VAR#
import os
os.chdir("../../")
import pandas as pd
import numpy as np
from statsmodels.tsa.vector_ar.vecm import VECM
from statsmodels.tsa.vector_ar.vecm import select_order
from scripts.python.tsa.mtsmodel import *
from scripts.python.tsa.ts_eval import *
import warnings
warnings.filterwarnings("ignore")
for country in ["palau", "samoa", "tonga", "solomon_islands", "vanuatu"]:
var = VARPipeline(country=country, data=None,
var_name=["total", "seats_arrivals_intl"],
exog=["covid", "stringency_index", "covid"])
var.read_and_merge()
var.transform()
var.varma_search()
var.fit()
var.get_fittedvalues()
var.evaluate_models()
pred_df = var.data[["date", "total", "pred_total"]]
saved_pred_path = var.country_data_folder + "/model/var_" + str(country) + ".csv"
pred_df.to_csv(saved_pred_path, encoding="utf-8")
Best P, Q, Trend Combination: (3, 1, 't')
Statespace Model Results
============================================================================================
Dep. Variable: ['total', 'seats_arrivals_intl'] No. Observations: 45
Model: VARMAX(3,1) Log Likelihood -124.461
+ intercept AIC 302.923
Date: Thu, 08 Jun 2023 BIC 351.703
Time: 20:22:04 HQIC 321.108
Sample: 0
- 45
Covariance Type: opg
===================================================================================
Ljung-Box (L1) (Q): 0.30, 0.06 Jarque-Bera (JB): 233.13, 35.28
Prob(Q): 0.58, 0.81 Prob(JB): 0.00, 0.00
Heteroskedasticity (H): 0.06, 0.12 Skew: 2.77, -0.34
Prob(H) (two-sided): 0.00, 0.00 Kurtosis: 12.68, 7.28
Results for equation total
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
drift 0.1532 0.152 1.008 0.313 -0.145 0.451
L1.total 0.6935 2.006 0.346 0.730 -3.238 4.625
L1.seats_arrivals_intl 0.0215 2.741 0.008 0.994 -5.352 5.394
L2.total -0.2521 2.208 -0.114 0.909 -4.580 4.076
L2.seats_arrivals_intl -0.2135 1.964 -0.109 0.913 -4.064 3.637
L3.total -0.0565 1.070 -0.053 0.958 -2.154 2.041
L3.seats_arrivals_intl -0.1320 0.925 -0.143 0.887 -1.945 1.681
L1.e(total) 0.0196 2.055 0.010 0.992 -4.008 4.047
L1.e(seats_arrivals_intl) -0.8520 2.658 -0.321 0.749 -6.062 4.358
beta.covid -4.5075 4.081 -1.105 0.269 -12.506 3.491
beta.stringency_index 0.0191 0.059 0.322 0.747 -0.097 0.136
beta.covid -4.5075 4.081 -1.105 0.269 -12.506 3.491
Results for equation seats_arrivals_intl
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
drift 0.2071 0.299 0.692 0.489 -0.380 0.794
L1.total 0.3064 0.731 0.419 0.675 -1.126 1.738
L1.seats_arrivals_intl -0.3916 1.027 -0.381 0.703 -2.405 1.622
L2.total 0.0982 1.310 0.075 0.940 -2.469 2.665
L2.seats_arrivals_intl -0.1935 1.288 -0.150 0.881 -2.717 2.330
L3.total -0.2270 0.373 -0.609 0.543 -0.957 0.503
L3.seats_arrivals_intl 0.0267 0.361 0.074 0.941 -0.681 0.735
L1.e(total) -0.0826 0.683 -0.121 0.904 -1.421 1.256
L1.e(seats_arrivals_intl) 0.1944 1.317 0.148 0.883 -2.386 2.775
beta.covid -4.9146 8.130 -0.605 0.546 -20.849 11.020
beta.stringency_index -0.0049 0.057 -0.085 0.932 -0.117 0.107
beta.covid -4.9146 8.130 -0.605 0.546 -20.849 11.020
Error covariance matrix
======================================================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------------------------------
sqrt.var.total 1.3587 0.529 2.568 0.010 0.322 2.396
sqrt.cov.total.seats_arrivals_intl 1.1035 0.298 3.704 0.000 0.520 1.687
sqrt.var.seats_arrivals_intl 0.6617 0.332 1.991 0.047 0.010 1.313
======================================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 1.24e+17. Standard errors may be unstable.
| MSE | RMSE | MAE | SMAPE | |
|---|---|---|---|---|
| naive | 1.298621e+06 | 1139.570483 | 677.477273 | 53.868245 |
| mean | 1.219030e+07 | 3491.460526 | 3125.890370 | 130.888109 |
| VAR (scaled) | 1.127006e+06 | 1061.605449 | 554.935555 | 38.243616 |
Best P, Q, Trend Combination: (1, 1, 'c')
Statespace Model Results
============================================================================================
Dep. Variable: ['total', 'seats_arrivals_intl'] No. Observations: 45
Model: VARMAX(1,1) Log Likelihood -150.021
+ intercept AIC 338.041
Date: Thu, 08 Jun 2023 BIC 372.368
Time: 20:23:31 HQIC 350.838
Sample: 0
- 45
Covariance Type: opg
===================================================================================
Ljung-Box (L1) (Q): 0.26, 0.21 Jarque-Bera (JB): 303.19, 83.91
Prob(Q): 0.61, 0.65 Prob(JB): 0.00, 0.00
Heteroskedasticity (H): 0.60, 1.22 Skew: 3.16, -0.89
Prob(H) (two-sided): 0.33, 0.70 Kurtosis: 14.03, 9.45
Results for equation total
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
intercept 0.7106 2.797 0.254 0.799 -4.771 6.192
L1.total 0.4323 0.911 0.475 0.635 -1.353 2.218
L1.seats_arrivals_intl 0.0696 0.881 0.079 0.937 -1.658 1.797
L1.e(total) 0.4995 0.887 0.563 0.573 -1.239 2.238
L1.e(seats_arrivals_intl) -0.9557 1.397 -0.684 0.494 -3.694 1.783
beta.covid -0.8085 4.216 -0.192 0.848 -9.071 7.454
beta.stringency_index -0.0890 0.120 -0.741 0.459 -0.324 0.146
beta.covid -0.8085 4.216 -0.192 0.848 -9.071 7.454
Results for equation seats_arrivals_intl
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
intercept 3.0195 1.317 2.293 0.022 0.439 5.600
L1.total -0.1394 0.746 -0.187 0.852 -1.602 1.323
L1.seats_arrivals_intl -0.3394 0.709 -0.479 0.632 -1.729 1.050
L1.e(total) 0.2423 0.605 0.400 0.689 -0.944 1.429
L1.e(seats_arrivals_intl) 0.2607 0.714 0.365 0.715 -1.138 1.659
beta.covid -1.5307 2.774 -0.552 0.581 -6.968 3.906
beta.stringency_index -0.1142 0.079 -1.450 0.147 -0.268 0.040
beta.covid -1.5307 2.774 -0.552 0.581 -6.968 3.906
Error covariance matrix
======================================================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------------------------------
sqrt.var.total 2.0024 0.816 2.453 0.014 0.403 3.602
sqrt.cov.total.seats_arrivals_intl 1.2602 0.397 3.177 0.001 0.483 2.038
sqrt.var.seats_arrivals_intl 0.8412 0.346 2.435 0.015 0.164 1.518
======================================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 2.04e+17. Standard errors may be unstable.
| MSE | RMSE | MAE | SMAPE | |
|---|---|---|---|---|
| naive | 7.970104e+06 | 2823.137282 | 1518.795455 | 49.120902 |
| mean | 4.747392e+07 | 6890.131975 | 6027.062716 | 155.537953 |
| VAR (scaled) | 1.029089e+07 | 3207.941282 | 1757.557409 | 141.614714 |
Best P, Q, Trend Combination: (2, 2, 't')
Statespace Model Results
============================================================================================
Dep. Variable: ['total', 'seats_arrivals_intl'] No. Observations: 36
Model: VARMAX(2,2) Log Likelihood -114.995
+ intercept AIC 283.990
Date: Thu, 08 Jun 2023 BIC 326.745
Time: 20:24:49 HQIC 298.913
Sample: 0
- 36
Covariance Type: opg
===================================================================================
Ljung-Box (L1) (Q): 0.00, 0.55 Jarque-Bera (JB): 296.03, 0.50
Prob(Q): 0.97, 0.46 Prob(JB): 0.00, 0.78
Heteroskedasticity (H): 0.23, 1.42 Skew: 2.89, 0.18
Prob(H) (two-sided): 0.02, 0.55 Kurtosis: 15.80, 2.54
Results for equation total
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
drift 0.0814 0.471 0.173 0.863 -0.842 1.005
L1.total 0.3433 1.638 0.210 0.834 -2.868 3.555
L1.seats_arrivals_intl 0.0070 2.680 0.003 0.998 -5.246 5.260
L2.total -0.0883 2.361 -0.037 0.970 -4.717 4.540
L2.seats_arrivals_intl -0.0139 2.239 -0.006 0.995 -4.402 4.375
L1.e(total) -0.0268 8.060 -0.003 0.997 -15.823 15.770
L1.e(seats_arrivals_intl) 0.1534 7.545 0.020 0.984 -14.634 14.940
L2.e(total) -0.2397 6.816 -0.035 0.972 -13.599 13.120
L2.e(seats_arrivals_intl) 0.3266 6.178 0.053 0.958 -11.782 12.435
beta.covid -1.9506 12.650 -0.154 0.877 -26.745 22.844
beta.stringency_index -0.0681 0.214 -0.318 0.750 -0.487 0.351
beta.covid -1.9506 12.650 -0.154 0.877 -26.745 22.844
Results for equation seats_arrivals_intl
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
drift 0.1251 0.377 0.332 0.740 -0.613 0.863
L1.total 0.3466 4.524 0.077 0.939 -8.520 9.214
L1.seats_arrivals_intl 0.3757 2.121 0.177 0.859 -3.782 4.533
L2.total -0.4958 3.786 -0.131 0.896 -7.916 6.925
L2.seats_arrivals_intl -0.0737 3.150 -0.023 0.981 -6.247 6.100
L1.e(total) -0.0065 13.351 -0.000 1.000 -26.174 26.161
L1.e(seats_arrivals_intl) -0.4660 12.451 -0.037 0.970 -24.870 23.938
L2.e(total) 0.5867 9.535 0.062 0.951 -18.101 19.274
L2.e(seats_arrivals_intl) -0.1605 8.794 -0.018 0.985 -17.397 17.076
beta.covid -2.3151 11.317 -0.205 0.838 -24.496 19.866
beta.stringency_index -0.0381 0.209 -0.183 0.855 -0.447 0.371
beta.covid -2.3151 11.317 -0.205 0.838 -24.496 19.866
Error covariance matrix
======================================================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------------------------------
sqrt.var.total 1.6572 0.897 1.847 0.065 -0.102 3.416
sqrt.cov.total.seats_arrivals_intl 1.6108 2.921 0.551 0.581 -4.115 7.337
sqrt.var.seats_arrivals_intl 0.9357 8.905 0.105 0.916 -16.518 18.389
======================================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 6.73e+17. Standard errors may be unstable.
| MSE | RMSE | MAE | SMAPE | |
|---|---|---|---|---|
| naive | 1.045461e+06 | 1022.477747 | 597.257143 | 69.556373 |
| mean | 7.898678e+06 | 2810.458659 | 2511.586420 | 147.552078 |
| VAR (scaled) | 5.478471e+05 | 740.166954 | 354.330235 | 61.940427 |
Best P, Q, Trend Combination: (1, 1, 'ct')
Statespace Model Results
============================================================================================
Dep. Variable: ['total', 'seats_arrivals_intl'] No. Observations: 24
Model: VARMAX(1,1) Log Likelihood -61.690
+ intercept AIC 165.380
Date: Thu, 08 Jun 2023 BIC 190.119
Time: 20:25:46 HQIC 171.943
Sample: 0
- 24
Covariance Type: opg
===================================================================================
Ljung-Box (L1) (Q): 1.75, 0.35 Jarque-Bera (JB): 0.37, 91.71
Prob(Q): 0.19, 0.55 Prob(JB): 0.83, 0.00
Heteroskedasticity (H): 0.83, 3.04 Skew: 0.28, 2.41
Prob(H) (two-sided): 0.80, 0.14 Kurtosis: 2.75, 11.28
Results for equation total
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
intercept 0.9646 7.078 0.136 0.892 -12.908 14.837
intercept 0.7162 8.942 0.080 0.936 -16.810 18.243
L1.total 0.0850 1.861 0.046 0.964 -3.563 3.733
L1.seats_arrivals_intl -0.1824 1.777 -0.103 0.918 -3.665 3.300
L1.e(total) 0.1519 2.814 0.054 0.957 -5.364 5.668
L1.e(seats_arrivals_intl) 1.0805 2.247 0.481 0.631 -3.323 5.484
beta.covid -1.4308 2.244 -0.638 0.524 -5.828 2.967
beta.stringency_index -0.1115 0.193 -0.579 0.562 -0.489 0.266
beta.covid -1.4308 2.244 -0.638 0.524 -5.828 2.967
Results for equation seats_arrivals_intl
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
drift 0.1455 0.969 0.150 0.881 -1.754 2.045
drift 0.3453 0.964 0.358 0.720 -1.545 2.235
L1.total 0.4916 0.740 0.664 0.506 -0.959 1.942
L1.seats_arrivals_intl -0.6662 0.520 -1.281 0.200 -1.686 0.353
L1.e(total) -0.3073 0.941 -0.327 0.744 -2.152 1.537
L1.e(seats_arrivals_intl) 0.8599 1.688 0.509 0.611 -2.449 4.169
beta.covid -1.3231 1.910 -0.693 0.488 -5.067 2.420
beta.stringency_index -0.1592 0.201 -0.791 0.429 -0.554 0.235
beta.covid -1.3231 1.910 -0.693 0.488 -5.067 2.420
Error covariance matrix
======================================================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------------------------------
sqrt.var.total 0.5525 0.456 1.212 0.225 -0.341 1.446
sqrt.cov.total.seats_arrivals_intl -0.3034 3.635 -0.083 0.933 -7.427 6.820
sqrt.var.seats_arrivals_intl 1.3951 0.885 1.576 0.115 -0.339 3.130
======================================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 1.55e+17. Standard errors may be unstable.
| MSE | RMSE | MAE | SMAPE | |
|---|---|---|---|---|
| naive | 1.721267e+05 | 414.881597 | 268.478261 | 46.835106 |
| mean | 1.290167e+06 | 1135.855000 | 1065.215278 | 100.969388 |
| VAR (scaled) | 6.502167e+04 | 254.993470 | 154.338247 | 17.694166 |
Best P, Q, Trend Combination: (2, 2, 'c')
Statespace Model Results
============================================================================================
Dep. Variable: ['total', 'seats_arrivals_intl'] No. Observations: 43
Model: VARMAX(2,2) Log Likelihood -156.966
+ intercept AIC 367.932
Date: Thu, 08 Jun 2023 BIC 415.485
Time: 20:27:14 HQIC 385.468
Sample: 0
- 43
Covariance Type: opg
===================================================================================
Ljung-Box (L1) (Q): 0.38, 1.22 Jarque-Bera (JB): 43.45, 85.76
Prob(Q): 0.54, 0.27 Prob(JB): 0.00, 0.00
Heteroskedasticity (H): 0.23, 0.85 Skew: 1.25, -0.85
Prob(H) (two-sided): 0.01, 0.76 Kurtosis: 7.24, 9.71
Results for equation total
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
intercept 2.7879 1.539 1.811 0.070 -0.229 5.805
L1.total 0.1296 0.453 0.286 0.775 -0.758 1.017
L1.seats_arrivals_intl -0.0458 0.782 -0.059 0.953 -1.579 1.487
L2.total -0.0978 0.427 -0.229 0.819 -0.936 0.740
L2.seats_arrivals_intl -0.0299 0.594 -0.050 0.960 -1.194 1.134
L1.e(total) -0.0571 0.491 -0.116 0.907 -1.020 0.906
L1.e(seats_arrivals_intl) 0.0051 0.687 0.007 0.994 -1.341 1.351
L2.e(total) -0.2549 0.350 -0.728 0.467 -0.941 0.431
L2.e(seats_arrivals_intl) -0.6611 0.605 -1.093 0.274 -1.847 0.524
beta.covid -4.3852 1.703 -2.575 0.010 -7.723 -1.047
beta.stringency_index -0.0641 0.029 -2.242 0.025 -0.120 -0.008
beta.covid -4.3852 1.703 -2.575 0.010 -7.723 -1.047
Results for equation seats_arrivals_intl
=============================================================================================
coef std err z P>|z| [0.025 0.975]
---------------------------------------------------------------------------------------------
intercept 2.2902 2.130 1.075 0.282 -1.884 6.464
L1.total 0.4332 0.457 0.949 0.343 -0.462 1.328
L1.seats_arrivals_intl 0.4219 0.582 0.725 0.469 -0.719 1.563
L2.total -0.6276 0.383 -1.637 0.102 -1.379 0.124
L2.seats_arrivals_intl -0.0903 0.357 -0.253 0.800 -0.790 0.609
L1.e(total) -0.3777 0.570 -0.663 0.507 -1.494 0.739
L1.e(seats_arrivals_intl) 0.2111 0.628 0.336 0.737 -1.019 1.441
L2.e(total) 0.1953 0.699 0.279 0.780 -1.175 1.565
L2.e(seats_arrivals_intl) -0.1561 0.455 -0.343 0.732 -1.048 0.736
beta.covid -2.1837 3.363 -0.649 0.516 -8.776 4.408
beta.stringency_index -0.0263 0.082 -0.321 0.748 -0.187 0.134
beta.covid -2.1837 3.363 -0.649 0.516 -8.776 4.408
Error covariance matrix
======================================================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------------------------------
sqrt.var.total 1.1858 0.351 3.376 0.001 0.497 1.874
sqrt.cov.total.seats_arrivals_intl 0.1719 0.856 0.201 0.841 -1.506 1.850
sqrt.var.seats_arrivals_intl 1.5067 0.289 5.218 0.000 0.941 2.073
======================================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 7e+18. Standard errors may be unstable.
| MSE | RMSE | MAE | SMAPE | |
|---|---|---|---|---|
| naive | 2.446383e+06 | 1564.091833 | 808.452381 | 45.153360 |
| mean | 2.273834e+07 | 4768.473803 | 4264.861006 | 156.566459 |
| VAR (scaled) | 1.600258e+06 | 1265.013157 | 554.204122 | 134.493067 |