Reporting of nonlinear data

[kula]

Hi Tom,
We have a time series data (BIST XKURY), and performing a nonlinearity test (BDS test) to the suitable ARMA model suggested the nonlinearity of the data. Then, we applied Markov switching in the means. As the next step, we obtained GARCH (1,1) model for variance. The application of the BDS test to the standardized residuals of the GARCH model revelaed that the nonlinearity is removed. We would like to learn whether we can report both Markov switching in the means and GARCH analyses. Or, does the GARCH model which removed the nonlinearity make the MS in the means void?
Thanks for you kind interest and reply in advance.

[TomDoan]

I'm confused about what's being applied to what. If you're applying a MS means model to the residuals from an ARMA, then you clearly have the wrong ARMA model, since that would imply fairly substantial residual serial correlation. If you're applying that to the data as an alternative to the ARMA (doesn't sound like a plausible alternative), what is the GARCH model being applied to?

[kula]

Hi Tom,

I am sorry regarding the confusion as there is no ARMA involved in those steps.

Following the nonlinearity test, we applied MS means model to the data to model the mean behaviour . Afterwards, to model the volatility, we obtained GARCH(1,1). We this time applied BDS test to the standardized residuals, and saw that nonlinearity is removed. What appears is that the data is nonlinear in the mean, and that nonlinearity is removed by the GARCH model. If this sequence is plausible, is it possible to report , together with the GARCH model, the MS means model that was nonlinear?

[TomDoan]

Sorry. What are you applying the GARCH to? A MS model doesn't supply residuals that can be passed through to another model.

The BDS test is really a blunt instrument---it tells you almost nothing about what's wrong, just that the series aren't i.i.d. (and there are very few models that predict that anything is i.i.d. any longer) in favor of some form of "clustering" of the failure. For instance

set hetero 1 400 = %if(t<=200,%ran(1.0),%ran(2.0))
@bdstest hetero

will reject i.i.d. very strongly (correctly, as they aren't), even though the departure is a simple change in variance halfway through the sample and nothing more complicated than that.

The @BDINDTESTS procedure (BD=Brockwell and Davis, not Brock and Dechert) does a battery of more pointed tests for departure from i.i.d.

[kula]

Hi Tom,
We express our sincere thanks as through your questions that we realize the steps we should not take. Following the application of MS means to the data, we obtained ARMA model for the sake of getting residuals to apply GARCH to. Now we become aware that it does not make any sense to apply ARMA (and naturally GARCH) following the MS means model. We think that if we are to use MS means model, we can not proceed beyond it . We must stop there, mustn't we?
Again many thanks for your kind interest and replies.

[TomDoan]

You can combine an ARMA mean model with a GARCH error process (just through the GARCH instruction). Note that it's quite possible that, if there is a GARCH error process, an ARMA model estimated first assuming homoscedastic errors might choose a model that is more complicated than the combined model (because the heteroscedastic errors can sometimes create spurious autocorrelations).

You can also combine a MS mean model with a fixed GARCH error process, but that has all the technical complications of the full MS-GARCH model (that is, the likelihood depending upon all previous regimes).