Testing for correlation between two time series using a parametric bootstrap

Zequn Sun, Thomas J. Fisher*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study the problem of determining if two time series are correlated in the mean and variance. Several test statistics, originally designed for determining the correlation between two mean processes or goodness-of-fit testing, are explored and formally introduced for determining cross-correlation in variance. Simulations demonstrate the theoretical asymptotic distribution can be ineffective in finite samples. Parametric bootstrapping is shown to be an effective tool in such an enterprise. A large simulation study is provided demonstrating the efficacy of the bootstrapping method. Lastly, an empirical example explores a correlation between the Standard & Poor's 500 index and the Euro/US dollar exchange rate while also demonstrating a level of robustness for the proposed method.

Original languageEnglish (US)
Pages (from-to)2042-2063
Number of pages22
JournalJournal of Applied Statistics
Issue number11
StatePublished - 2021


  • Causality
  • cross-correlation
  • portmanteau
  • time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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