Diagnostic checking in FARIMA models with uncorrelated but non-independent error terms
| Autor: | Boubacar Maïnassara, Yacouba, Esstafa, Youssef, Saussereau, Bruno |
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| Přispěvatelé: | Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability AMS 2000 subject classifications: Primary 62M10 [STAT.AP]Statistics [stat]/Applications [stat.AP] 62P05 Nonlinear processes Self-normalization Machine Learning (stat.ML) [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] [STAT.OT]Statistics [stat]/Other Statistics [stat.ML] Residual autocorrelations Long-memory processes and phrases: Nonlinear processes Statistics - Applications Statistics - Machine Learning secondary 91B84 62F05 Box-Pierce and Ljung-Box portmanteau tests Applications (stat.AP) Weak FARIMA models 62F03 Statistics Probability and Uncertainty Least squares estimator Residual autocorre- lations |
| Popis: | 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. arXiv admin note: text overlap with arXiv:1902.03000, arXiv:1910.07213 |
| Databáze: | OpenAIRE |
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