Cointegration testing using the ranges

Abstract

In this paper we propose a method for testing the hypothesis of cointegration in pairs of univariate time series. One of our method's main advantages lies in that it does not impose any restriction on the time series models. Another is that cointegration can be tested regardless of the form of the relationship. Essentially, our test rests on a definition of cointegration which requires the sinchronicity up to a constant delay of the relevant informational events for the series. Thus cointegration can bp tested independently on what form of relationship holds between the variables. We propose three alternative test statistics and obtain, under some assumptions,' their asymptotic null distribution. We also propose some graphical techniques consisting in plotting functions of the range sequences for the pairs of series. These plots could help in detecting nonlinearities as well as nonstationarities in the cointegrating relationship. Also we show how nonlinearity and/or nonstationadty' ill. the relationship can be detected by analyzing the cross-difference of ranges. We :Q,n ally report some experiments on financial and monetary time series that compare the performances of our test statistics with more standard ones.