Beginner problems in DCC-GARCH

[juustone]

Sorry, table 10 was just an example what I was advised to likewise calculate… Does not concern directly my work.

Your data for Russia and Georgia show almost no relationship between the two---the periods of high volatility are basically disjoint.

So the null hypothesis (there´s no autocorrelation in the series) remains?!

[TomDoan]

Sorry, table 10 was just an example what I was advised to likewise calculate… Does not concern directly my work.

As I believe I said earlier, that doesn't really help---all four tests in Table 10 are labeled the same, so without a footnote describing what each is actually testing, I really can't help.

Your data for Russia and Georgia show almost no relationship between the two---the periods of high volatility are basically disjoint.

So the null hypothesis (there´s no autocorrelation in the series) remains?!

There doesn't seem to be serial correlation in the mean. The diagnostics that are showing problems are the ones testing more complex forms of dependence in the Z2 series. The Georgia data seems to show a pretty strong structural break in the variance around observation 1500---prior to that, a single GARCH model seems to fit it fairly well, but not if you run through the full data set.

[juustone]

Thanks for all your help dear Tom!

I have final question that I´ve been struggling with.

How I can make (separate) graphs of garch volatility and dynamic conditional correlations?

In garch volatility graph I want to present the heteroskedastic variance time series for each country, by weights given by the univariate garch coefficients.
For this matter I used the following code:

Code: Select all

garch(p=1,q=1,resids=u,hseries=h) / lrussia
GRAPH(STYLE=LINE) 1
# H

Is this right?

For pairwise I want to graph correlation between ith and jth term (Pijt, Bollerslev). I know that Pijt is dependent on respective the Univar. Garch values and dcc weight at the moment t, but can you help me how to make graph out of this? GARCHMV.RPF -example?!

From the code garch(p=1,q=1,mv=dcc,variances=koutmos,hmatrices=hh) / $
lven leur - I get the error message: ## SX11. Identifier KOUTMOS is Not Recognizable. Incorrect Option Field or Parameter Order?
>>>>,variances=koutmos,<<<<

and from set lvenleur = %cvtocorr(hh(t))(1,1) - ## MAT15. Subscripts Too Large or Non-Positive
Error was evaluating entry 2121


Thanks again!

[juustone]

I would be really grateful if someone could help me on this matter.

Since I managed to get dcc-graphs, I´m deeply in need of garch volatility (variance) graphs.

I tried to use following code for it:

garch(p=1,q=1,resids=u,hseries=h) / lrussia
GRAPH(STYLE=LINE) 1
# H

But the results seems to be quite weird. How to measure it correctly ?

Thanks!

[TomDoan]

Why do you find that weird? That looks like a GARCH variance estimate for a series with one major volatility episode. You might want to graph this in standard deviation form, which will at least compress the scale a bit.

[juustone]

Thank you Tom!

It was the huge scale and lack of effects of 2014 crises that made me hesitate.

How do I graph it in standard dev. form?

[TomDoan]

set stddev = sqrt(h)
GRAPH(STYLE=LINE) 1
# stddev

[menykeko]

Dear Tom,
Please help clarify the difference between DCC(1) and DCC (2) in a DCC model.

Thanks

[TomDoan]

These have been renamed to DCC(A) and DCC(B). DCC(1) is the "ARCH" and DCC(2) the "GARCH" coefficient in the DCC recursion.

[koskelo]

Hi dear Tom,

I have a question related to above questions & answer.

I have estimated condition correlation of stocks and bonds with pairwise regression with DCC-model and got that DCC-arch-effect is statistically insignificant while DCC-garch-effect was strongly significant. What is explanation of this? In all examples both of them are significant, so I could not find the result.

Other question: what is the explanation of insignificant variance?

Thanks for answers!

BR

Simo Koskelo

[TomDoan]

How much data do you have?

The B in the DCC model is almost always much larger than the A---A's are typically .10 or smaller (often *much* smaller). If A is small relative to its standard error, it obviously doesn't mean that A can be negative since that really won't work, but it means that its value isn't well determined. If the data can be fit reasonably well by a simpler CC model, the A should be quite small.

[koskelo]

Thanks for your answer!


I have (daily) data including over 2000 observations, so should be enough.

The A is small (0.013) but with t-stat of 1.1 which does make it as insignificant (should be around 2), while B´s 0.95 and 16.2 (significant). The question was considering on parameters significance, which still confuses me, since in empirical literature there´s no such situation. CC model works fine.

So still, if you could help and conclude how to read my results; what´s the meaning when A is insig. and B´s significant, is there correlation?

[TomDoan]

Thanks for your answer!


I have (daily) data including over 2000 observations, so should be enough.

The A is small (0.013) but with t-stat of 1.1 which does make it as insignificant (should be around 2), while B´s 0.95 and 16.2 (significant). The question was considering on parameters significance, which still confuses me, since in empirical literature there´s no such situation. CC model works fine.

Remember that the empirical literature has a strong selection bias---if the results are hard to interpret, they don't get published.

So still, if you could help and conclude how to read my results; what´s the meaning when A is insig. and B´s significant, is there correlation?

The closer B is to 1, the smaller A has to be since their sum has to be less than 1. You can't interpret "t-statistics" the typical way for a parameter that has a lower bound if you're near the lower bound---the confidence interval will have to skew somewhat to the right (perhaps something like .005 to .0400 for 95%). The point about CC however, is that if CC is adequate, theoretically you could have B=1 and A=0 (if Q0 hit the right value). If Q0 isn't quite right, you'll need some period to period adjustment (A) but not much. B will (effectively) always be significant---even if a DCC model is completely wrong, there's almost no chance that you will get a B value that's small.

As an example, I generated a couple of correlated Normal series (no GARCH properties) and estimated a DCC model with them. The results are a bit more extreme than yours, but you can see that the A is (quite) insignificant.

Code: Select all

MV-DCC GARCH  - Estimation by BFGS
Convergence in    67 Iterations. Final criterion was  0.0000065 <=  0.0000100
Usable Observations                      1000
Log Likelihood                     -2867.8488

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Mean(X1)                      0.039939839  0.030003658      1.33117  0.18313452
2.  Mean(X2)                     -0.001483742  0.035434757     -0.04187  0.96660033

3.  C(1)                          1.677464382  1.033873554      1.62250  0.10469539
4.  C(2)                          1.280130700  0.728487335      1.75724  0.07887606
5.  A(1)                          0.014758464  0.026570148      0.55545  0.57858496
6.  A(2)                         -0.037702776  0.023810455     -1.58345  0.11331787
7.  B(1)                         -0.567003403  0.933373781     -0.60748  0.54353419
8.  B(2)                          0.094643316  0.537769241      0.17599  0.86029989
9.  DCC(A)                        0.005592756  0.013670311      0.40912  0.68245382
10. DCC(B)                        0.853276718  0.200866900      4.24797  0.00002157

[koskelo]

Thank you Tom for an amazing answer!


Sorry to still continue on this matter, but I´d like to make this clear once and for all; at which point I can say that the two series are conditionally correlated? I mean, I understand the part of t-sats in this matter now, but if B´s "always" close to 1 and the series are seemingly correlated, what is the explanation literally of small (insignificant) A ? Since if B´s generally 0.9, will it make the series always correlated?

Is it just that the short-run persistence of shocks (ARCH) to return i is not as remarkable as the contribution of shocks to return i in long-run (GARCH) ?

[TomDoan]

The "alternative" to DCC isn't no correlation; it's constant correlation. Unfortunately, they don't formally nest, so there is no simple way to test whether you need DCC rather than just CC---in practice, the only way to approximate CC in the DCC framework is with a small A and fairly large B. If you graph the correlations out of your DCC model, you'll probably find that they don't move very much, maybe a range of .1 or so. In the example I did above, the CC estimate was .52 and the DCC estimates ran from roughly .50 to .54. As with standard GARCH models, A+B is a measure of persistence, and A is a measure of short-term movements so a small A will mean very small slow changes. If you look at the graph of the correlations at the end of https://estima.com/ratshelp/index.html?garchmvrpf.html, you'll see that those are moving quite rapidly in cases. And that's with an A of roughly .05.