Model identification for time series with dependent innovations

Abstract

This paper investigates the impact of dependent but uncorrelated inno- vations (errors) on the traditional autoregressive moving average model (ARMA) order determination schemes such as autocorrelation function (ACF), partial auto- correlation function (PACF), extended autocorrelation function (EACF), and the unit-root test. The ARMA models with iid innovations have been studied exten- sively and are well-posed, but their properties with dependent but uncorrelated innovations are relatively less studied. In the presence of such innovations, we show that the ACF, PACF, and EACF are significantly impacted while the unit- root test is not affected. We also propose a new order determination scheme to address those impacts for analyzing time series with uncorrelated innovations.