Testing for the equivalence of several sets of time series and its multiple comparison procedure

Abstract

We propose test statistics for testing for the equivalence of the mean functions with respect to time for two sets of time series and that for several sets of time series. We also propose multiple comparison procedures for testing for the equivalence of the mean functions with respect to time under several sets of time series. Multiple comparison procedure 1 was compared with some of the previously studied methods by simulation and proposed method 1 gave 1 for empirical power and almost 1 for empirical probability of correct decision when the standard deviation of pseudo normal random numbers was small whereas the other methods gave almost 0 for both empirical power and empirical probability of correct decision whatever the standard deviation of pseudo normal random numbers. On the proposed method for testing for the equivalence of all the mean functions for several sets of time series against that at least one of the mean functions is different from the others, we found that empirical powers of the proposed method were almost 1 when the standard deviation of pseudo normal random numbers was small by simulation.

Keywords:

• Harmonic regression
• Holm’s method
• Nair’s F_max statistic
• non parametric regression
• periodicity