Detecting Conditional Independence for Modeling Non-Gaussian Time Series

Entropy based dependence measures are used as an alternative to correlation for determining the lag dependency of time series models. In this study, we explore the properties of partial autoinformation function (PAIF) to identify the lag dependency of non-linear and non-Gaussian autoregressive models. Non-parametric estimators of autoinformation function (AIF) and PAIF are obtained and then studied its asymptotic properties. A bootstrap algorithm is developed for testing significance of PAIF at different lags. Finally, we present numerical study to illustrate the use of AIF and PAIF for identifying the order of AR processes.