A bootstrapped spectral test for adequacy in weak ARMA models

Ke ZHU, Wai Keung LI

Research output: Contribution to journalArticlespeer-review

20 Citations (Scopus)


This paper proposes a Cramér–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. 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. Copyright © 2015 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)113-130
JournalJournal of Econometrics
Issue number1
Early online dateFeb 2015
Publication statusPublished - Jul 2015


Zhu, K., & Li, W. K. (2015). A bootstrapped spectral test for adequacy in weak ARMA models. Journal of Econometrics, 187(1), 113-130. doi: 10.1016/j.jeconom.2015.02.005


  • Block-wise random weighting method
  • Diagnostic checking
  • Least squares estimation
  • Spectral test
  • Weak ARMA models
  • Wild bootstrap


Dive into the research topics of 'A bootstrapped spectral test for adequacy in weak ARMA models'. Together they form a unique fingerprint.