Abstract

In this thesis, we consider the two-sample problem of time series. Given two time series data x_1,...,x_n and y_1,...,y_m, we would like to test whether they follow the same time series model. First, we develop a unified procedure for this testing problem. The procedure consists of three steps: testing stationarity, comparing correlation structures and comparing residual distributions. Then, we apply the established procedure to analyze real data. We also propose a modification to a nonparametric two-sample test, which can be applied to high dimensional data with equal means and variances.