Thanks for your reply. I found from Elder’s dissertation, which built the same model as in the 2010 paper, that he conducted the LM test for omitted ARCH. First all he estimated a homoscedastic VAR, and then find the residual vector u_t = B^{-1}\epsilon_t. The components of u_t ‘s are tested separately by LM ARCH test. Though this procedure is not emphasized in the 2010 paper, I think it is necessary in order to make the argument rigorous.
1. He does not consider the ARCH test for u_t vector as a whole but consider the components separately. Do these two tests generally provide similar results?
2. Should the ARCH test on the (univariate) AR model generally provide similar results to the above two tests? I am thinking of building a bivariate model following their 2010 paper, and now I just have one of the data series. The other series is relatively harder to obtain. I wonder if the ARCH test on the univariate AR model could provide some guideline on the adequacy of applying their model.
done immediately after the original VAR is estimated. This transforms the OLS residuals (u) to the structural residuals (vresids) and tests for ARCH on each of the structural residuals. As written, this is specific to the Cholesky factor structural model used in the oil-GDP paper. With a different structural model, you would get a different factor matrix for the covariance matrix %SIGMA.
1. Now I somehow understand why Elder 1995 consider the univariate tests instead of the multivariate test. Let us consider the 2010 paper case with oil (exogenous) and GDP. Since the impact of oil volatility on GDP is interested, one might need to conduct the ARCH test of oil residual in the bivariate VAR framework in order to justify the analysis of oil vol on GDP. The results of ARCH test on the bivariate model as a whole or on GDP are relatively uninterested. (Elder 2010 compares the BIC to justify the modeling.) Is it right?
No. The point is that the "structural" part of the VAR is supposed to create structural residuals which are uncorrelated contemporaneously, and individually and jointly uncorrelated across time. The structural residuals are modeled as separate univariate GARCH processes---this is testing whether there actually is a "GARCH" effect to model.
Thank you very much for your reply. I try to fit the model to a bivariate dateset, but the model does not seem to converge.
1.
Is there anything I need to change in order to let it run, say, the starting guess of iterations? When I run the ARCH tests on the data, I find the ARCH effect insignificant at 5% level. I just want to see the model interpret such a dataset.
2.
Is it rigorous to choose between homoscedastic VAR and VAR-GARCH-M purely based on SIC (whichever has a lower SIC)?
Thank you very much for your reply. I try to fit the model to a bivariate dateset, but the model does not seem to converge.
1.
Is there anything I need to change in order to let it run, say, the starting guess of iterations? When I run the ARCH tests on the data, I find the ARCH effect insignificant at 5% level. I just want to see the model interpret such a dataset.
2.
Is it rigorous to choose between homoscedastic VAR and VAR-GARCH-M purely based on SIC (whichever has a lower SIC)?
You would probably benefit from rescaling your second variable, which is many orders of magnitude different from the first. That would bring the coefficients down to similar magnitudes.
Are your data series at all similar to the ones in Elder and Serletis? This was not a model designed to apply to any two variables, but was specifically for oil prices and a macroeconomic aggregate. Comparing with SIC is fine, though it looks rather clear that the GARCH part doesn't matter. You can't do a nested hypothesis test since if the GARCH isn't present, the M term is unidentified.
Thanks for your reply. I believe that my data is ok. The basic thing I’d like to do is to investigate the impact of the conditional volatility of the first (relatively exogenous) variable on the second variable.
Following your advice, I try to rescale the data and obtain the convergence. The homoscedastic VAR gives me lag =1, so I modify as follows
* compute nlags=4
compute nlags=1
However, I don’t see the complete results but just see “## MAT13. Store into Out-of-Range Matrix or Series Element”.
It works for nlags = 4, 5 but not for 1, 2, 3.
BTW, How can we determine the lag order of the GARCH? How could we modify the program for that lag order? Sorry that I am new to RATS.
Thanks,
Miao
## IO30. There is no series DATE on the file
VAR/System - Estimation by Least Squares
Monthly Data From 1998:10 To 2013:08
Usable Observations 179
Dependent Variable DLFX
Mean of Dependent Variable -0.103184166
Std Error of Dependent Variable 1.216209782
Standard Error of Estimate 1.054604228
Sum of Squared Residuals 195.74545379
Durbin-Watson Statistic 1.6679
Dependent Variable FLOW
Mean of Dependent Variable 8.615027933
Std Error of Dependent Variable 25.456918618
Standard Error of Estimate 23.412466054
Sum of Squared Residuals 96473.267741
Durbin-Watson Statistic 1.9969
Everything works well with the latest file. I have one question regarding the memory used in RATS. When I let a rpf file run first after I opened RATS, I obtained some results. Then I ran other programs and came back to run the file that ran first, but the results were different from the results obtained in the first run. Is there anything I need to do to clear the memory (instead of closing RATS and opening it again)?
Everything works well with the latest file. I have one question regarding the memory used in RATS. When I let a rpf file run first after I opened RATS, I obtained some results. Then I ran other programs and came back to run the file that ran first, but the results were different from the results obtained in the first run. Is there anything I need to do to clear the memory (instead of closing RATS and opening it again)?
Thanks!
Miao
Use the menu operation File-Clear Memory, or the toolbar icon with the hand and the yellow rag.
Thanks for your reply. I change the dataset and run the codes, but no convergence is obtained for nlags=1. However, I do have convergence for nlags=2. Is there anything I can modify in order to gain convergence for nlags=1?
* The nlags is modified as follows
* compute nlags=4
compute nlags=1
Have you looked at your oil price series carefully? It not only isn't showing GARCH behavior (which is necessary for the "M" effect to be identified), but it's getting a negative coefficient on the lagged squared residual, which could make the estimation rather unstable.
Hi Tom
I wish to extend the bivariate Elder-Serletis(2010) VAR-GARCH-M model in a five variable (or at least three variables) setup. Is it possible? How could I modify the codes for it? Thank you so much.
KI
That depends upon what features of the model you want. It's relatively straightforward if you want to allow the "M" effect only for the first variable, and in square root form. If you want to allow for more general M effects, the changes are more extensive.
Hi Tom
Suppose I have 3 variables in the system--A,B, and C. I allow the "M" effect only for B variable, and in square root form. So, I want to see how uncertainty of B affects A. How the changes can be incorporated in the code? Thank you so much.
KI
Is the "structural" part of the Elder-Serletis model important? If you're just interested in the M effect of B on A, you can handle that using the methods described on page UG-301 of the RATS v8 User's Guide. If you want the SVAR model, is it the variance of the 2nd structural shock or the variance of variable B that you want? The two aren't the same.
I have questions about the variables. Could you check if I understand them correctly?
1.
GDPTOPLUS ：Response of GDP growth to Positive oil shock
GDPTOMINUS : Response of GDP growth to Negative oil shock
GDPTOPLUSNOM : Response of GDP growth to Positive oil shock without M effect
GDPTOMINUSNOM : Response of GDP growth to Negative oil shock without M effect
UPPER(1) , LOWER(1)：Confidence interval for “GDPTOPLUS”
UPPER(2), LOWER(2) : Confidence interval for “GDPTOMINUS”
Two figures show the confidence bands for GDPTOPLUS and GDPTOMINUS,
RESP(1) , RESP(2)：What are they? Are they the medians (50th percentiles) of the confidence bands?
2.
By “Without M effect”, does it mean that the IRF is computed from exactly the same estimated coefficients of M-model, but the coefficient of H_{1,1} terms in the mean equation is set to zero