Francq, Christian and Zakoian, Jean-Michel
(2009):
*Bartlett's formula for a general class of non linear processes.*

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## Abstract

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum of two terms. The first term corresponds to the standard Bartlett's formula for linear processes, involving only the autocorrelation function of the observed process. The second term, which is specific to nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of the linear innovation process and the autocorrelation function of its square. This formula is obtained under a symmetry assumption on the linear innovation process. An application to GARCH models is proposed.

Item Type: | MPRA Paper |
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Original Title: | Bartlett's formula for a general class of non linear processes |

Language: | English |

Keywords: | Bartlett's formula, nonlinear time series model, sample autocorrelation, GARCH model, weak white noise |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes |

Item ID: | 13224 |

Depositing User: | Pr. Jean-Michel Zakoian |

Date Deposited: | 07 Feb 2009 05:38 |

Last Modified: | 27 Sep 2019 00:43 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/13224 |