Panel GARCH? (Cermeno and Grier, 2006)

[TomDoan]

As mentioned above, I am looking for unrestricted coefficient of variance equations. can you find way to make variance equations coefficients vary?
Don't worry about mean equation!

The unrestricted version is just a DVECH (the default for GARCH).

[behnam]

Hi,
i am using panel garch - DVECH similar to Cermeno and Grier,2006 but i don't know why it isn't correct . because garch coefficients sums are more than one(i.e delta+ gamma>1, and vcs(3,2) is negative).i read all the posts in this subject but still can't understand why it should be like this since all of variables have arch effects and null hypothesis of archtest rejects. please help me and give me some advise.
thanks a lot,

real exchange rate.xlsx

(28.69 KiB) Downloaded 1637 times

AR(1).RPF

(2.81 KiB) Downloaded 1908 times

results.RPF

(1.94 KiB) Downloaded 1883 times

[TomDoan]

Hi,
i am using panel garch - DVECH similar to Cermeno and Grier,2006 but i don't know why it isn't correct . because garch coefficients sums are more than one(i.e delta+ gamma>1, and vcs(3,2) is negative).i read all the posts in this subject but still can't understand why it should be like this since all of variables have arch effects and null hypothesis of archtest rejects. please help me and give me some advise.
thanks a lot,

It's not clear that that's a good choice of model for your data---the dynamics for the four are very different, so forcing a common set of GARCH coefficients doesn't seem to be wise. Regarding the results, other than "BAN" (Bangladesh?), none of the series has a stable univariate GARCH representation. IND (India?) and MAL (Malaysia?) both have one single incident of extremely high variance which can only work with a GARCH model if the GARCH recursion coefficients sum to greater than one. IRI (Iran?) has just two dominant episodes. IND also has a long stretch at the beginning with almost no movement (at least compared to the high-variance episode)---if it was largely pegged during that period, it won't be fit by a GARCH process.

[behnam]

Hi tom,
Thanks alot for your help.
so you mean that just bangladesh will be fit by garch process during that period, am i right sir?
there isn't anyway for using garch model especially for iran like changing time period(don't worry about garch form)?
what about using this constraint : vcs.ge.0 and lambda+gamma>=1 ... do you think it is a good way and results are valid ?in this circumstances delta+gamma is exactly one. i attach results with this constraint.

RER.RPF

(1.94 KiB) Downloaded 1920 times

[TomDoan]

The only series for which it seems to be possible to fit with a single GARCH model over the sample range is Bangladesh. The others seem to have some form of structural break in the variance process.

BTW, there is nothing wrong with an off-diagonal coefficient being negative. These series are not very closely related so the correlation would likely be somewhere around zero anyway (either slightly positive or slightly negative).

[behnam]

test(title="Wald Test for vbs and vas")
# 2 3
# vbs(1,1)=vbs(2,2)=vbs(3,3)=vbs(4,4) vbs(2,1)=vbs(3,1)=vbs(3,2)=vbs(4,1)=vbs(4,2)=vbs(4,3) vas(1,1)=vas(2,2)=vas(3,3)=vas(4,4) vas(2,1)=vas(3,1)=vas(3,2)=vas(4,1)=vas(4,2)=vas(4,3)
compute funcunr=%funcval
nonlin(parmset=garchparms) vbs(1,1)=vbs(2,2)=vbs(3,3)=vbs(4,4) vbs(2,1)=vbs(3,1)=vbs(3,2)=vbs(4,1)=vbs(4,2)=vbs(4,3) vas(1,1)=vas(2,2)=vas(3,3)=vas(4,4) vas(2,1)=vas(3,1)=vas(3,2)=vas(4,1)=vas(4,2)=vas(4,3)
frml hf = vcs+vbs.*h{1}+vas.*uu{1}
maximize(parmset=meanparms+garchparms,pmethod=simplex,piters=10,method=bfgs,iters=400) logl gstart gend
compute funcres=%funcval
cdf(title="Likelihood Ratio Test") chisqr -2*(funcres-funcunr)

Hi tom,
i want to test likelihood ratio for arch and garch coefficients and use it for tests of equality between coefficients(vbs and vas)but i am not sure whether it is correct
and about degree of freedom is it right?
thanks in alot

[TomDoan]

The TEST instruction is completely wrong---a Wald test would be done with a RESTRICT instruction and it would be a very complicated instruction.

In your PARMSET, you just have the equated coefficients but never list the free ones. You need to tack VAS(4,4) VBS(4,4) VAS(4,3) and VBS(4,3) onto the end.

You didn't include the degrees of freedom on your CDF instruction. But just count the number of = in your PARMSET description.

[FaeK]

Hi Tom,

Hope that all is well. I wanted to include exogenous variables in the variance equation from the code posted above for the panel garch. Is this possible? Any insights are much appreciated.

Many thanks,
Faek

[TomDoan]

It's certainly possible. Do you know what adjustments you want to make to the formulas governing the variances and covariances above?

[FaeK]

Many thanks. For example, to see the impact of an exogenous variable, denoted by X, on the conditional variances of another variable (let's say Y) as bellow:


σ{i,t}² =α{i}+δσ{i,t-1}²+γu{i,t-1}² +w*X(i,t-1) for i=1,...N
σ{ij,t}² =η{ij}+λσ{ij,t-1}+ρu{i,t-1}u{j,t-1} for i≠j

Many thanks for everything,
Faek

[TomDoan]

As it says in the comments:

* The initial few lines of this set the estimation range, which needs to
* be done explicitly, and the number of variables.
*
compute gstart=2,gend=6237
compute n=3

If you have questions about the various data types, you should look at Chapter 1 of the User's Guide. VECTORS (of various other types) are one-dimensional organizers of information, here in all cases, one per dependent variable. For instance, the VEC[VEC] BMEAN(N) is a VECTOR of coefficient VECTORS for the 3 (N=3) variables. Writing it that way allows both the number of variables and the composition of the mean equations to change without having to rewrite the entire calculation.

[soha]

Hi,

Many thanks for your reply.

Can it be applied for more than 3 series please, around 12 series? If yes, I need to change n=3 to n=12, am I wright please?

Regards
Soha

[TomDoan]

Change the 3 to 12 and increase those set instructions to define y(1) to y(12).

Note: this assumes the 12 series have similar enough dynamics to allow a highly restricted model to describe all of them. If they don't, then you need to use something like a CC or DCC model instead.

compute n=3
dec vect[series] y(n) u(n)
dec vect[frml] resid(n)
set y(1) = xjpn
set y(2) = xfra
set y(3) = xsui

[soha]

Dear TomDoan,

Many thanks for your reply.

Is it possible to study the effect of different independent variables please?

Regards
Soha

[TomDoan]

Yes. However, you would need to decide how you want to include all those effects.