I'm exploring the issue of modelling non-linear time series. I have read in several articles that a correct strategy is often to start by fitting a linear model (for example a simple Autoregressive model) and if it is not satisfactory, then try to fit a TAR, SETAR or Markov Switching Model,.... I think this is a classical approach.

In the papers that I have read, in order to detect deviation from linearity most authors apply several test over the residuals of the simple first estimated AR model (for example RESET test, BDS test, Mc. Leod test are common in this context). Then after reject the Null in these test, they proceed with the non-linear model.

My question is: before to try with my real series, playing with some series in Gretl, I have seen that after estimating an AR model or ARIMA model with the options built in Gretl-GUI, the "test" post-estimation option only allows to test for Normality or ARCH (I think this is Mc Leod test), but other options as RESET or Non-linearity are not activated.

Only after estimating a model via OLS menu with the dependent variable and its lags -that is not the same of estimating the AR(1) model, so the constant change as usual- these post-estimation options are allowed.(I think this kind of models is the preferred process in most papers)

I think this Gretl behavior is due that in an ARIMA context you can add AR or MA terms in your model until to get residuals to be white noise. So, no more steps are needed.

However, I have checked that in Eviews the options RESET, etc. are (like not in Gretl) allowed after estimating both, the AR(1) model and the equation with the lagged dependent variable.

Y C AR(1)  AR residual term model

Y C Y(-1) model with the lagged endogenous variable

So, my curiosity and second question: Why this difference among Gretl and Eviews, the disallowed options in Gretl are for some special considerations?

With the specification of lagged dependent variable there is not poblem because the options are allowed in both software. But, if I want to perform this kind of analysis in Gretl, with an AR model, which is the correct form to proceed?. Save the residuals of my estimated AR model and export them to R or other software to perform the BDS or RESET test as usual in literature?

Thanks in advance.

José Perles

University of Alicante

Spain