Testing for correlation between two time series using a parametric bootstrap

ABSTRACT

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.

Keywords:

• Causality
• cross-correlation
• GARCH
• portmanteau
• time series

2010 Mathematics Subject Classifications:

• 62M10
• 62F40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Source code for the simulations, data analysis and the analysed data are available on the corresponding author's github repository: https://github.com/tjfisher19/meanVarianceCausality. Additional simulation results are available in the Supplemental materials.