries of your timeline ---
start_date = dfdiff["date"].min()
end_date = dfdiff["date"].max()

# --- 2. Generate month-end dates ---
# Note: Pandas recently updated frequency strings. 
# Use freq='ME' (Month End) for newer Pandas, or freq='M' if you are on an older version.
month_ends = pd.date_range(start=start_date, end=end_date, freq='ME')

# --- 3. Draw the lines ---
for me_date in month_ends:
    ax.axvline(x=me_date, color='gray', linestyle=':', alpha=0.4)

ax.legend(loc="upper left")
plt.show()

df

	const	date	sofr_rate	iorb	reserves	rrp_on_bil	rrp_foreign_mm	sofr_vol	tgcr_vol	rrp_foreign_bil	rrp_total_bil	repo_vol_total	sofr_iorb_diff	total_rrp	leverage_ratio	sofr_iorb_diff_diff	rrp_total_bil_diff	leverage_ratio_diff	reserves_diff
0	1.0	2020-01-08	1.55	1.55	1654086.0	0.876	274047.0	1007.0	355.0	274.047	274.923	1362.0	0.00	274.923	0.000609	NaN	NaN	NaN	NaN
1	1.0	2020-01-09	1.55	1.55	1654086.0	0.401	274047.0	1011.0	361.0	274.047	274.448	1372.0	0.00	274.448	0.000611	0.00	-0.475	2.418028e-06	0.0
2	1.0	2020-01-10	1.55	1.55	1654086.0	0.627	274047.0	1013.0	367.0	274.047	274.674	1380.0	0.00	274.674	0.000612	0.00	0.226	1.208843e-06	0.0
3	1.0	2020-01-13	1.54	1.55	1654086.0	1.000	274047.0	1021.0	377.0	274.047	275.047	1398.0	-0.01	275.047	0.000617	-0.01	0.373	4.835566e-06	0.0
4	1.0	2020-01-14	1.55	1.55	1654086.0	0.656	274047.0	1009.0	371.0	274.047	274.703	1380.0	0.00	274.703	0.000610	0.01	-0.344	-7.253429e-06	0.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1522	1.0	2026-02-02	3.69	3.65	2901600.0	10.415	326048.0	3307.0	1299.0	326.048	336.463	4606.0	0.04	336.463	0.001140	0.01	0.786	1.102681e-05	0.0
1523	1.0	2026-02-03	3.69	3.65	2901600.0	1.785	326048.0	3268.0	1297.0	326.048	327.833	4565.0	0.04	327.833	0.001126	0.00	-8.630	-1.343595e-05	0.0
1524	1.0	2026-02-04	3.65	3.65	2925170.0	2.414	324445.0	3310.0	1306.0	324.445	326.859	4616.0	0.00	326.859	0.001131	-0.04	-0.974	5.283817e-06	23570.0
1525	1.0	2026-02-05	3.65	3.65	2925170.0	1.748	324445.0	3228.0	1290.0	324.445	326.193	4518.0	0.00	326.193	0.001103	0.00	-0.666	-2.802918e-05	0.0
1526	1.0	2026-02-06	3.65	3.65	2925170.0	3.111	324445.0	3228.0	1290.0	324.445	327.556	4518.0	0.00	327.556	0.001103	0.00	1.363	-5.140793e-10	0.0

1527 rows × 19 columns

dfdiff.sort_values(by="sofr_iorb_diff_diff")[["date", "sofr_iorb_diff_diff"]].tail(40)

	date	sofr_iorb_diff_diff
1460	2025-10-30	0.02
1290	2025-02-28	0.03
1457	2025-10-27	0.03
1468	2025-11-12	0.03
1476	2025-11-24	0.03
1521	2026-01-30	0.03
1455	2025-10-23	0.03
1289	2025-02-27	0.03
1322	2025-04-15	0.03
1330	2025-04-28	0.03
1329	2025-04-25	0.04
1385	2025-07-15	0.04
1282	2025-02-18	0.04
1364	2025-06-16	0.04
1372	2025-06-26	0.04
1413	2025-08-22	0.04
1478	2025-11-26	0.04
1458	2025-10-28	0.04
1448	2025-10-14	0.04
1477	2025-11-25	0.05
1471	2025-11-17	0.05
1419	2025-09-02	0.05
1436	2025-09-25	0.05
1350	2025-05-27	0.05
1332	2025-04-30	0.05
1371	2025-06-25	0.06
1374	2025-06-30	0.06
1393	2025-07-25	0.06
1397	2025-07-31	0.07
1311	2025-03-31	0.07
1317	2025-04-08	0.07
1453	2025-10-21	0.07
1479	2025-11-28	0.07
1490	2025-12-15	0.08
1428	2025-09-15	0.09
1449	2025-10-15	0.10
1498	2025-12-26	0.10
1439	2025-09-30	0.11
1501	2025-12-31	0.16
1461	2025-10-31	0.18

dfdiff["sofr_iorb_diff_diff"].mean()

np.float64(0.00032388663967611363)

start = dfdiff.sort_values(by="date")[dfdiff.sort_values(by="date")["date"] == dt.datetime(2025,8,29)].index
int(start[0])
dfdiff.sort_values(by="date")[["date", "sofr_iorb_diff_diff"]].loc[int(start[0])-10: int(start[0])+10]

	date	sofr_iorb_diff_diff
1408	2025-08-15	0.02
1409	2025-08-18	-0.02
1410	2025-08-19	-0.01
1411	2025-08-20	-0.02
1412	2025-08-21	0.01
1413	2025-08-22	0.04
1414	2025-08-25	0.01
1415	2025-08-26	0.01
1416	2025-08-27	-0.02
1417	2025-08-28	-0.02
1418	2025-08-29	0.00
1419	2025-09-02	0.05
1420	2025-09-03	0.00
1421	2025-09-04	0.02
1422	2025-09-05	0.01
1423	2025-09-08	-0.02
1424	2025-09-09	0.00
1425	2025-09-10	-0.01
1426	2025-09-11	0.02
1427	2025-09-12	0.01
1428	2025-09-15	0.09

print(results.summary())

                                   OLS Regression Results                                   
============================================================================================
Dep. Variable:     norm_rolling_sofr_iorb_diff_diff   R-squared:                       0.445
Model:                                          OLS   Adj. R-squared:                  0.438
Method:                               Least Squares   F-statistic:                     65.01
Date:                              Tue, 10 Feb 2026   Prob (F-statistic):           6.80e-31
Time:                                      14:24:24   Log-Likelihood:                -277.21
No. Observations:                               247   AIC:                             562.4
Df Residuals:                                   243   BIC:                             576.5
Df Model:                                         3                                         
Covariance Type:                          nonrobust                                         
====================================================================================================
                                       coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------------------
norm_rolling_leverage_ratio_diff     0.8067      0.080     10.116      0.000       0.650       0.964
norm_rolling_reserves_diff           0.2317      0.083      2.793      0.006       0.068       0.395
norm_rolling_rrp_total_bil_diff      0.0750      0.055      1.370      0.172      -0.033       0.183
const                            -4.163e-17      0.048  -8.73e-16      1.000      -0.094       0.094
==============================================================================
Omnibus:                       29.572   Durbin-Watson:                   0.537
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               86.585
Skew:                          -0.474   Prob(JB):                     1.58e-19
Kurtosis:                       5.741   Cond. No.                         3.16
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

dfdiffcopy = dfdiff
dfdiffcopy["month_leverage"] = dfdiff['norm_leverage_ratio_diff'] * dfdiff["end-of-month"]
dfdiffcopy["month_reserves"] = dfdiff['norm_reserves_diff'] * dfdiff["end-of-month"] 
dfdiffcopy["month_rrp"] = dfdiff['norm_rrp_total_bil_diff'] * dfdiff["end-of-month"] 
input_df = dfdiffcopy[['norm_leverage_ratio_diff', 'norm_reserves_diff', 'norm_rrp_total_bil_diff', 'end-of-month', 'const']]

model = sm.OLS(dfdiffcopy["norm_sofr_iorb_diff_diff"], input_df)
results = model.fit()
print(results.summary())

                               OLS Regression Results                               
====================================================================================
Dep. Variable:     norm_sofr_iorb_diff_diff   R-squared:                       0.368
Model:                                  OLS   Adj. R-squared:                  0.358
Method:                       Least Squares   F-statistic:                     35.25
Date:                      Wed, 11 Feb 2026   Prob (F-statistic):           3.41e-23
Time:                              16:55:04   Log-Likelihood:                -293.28
No. Observations:                       247   AIC:                             596.6
Df Residuals:                           242   BIC:                             614.1
Df Model:                                 4                                         
Covariance Type:                  nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
norm_leverage_ratio_diff     0.5252      0.064      8.224      0.000       0.399       0.651
norm_reserves_diff           0.2492      0.057      4.399      0.000       0.138       0.361
norm_rrp_total_bil_diff      0.1555      0.058      2.697      0.007       0.042       0.269
end-of-month                 0.5565      0.316      1.760      0.080      -0.066       1.179
const                       -0.0248      0.053     -0.468      0.640      -0.129       0.079
==============================================================================
Omnibus:                       35.839   Durbin-Watson:                   2.093
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              124.204
Skew:                          -0.537   Prob(JB):                     1.07e-27
Kurtosis:                       6.304   Cond. No.                         7.52
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.