Modelling time series with conditional heteroscedasticity

Abstract

Over the last fifteen years, the interest in nonlinear time series models has been steadily increasing. Univariate time-series models may not work sucessfully it theyrestrict only to linear functions of past observations. The same past may well contain useful information for the present and future if the dependence is nonlinear. Among nonlinear functions we shall consider the simplest of the family of heteroscedastic models - the autoregressive conditional heteroscedastic or ARCH model that is based on the conditional variance structure. This model was first applied by Engle (1982) to estimate should variance of U.K. Inflation. The aim of this article is to find out whether ARCH models should also be applied to quarterly time series of the Portuguese Imports for the period 1976-2004.