python - 在 Python 中使用不同的独立回归器运行 VARMAX 方程

Question

我想将特定的外生变量分配给特定的回归。具体来说，请考虑下面的代码。如何将方程 dln_inv 的 beta.exog_only_for_inc_equation 系数限制为零，并将方程 dln_inc 的 beta.exog_only_for_inv_equation 系数限制为零？

import numpy as np
import pandas as pd
import statsmodels.api as sm
import matplotlib.pyplot as plt
dta = sm.datasets.webuse('lutkepohl2', 'https://www.stata-press.com/data/r12/')
dta.index = dta.qtr
endog = dta.loc['1960-04-01':'1978-10-01', ['dln_inv', 'dln_inc', 'dln_consump']]

endog['exog_only_for_inv_equation']=[endog.index[i].quarter for i in range(len(endog.index))]
endog['exog_only_for_inc_equation']=endog['dln_consump']
exog = endog[['exog_only_for_inv_equation','exog_only_for_inc_equation']]
mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(2,0), trend='n', exog=exog)
res = mod.fit(maxiter=1000, disp=False)
print(res.summary())


 Statespace Model Results                             
==================================================================================
Dep. Variable:     ['dln_inv', 'dln_inc']   No. Observations:                   75
Model:                            VARX(2)   Log Likelihood                 363.197
Date:                    Wed, 22 Apr 2020   AIC                           -696.394
Time:                            22:49:07   BIC                           -661.631
Sample:                        04-01-1960   HQIC                          -682.513
                             - 10-01-1978                                         
Covariance Type:                      opg                                         
===================================================================================
Ljung-Box (Q):                60.43, 38.85   Jarque-Bera (JB):           8.31, 4.57
Prob(Q):                        0.02, 0.52   Prob(JB):                   0.02, 0.10
Heteroskedasticity (H):         0.46, 0.42   Skew:                      0.13, -0.55
Prob(H) (two-sided):            0.06, 0.04   Kurtosis:                   4.61, 3.48
                                    Results for equation dln_inv                                   
===================================================================================================
                                      coef    std err          z      P>|z|      [0.025      0.975]
---------------------------------------------------------------------------------------------------
L1.dln_inv                         -0.2468      0.094     -2.624      0.009      -0.431      -0.062
L1.dln_inc                          0.2937      0.481      0.610      0.542      -0.649       1.237
L2.dln_inv                         -0.1873      0.152     -1.235      0.217      -0.485       0.110
L2.dln_inc                         -0.0805      0.413     -0.195      0.846      -0.891       0.730
beta.exog_only_for_inv_equation    -0.0007      0.004     -0.172      0.863      -0.009       0.008
beta.exog_only_for_inc_equation     1.2446      0.639      1.947      0.052      -0.008       2.497
                                    Results for equation dln_inc                                   
===================================================================================================
                                      coef    std err          z      P>|z|      [0.025      0.975]
---------------------------------------------------------------------------------------------------
L1.dln_inv                          0.0606      0.033      1.830      0.067      -0.004       0.126
L1.dln_inc                          0.0170      0.133      0.128      0.898      -0.243       0.277
L2.dln_inv                          0.0116      0.035      0.333      0.739      -0.056       0.080
L2.dln_inc                         -0.0187      0.130     -0.143      0.886      -0.273       0.236
beta.exog_only_for_inv_equation     0.0018      0.001      1.756      0.079      -0.000       0.004
beta.exog_only_for_inc_equation     0.7046      0.111      6.321      0.000       0.486       0.923
                                  Error covariance matrix                                   
============================================================================================
                               coef    std err          z      P>|z|      [0.025      0.975]
--------------------------------------------------------------------------------------------
sqrt.var.dln_inv             0.0434      0.004     12.267      0.000       0.036       0.050
sqrt.cov.dln_inv.dln_inc  5.319e-06      0.002      0.003      0.998      -0.004       0.004
sqrt.var.dln_inc             0.0106      0.001     10.475      0.000       0.009       0.013
============================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

Answer 1

我不得不仔细阅读 statsmodels.tsa.statespace.dynamic_factor.DynamicFactor 上的文档。

在 mod 之后，使用以下几行更改代码

with mod.fix_params({'beta.exog_only_for_inc_equation.dln_inv': 0,'beta.exog_only_for_inv_equation.dln_inc':0}):
        res = mod.fit()
print(res.summary())

这将产生:

    Statespace Model Results                             
    ==================================================================================
    Dep. Variable:     ['dln_inv', 'dln_inc']   No. Observations:                   75
    Model:                            VARX(2)   Log Likelihood                 359.238
    Date:                    Sat, 25 Apr 2020   AIC                           -692.475
    Time:                            00:52:20   BIC                           -662.348
    Sample:                        04-01-1960   HQIC                          -680.446
                                 - 10-01-1978                                         
    Covariance Type:                      opg                                         
    ===================================================================================
    Ljung-Box (Q):                61.97, 39.25   Jarque-Bera (JB):          14.10, 2.67
    Prob(Q):                        0.01, 0.50   Prob(JB):                   0.00, 0.26
    Heteroskedasticity (H):         0.44, 0.39   Skew:                      0.10, -0.40
    Prob(H) (two-sided):            0.05, 0.02   Kurtosis:                   5.11, 3.47
                                            Results for equation dln_inv                                       
    ===========================================================================================================
                                                  coef    std err          z      P>|z|      [0.025      0.975]
    -----------------------------------------------------------------------------------------------------------
    L1.dln_inv                                 -0.2537      0.095     -2.663      0.008      -0.440      -0.067
    L1.dln_inc                                  0.5490      0.442      1.243      0.214      -0.317       1.415
    L2.dln_inv                                 -0.1359      0.175     -0.778      0.436      -0.478       0.206
    L2.dln_inc                                  0.4770      0.371      1.286      0.198      -0.250       1.204
    beta.exog_only_for_inv_equation             0.0015      0.005      0.321      0.748      -0.008       0.011
    beta.exog_only_for_inc_equation (fixed)          0        nan        nan        nan         nan         nan
                                            Results for equation dln_inc                                       
    ===========================================================================================================
                                                  coef    std err          z      P>|z|      [0.025      0.975]
    -----------------------------------------------------------------------------------------------------------
    L1.dln_inv                                  0.0615      0.035      1.737      0.082      -0.008       0.131
    L1.dln_inc                                  0.0584      0.105      0.557      0.577      -0.147       0.264
    L2.dln_inv                                  0.0091      0.031      0.289      0.773      -0.052       0.071
    L2.dln_inc                                  0.0181      0.126      0.144      0.886      -0.229       0.265
    beta.exog_only_for_inv_equation (fixed)          0        nan        nan        nan         nan         nan
    beta.exog_only_for_inc_equation             0.8123      0.115      7.070      0.000       0.587       1.038
                                      Error covariance matrix                                   
    ============================================================================================
                                   coef    std err          z      P>|z|      [0.025      0.975]
    --------------------------------------------------------------------------------------------
    sqrt.var.dln_inv             0.0445      0.003     14.175      0.000       0.038       0.051
    sqrt.cov.dln_inv.dln_inc -5.595e-05      0.002     -0.028      0.978      -0.004       0.004
    sqrt.var.dln_inc             0.0108      0.001     11.536      0.000       0.009       0.013
    ============================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

要查找参数的名称，只需键入

res.param_names

这将显示您可以使用的所有参数名称。对于上面的例子，

['L1.dln_inv.dln_inv',
 'L1.dln_inc.dln_inv',
 'L2.dln_inv.dln_inv',
 'L2.dln_inc.dln_inv',
 'L1.dln_inv.dln_inc',
 'L1.dln_inc.dln_inc',
 'L2.dln_inv.dln_inc',
 'L2.dln_inc.dln_inc',
 'beta.exog_only_for_inv_equation.dln_inv',
 'beta.exog_only_for_inc_equation.dln_inv',
 'beta.exog_only_for_inv_equation.dln_inc',
 'beta.exog_only_for_inc_equation.dln_inc',
 'sqrt.var.dln_inv',
 'sqrt.cov.dln_inv.dln_inc',
 'sqrt.var.dln_inc']

希望这证明是有用的。