Two-sample comparisons for serially correlated data

Abstract

The purpose of this study is to derive new tests for the equality of the means in two independent or dependent stationary time series, based on bootstrap critical values. Required properties of these tests include satisfactory probability of Type I errors, and high power. It is shown how critical points for various sample sizes and significance levels can be obtained by applying the parametric bootstrap. A limited Monte Carlo simulation study is conducted to illustrate the validity of the bootstrap approximation of the exact critical values, by producing satisfactory probability of Type I errors. It also shows that the newly proposed tests compare favourably with standard two-sample tests in the absence of serial correlation, under the null hypothesis of equal means, but are more powerful than the well-known t -test if small and moderate correlation structures are present, for a wide range of parameter values. All findings and conclusions of the Monte Carlo simulations are reported.