Comparing Time Series

Suppose that we observe two independent stationary time series and let us assume that the one is related with the other by means of a semiparametric model. A statistical methodology is outlined here where the information from both time series is combined and used on the comparison of the two data sets. The methodology is based on empirical likelihood inference which in turn is based on the so called density ratio model. The density ratio model specifies that the log--likelihood ratio of two unknown densities is of some known parametric linear form. The density ratio model has been succesfully applied to independent data especially in the context of two sample comparison. In this work we outline a methodology which extends the density ratio model to stationary time series.