State-dependent Autoregressive Models with p Lags Properties, Estimation and Forecasting

Abstract

In this paper we consider a class of nonlinear autoregressive models in which
a specific type of dependence structure between the error term and the lagged
values of the state variable is assumed. We show that there exists an equivalent
representation given by a p-th order state-dependent autoregressive (SDAR(p))
model where the error term is independent of the last p lagged values of the
state variable (yt−1, . . . , yt−p) and the autoregressive coefficients are specific
functions of them. We discuss a quasi-maximum likelihood estimator of the
model parameters and we prove its consistency and asymptotic normality. To
test the forecasting ability of the SDAR(p) model, we propose an empirical
application to the quarterly Japan GDP growth rate which is a time series
characterized by a level-increment dependence. A comparative analyses is
conducted taking into consideration some alternative and competitive models
for nonlinear time series such as SETAR and AR-GARCH models.