Multiple Hypotheses Testing and Model Selection

Abstract

It is of interest to study the presence (or the absence) of specific dynamic relations between time series. Chen and Lee (1990a, b) proposed a multiple hypotheses testing procedure in a vector ARMA framework to identify the possible dynamic relation (which include independent, contemporaneous relation, unidirectional relation and feedback relation) between time series. This paper considers a more general procedure for model selection that includes strong form relationship. The procedure is a sequential inference procedure based on multiple likelihood ratio tests on models with various parametric constraints. The significance levels to be used in these various test are critical, which are connected to the penalty term in model selection criteria such as AIC and BIC. The use of adapting versus fixed significance levels, and how the model selection criteria are adjusted to handle strong form relationship will be discussed in detail. The procedure seeks to move up a hierarchical structure of models with increasing parameter restrictiveness without significantly reducing the likelihood. As such, the testing procedure does not have to go through all models to select the best as the usual selection criteria do. Extensive simulation studies of series with moderate sample size indicate that by choosing the significance levels appropriately, the procedure performs satisfactorily. For illustration, we study the US and UK price level and interest rate series analyzed in Chen and Lee (1990), and the three flour price series in Tiao and Tsay (1989). (Joint with K.S. Man)