When Is a Time Series I(0)? Evaluating the Memory Properties of Nonlinear Dynamic Models

The paper proposes that a useful concept of I(0) is deÞned by requiring the time series to satisfy a functional central limit theorem, and considers sufficient conditions for this property to hold in a variety of time series models. First, a new result is given for semiparametric linear processes, whose conditions are shown to be close to necessary. Second, a range of popular nonlinear models is considered. The key concept employed is that of near-epoch dependence on an independent process, a condition that can be checked by straightforward manipulations in the cases considered. The rates of memory decay are derived as simple functions of model parameters. General formulae for these rates are derived for the ARMA, bilinear and GARCH models, and leading examples of the TAR class. A simulation approach is also demonstrated, applicable to cases that are analytically intractable.