Open Access
November 2013 Long-range dependent time series specification
Jiti Gao, Qiying Wang, Jiying Yin
Bernoulli 19(5A): 1714-1749 (November 2013). DOI: 10.3150/12-BEJ427


In this paper we propose using a nonparametric model specification test for parametric time series with long-range dependence (LRD). To establish asymptotic distributions of the proposed test statistic, we develop new central limit theorems for certain weighted quadratic forms of stationary time series with LRD. To implement our proposed test in practice, we develop a computer-intensive parametric bootstrap simulation procedure for finding simulated critical values. As a result, our finite-sample studies demonstrate that both the proposed theory and the simulation procedure work well, and that the proposed test has little size distortion and reasonable power.


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Jiti Gao. Qiying Wang. Jiying Yin. "Long-range dependent time series specification." Bernoulli 19 (5A) 1714 - 1749, November 2013.


Published: November 2013
First available in Project Euclid: 5 November 2013

zbMATH: 1280.62105
MathSciNet: MR3129031
Digital Object Identifier: 10.3150/12-BEJ427

Keywords: central limit theorem , Gaussian process , linear process , long-range dependence , parametric time series regression , specification testing

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

Vol.19 • No. 5A • November 2013
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