## Bernoulli

• Bernoulli
• Volume 19, Number 5A (2013), 1714-1749.

### Long-range dependent time series specification

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 19, Number 5A (2013), 1714-1749.

Dates
First available in Project Euclid: 5 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1383661200

Digital Object Identifier
doi:10.3150/12-BEJ427

Mathematical Reviews number (MathSciNet)
MR3129031

Zentralblatt MATH identifier
1280.62105

#### Citation

Gao, Jiti; Wang, Qiying; Yin, Jiying. Long-range dependent time series specification. Bernoulli 19 (2013), no. 5A, 1714--1749. doi:10.3150/12-BEJ427. https://projecteuclid.org/euclid.bj/1383661200

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