Diagnostic checking in FARIMA models with uncorrelated but non-independent error terms
This work addresses diagnostic testing for time series models in econometrics and finance, but it is incremental as it extends existing methods to weak FARIMA models.
The authors tackled the problem of diagnostic checking in FARIMA models with uncorrelated but non-independent error terms, deriving asymptotic distributions for modified portmanteau tests and proposing a self-normalization method, with simulation studies and applications to financial returns validating their theoretical results.
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 asymp-totic 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 illustrate the practical relevance of our theoretical results. AMS 2000 subject classifications: Primary 62M10, 62F03, 62F05; secondary 91B84, 62P05.