Tests for comparing time series of unequal lengths

Journal of Statistical Computation and Simulation

Jorge Caiado, Nuno Crato and Daniel Peña

This paper deals with hypothesis testing for independent time series with unequal length. It proposes a spectral test based on the distance between the periodogram ordinates and a parametric test based on the distance between the parameter estimates of fitted autoregressive moving average models. Both tests are compared with a likelihood ratio test based on the pooled spectra. In all cases, the null hypothesis is that the two series under consideration are generated by the same stochastic process. The performance of the three tests is investigated by a Monte Carlo simulation study.