Model Identification for Time Series with Dependent Innovations

This paper investigates the impact of dependent but uncorrelated innovations (errors) on the traditional autoregressive moving average model (ARMA) order determination schemes such as autocorrelation function (ACF), partial autocorrelation function (PACF), extended autocorrelation function (EACF) and unit-root test. The ARMA models with iid innovations have been studied extensively 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 unitroot test is not affected. We also propose a new order determination scheme to address those impacts for analyzing time series with uncorrelated innovations.