Hi, I am trying to measure the volatility spillover effect from S&P500 to FTSE100 using bivariate BEKK-GARCH model. My code inp and outputs are forwarded to the email. The volatility spillover effect is measured as the sum of the off-diagonal coefficients of the variance equation matrices A and B, which is E[1,2] = |A[1,2]| + |B[1,2]|. Next, I need do the Wald test to test the off-diagonal coefficients? (whether they are significant or not; meaning there is volatility spillover from sp500 to ftse or not). I do not know how to write the codes for the Wald test to following my codes (I am not good at coding that much, i usually use drop-down menu but i see it is not available in my case). Does anyone know how to write Wald test codes to following below codes? I am not familiar with coding stuff and bundle context that's why I am asking here. My codes are:
set verbose offlist returns = spx_return ftse_returnscalar VAR_lags = 1list VAR_exog = constbundle Modelbekk = BEKK_setup(returns, VAR_lags, VAR_exog)BEKK_estimate(&Modelbekk, 10)BEKK_printout(&Modelbekk)
code_bekk.inp
Description: Binary data
gretl version 2021a
Current session: 2021-02-01 09:07
? set verbose off
Starting values
Pi:
0.000397 0.000064
-0.050955 0.133430
0.048358 0.002170
C:
0.000467 0.000000
0.000084 0.000448
A:
0.400000 0.000000
0.000000 0.400000
B:
0.900000 0.000000
0.000000 0.900000
10: Criterion 16627.1439457 (step 6.4e-05, norm 6.96e+00)
20: Criterion 16639.9354776 (step 0.2, norm 6.70e+00)
30: Criterion 16652.2439366 (step 1, norm 3.15e+00)
40: Criterion 16653.4840924 (step 2.048e-08, norm 1.68e+00)
50: Criterion 16653.5545298 (step 0.008, norm 2.29e+00)
60: Criterion 16653.7788126 (step 0.2, norm 1.23e+00)
70: Criterion 16653.8324826 (step 1, norm 5.57e-01)
80: Criterion 16653.8374905 (step 0.0016, norm 7.16e-01)
90: Criterion 16653.8380972 (step 0.2, norm 2.49e-01)
--- FINAL VALUES:
Criterion 16653.8381579 (step 8.192e-10, norm 3.64e-02)
Function evaluations: 466
Evaluations of gradient: 94
BEKK Model --- vcvtype = QMLE (Sandwich)
Conditional mean equations:
Equation 1: spx_return
coefficient std. error z p-value
--------------------------------------------------------------
const 0.000712991 0.000165512 4.308 1.65e-05 ***
spx_return_1 -0.0627606 0.0236555 -2.653 0.0080 ***
ftse_return_1 0.0369226 0.0212449 1.738 0.0822 *
Equation 2: ftse_return
coefficient std. error z p-value
--------------------------------------------------------------
const 0.000331985 0.000161217 2.059 0.0395 **
spx_return_1 0.115157 0.0253740 4.538 5.67e-06 ***
ftse_return_1 -0.0237711 0.0233471 -1.018 0.3086
Conditional variance parameters:
coefficient std. error z p-value
------------------------------------------------------------
C[ 1, 1] 0.00112042 0.000408521 2.743 0.0061 ***
C[ 2, 1] -0.00352084 0.000356764 -9.869 5.68e-23 ***
C[ 1, 2] 0.00000 0.00000 NA NA
C[ 2, 2] 4.75878e-09 1.36761e-07 0.03480 0.9722
coefficient std. error z p-value
-------------------------------------------------------
A[ 1, 1] 0.363313 0.0406707 8.933 4.14e-19 ***
A[ 2, 1] -0.260204 0.0814664 -3.194 0.0014 ***
A[ 1, 2] 0.119805 0.0381856 3.137 0.0017 ***
A[ 2, 2] 0.318363 0.0496000 6.419 1.38e-10 ***
coefficient std. error z p-value
-------------------------------------------------------
B[ 1, 1] 0.925578 0.0125063 74.01 0.0000 ***
B[ 2, 1] 0.249773 0.0701406 3.561 0.0004 ***
B[ 1, 2] -0.137171 0.0754339 -1.818 0.0690 *
B[ 2, 2] 0.754724 0.0368823 20.46 4.60e-93 ***
Sample size = 2451
Average loglikelihood = 6.79471
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