Diagnostic checking in FARIMA models with uncorrelated but non-independent error terms

Abstract

This work considers the problem of modified Portmanteau tests for testing the adequacy of FARIMA models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak FARIMA). We first study the joint distribution of the least squares estimator and the noise empirical autocovariances. We then derive the asymptotic distribution of residual empirical autocovariances and autocorrelations. We deduce the asymptotic distribution of the Ljung-Box (or Box-Pierce) modified Portmanteau statistics for weak FARIMA models. We also propose another method based on a self-normalization approach to test the adequacy of FARIMA models. Finally some simulation studies are presented to corroborate our theoretical work. An application to the Standard & Poor’s 500 and Nikkei returns also illustrates the practical relevance of our theoretical results.