Re: [Gretl-users] GARCH

On Sun, 25 Dec 2005, sudip mukherjee wrote: What do the data series look like? An important point about the GARCH model is that the assumed error process handles _only_ conditional heteroskedasticity (a non-constant error variance, varying in an autoregressive manner). If the series in question has a definite trend, or is autoregressive in its level, then a simple GARCH model will not be appropriate and the likely symptom is non-convergence of the estimation procedure. It may be possible to overcome this problem by including suitable independent variables in the GARCH model (e.g. variables that have the effect of "taking out" the trend in the dependent variable). Alternatively, it may be necessary to use some transformation of the variable of interest, such as percentage change or log-difference. As a simple example, look at the data file djclose.gdt (supplied with gretl). This contains daily closing values of the Dow Jones index. If you try a simple GARCH model for djclose, the procedure will not converge. This is, I would say, the "correct" result, since the Dow has a strong upward trend and cannot reasonably be represented as fluctuations of varying amplitude around a constant mean. But if you form the log-difference of the dclose variable and run a GARCH, you get sensible estimates. I can't say with perfect confidence that gretl fails to produce GARCH estimates _only_ when the GARCH model is clearly inappropriate. Nonetheless, I think it's quite likely that non-convergence in gretl is an indication of a problem with the model. If you find a data series for which gretl will not produce GARCH estimates, but (say) R succeeds in producing sensible estimates, please let us know and we'll take a look at the case. Allin Cottrell