A bootstrapped spectral test for adequacy in weak ARMA models

Zhu, Ke and Li, Wai-Keung (2013): A bootstrapped spectral test for adequacy in weak ARMA models.

Abstract

This paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained by using the Hillbert space approach. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of order $n^{-1/2}$. Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S\&P 500 stock index.

• Item Type: MPRA Paper
• Language: English
• Keywords: Block-wise random weighting method; Diagnostic checking; Least squares estimation; Spectral test; Weak ARMA models; Wild bootstrap.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General

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