The balance between size and power in testing for linear association for two stationary AR(1) processes

Abstract

The classical statistical procedure in testing the null hypothesis of zero correlation for two independent stationary AR(1) processes produces spurious correlations, contrast to the alternative testing approach that has been proposed by Agiakloglou and Tsimpanos (2012). This study examines the trade-offs between size distortions and power using both testing techniques, including the case where the true values of the autoregressive parameters are replaced by their estimates.

Keywords:

• Correlation coefficient
• spurious correlation
• hypothesis testing for correlation
• stationary AR(1) processes

JEL Classification:

• C10
• C22

Notes

¹ The simulation process is implemented by R which uses maximum likelihood estimation to obtain the estimates of the autoregressive parameters, as Ansley and Newbold (1980) have suggested.