我正在使用R中的{vars}包来比较VAR和SVAR的结果。 代码和结果如下，但是这是我无法理解的三件事。
1）SVAR针对不同方法（“直接”和“评分”）给出不同的输出。我们可以说其中一个比另一个更合理的理论原因吗？
2）SVAR（）函数提供了一个链接结构形式和简化形式的矩阵，其元素对应于t周期项的系数（同时效应的参数）。 但是我无法获得其他形式的输出，例如“ print（summary（var_result））” 提供VAR羊肚菌？ 仅凭A矩阵来解释估计值并不容易。 我可以简单地
3）我可以了解A矩阵提供的结构参数的重要性吗？ 我找到了一项研究，其中作者重新提出了SVAR结构参数的“两个标准偏差显着性”。是判断变量是否有效的唯一方法吗？
> # load {vars} package and data
> library(vars)
> data(Canada)
>
> # select a lag level based on AIC
> optimal_lag <- VARselect(Canada,lag.max=10)$selection[1]
>
> # estimate VAR
> var_result <- VAR(Canada, p=optimal_lag, type='const')
>
> print(summary(var_result))
VAR Estimation Results:
=========================
Endogenous variables: e, prod, rw, U
Deterministic variables: const
Sample size: 81
Log Likelihood: -150.609
Roots of the characteristic polynomial:
1.004 0.9283 0.9283 0.7437 0.7437 0.6043 0.6043 0.5355 0.5355 0.2258 0.2258 0.1607
Call:
VAR(y = Canada, p = optimal_lag, type = "const")
Estimation results for equation e:
==================================
e = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + e.l3 + prod.l3 + rw.l3 + U.l3 + const
Estimate Std. Error t value Pr(>|t|)
e.l1 1.75274 0.15082 11.622 < 2e-16 ***
prod.l1 0.16962 0.06228 2.723 0.008204 **
rw.l1 -0.08260 0.05277 -1.565 0.122180
U.l1 0.09952 0.19747 0.504 0.615915
e.l2 -1.18385 0.23517 -5.034 3.75e-06 ***
prod.l2 -0.10574 0.09425 -1.122 0.265858
rw.l2 -0.02439 0.06957 -0.351 0.727032
U.l2 -0.05077 0.24534 -0.207 0.836667
e.l3 0.58725 0.16431 3.574 0.000652 ***
prod.l3 0.01054 0.06384 0.165 0.869371
rw.l3 0.03824 0.05365 0.713 0.478450
U.l3 0.34139 0.20530 1.663 0.100938
const -150.68737 61.00889 -2.470 0.016029 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3399 on 68 degrees of freedom
Multiple R-Squared: 0.9988, Adjusted R-squared: 0.9985
F-statistic: 4554 on 12 and 68 DF, p-value: < 2.2e-16
Estimation results for equation prod:
=====================================
prod = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + e.l3 + prod.l3 + rw.l3 + U.l3 + const
Estimate Std. Error t value Pr(>|t|)
e.l1 -0.14880 0.28913 -0.515 0.6085
prod.l1 1.14799 0.11940 9.615 2.65e-14 ***
rw.l1 0.02359 0.10117 0.233 0.8163
U.l1 -0.65814 0.37857 -1.739 0.0866 .
e.l2 -0.18165 0.45083 -0.403 0.6883
prod.l2 -0.19627 0.18069 -1.086 0.2812
rw.l2 -0.20337 0.13337 -1.525 0.1319
U.l2 0.82237 0.47034 1.748 0.0849 .
e.l3 0.57495 0.31499 1.825 0.0723 .
prod.l3 0.04415 0.12239 0.361 0.7194
rw.l3 0.09337 0.10285 0.908 0.3672
U.l3 0.40078 0.39357 1.018 0.3121
const -195.86985 116.95813 -1.675 0.0986 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6515 on 68 degrees of freedom
Multiple R-Squared: 0.98, Adjusted R-squared: 0.9765
F-statistic: 277.5 on 12 and 68 DF, p-value: < 2.2e-16
Estimation results for equation rw:
===================================
rw = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + e.l3 + prod.l3 + rw.l3 + U.l3 + const
Estimate Std. Error t value Pr(>|t|)
e.l1 -4.716e-01 3.373e-01 -1.398 0.167
prod.l1 -6.500e-02 1.393e-01 -0.467 0.642
rw.l1 9.091e-01 1.180e-01 7.702 7.63e-11 ***
U.l1 -7.941e-04 4.417e-01 -0.002 0.999
e.l2 6.667e-01 5.260e-01 1.268 0.209
prod.l2 -2.164e-01 2.108e-01 -1.027 0.308
rw.l2 -1.457e-01 1.556e-01 -0.936 0.353
U.l2 -3.014e-01 5.487e-01 -0.549 0.585
e.l3 -1.289e-01 3.675e-01 -0.351 0.727
prod.l3 2.140e-01 1.428e-01 1.498 0.139
rw.l3 1.902e-01 1.200e-01 1.585 0.118
U.l3 1.506e-01 4.592e-01 0.328 0.744
const -1.167e+01 1.365e+02 -0.086 0.932
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7601 on 68 degrees of freedom
Multiple R-Squared: 0.9989, Adjusted R-squared: 0.9987
F-statistic: 5239 on 12 and 68 DF, p-value: < 2.2e-16
Estimation results for equation U:
==================================
U = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + e.l3 + prod.l3 + rw.l3 + U.l3 + const
Estimate Std. Error t value Pr(>|t|)
e.l1 -0.61773 0.12508 -4.939 5.39e-06 ***
prod.l1 -0.09778 0.05165 -1.893 0.062614 .
rw.l1 0.01455 0.04377 0.332 0.740601
U.l1 0.65976 0.16378 4.028 0.000144 ***
e.l2 0.51811 0.19504 2.656 0.009830 **
prod.l2 0.08799 0.07817 1.126 0.264279
rw.l2 0.06993 0.05770 1.212 0.229700
U.l2 -0.08099 0.20348 -0.398 0.691865
e.l3 -0.03006 0.13627 -0.221 0.826069
prod.l3 -0.01092 0.05295 -0.206 0.837180
rw.l3 -0.03909 0.04450 -0.879 0.382733
U.l3 0.06684 0.17027 0.393 0.695858
const 114.36732 50.59802 2.260 0.027008 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2819 on 68 degrees of freedom
Multiple R-Squared: 0.9736, Adjusted R-squared: 0.969
F-statistic: 209.2 on 12 and 68 DF, p-value: < 2.2e-16
Covariance matrix of residuals:
e prod rw U
e 0.11550 -0.03161 -0.03681 -0.07034
prod -0.03161 0.42449 0.05589 0.01494
rw -0.03681 0.05589 0.57780 0.03660
U -0.07034 0.01494 0.03660 0.07945
Correlation matrix of residuals:
e prod rw U
e 1.0000 -0.14276 -0.1425 -0.73426
prod -0.1428 1.00000 0.1129 0.08136
rw -0.1425 0.11286 1.0000 0.17084
U -0.7343 0.08136 0.1708 1.00000
>
> # prepare a matrix determining the structure ("A-matrix")
> amat <- diag(4)
> amat[2,1] <- NA
> amat[3,1] <- NA
> amat[3,2] <- NA
> amat[4,1] <- NA
> amat[4,2] <- NA
> amat[4,3] <- NA
>
> # estimate the structure matrix (A-matrix) of SVAR
> svar_result_direct <- SVAR(var_result,
+ estmethod = "direct",
+ Amat = amat,
+ Bmat = NULL
+ )
>
> print(svar_result_direct)
SVAR Estimation Results:
========================
Estimated A matrix:
e prod rw U
e 1.0000 0.000000 0.00000 0
prod 0.2214 1.000000 0.00000 0
rw 0.2229 -0.118573 1.00000 0
U 0.5908 0.004521 -0.03034 1
>
> svar_result_scoring <- SVAR(var_result,
+ estmethod = "scoring",
+ Amat = amat,
+ Bmat = NULL,
+ hessian = TRUE,
+ max.iter=1000
+ )
>
> print(svar_result_scoring)
SVAR Estimation Results:
========================
Estimated A matrix:
e prod rw U
e 1.0000 0.00000 0.00000 0
prod 0.2737 1.00000 0.00000 0
rw 0.2885 -0.11019 1.00000 0
U 0.6043 0.01324 -0.02614 1
>
> # get an impulse response function from the VAR model
> irf_var<- irf(var_result,
+ impulse = 'prod',
+ response='rw',
+ ortho = TRUE,
+ n.ahead=9,
+ cumulative = FALSE,
+ ci=0.95, runs=300, seed=1
+ )
>
> # get an impulse response function from the SVAR model (direct)
> irf_svar_direct <- irf(svar_result_direct,
+ impulse = 'prod',
+ response='rw',
+ ortho = TRUE,
+ n.ahead=9,
+ cumulative = FALSE,
+ ci=0.95, runs=300, seed=1
+ )
>
> # get an impulse response function from the SVAR model (scoring)
> irf_svar_scoring <- irf(svar_result_scoring,
+ impulse = 'prod',
+ response='rw',
+ ortho = TRUE,
+ n.ahead=9,
+ cumulative = FALSE,
+ ci=0.95, runs=300, seed=1
+ )
>
> # responses from VAR
> print(irf_var$irf[[1]][,1])
[1] 0.07105517 0.02268411 -0.22425320 -0.28549901 -0.26469213 -0.24747701
[7] -0.23255281 -0.20698327 -0.16623158 -0.11526732
>
> # responses from SVAR (direct)
> print(irf_svar_direct$irf[[1]][,1])
[1] 0.11857308 0.04279212 -0.34463238 -0.43752109 -0.40657794 -0.38464427
[7] -0.36358998 -0.32361842 -0.26004585 -0.18052970
>
> # responses from SVAR (scoring)
> print(irf_svar_scoring$irf[[1]][,1])
[1] 0.11018799 0.03517713 -0.34775809 -0.44273434 -0.41046831 -0.38377215
[7] -0.36062863 -0.32097695 -0.25778173 -0.17874948
>