The Power of Cointegration Tests versus Data Frequency and Time Spans

1. Introduction In the empirical literature of cointegration analysis, researchers often face the limitation of using relatively short time spans of data. In many cases, this is simply due to the absence of longer spans of data. In other cases, some equilibrium relationships have to be studied for certain time periods. For instance, when the models require a flexible exchange rate or a variable price of gold, studies have to be undertaken for the flexible exchange rate period, starting from the early 1970s, or for the period since 1968 when the price of gold was allowed to fluctuate. With the limits of relatively short time spans, many researchers chose to use relatively high frequency data to conduct the studies. Such attempts have been criticized in the literature. Hakkio and Rush (1991) argue that "the frequency of observation plays a very minor role" (p. 572) in exploring a cointegration relationship, because "cointegration is a long-run property and thus we often need long spans of data to properly test it" (p. 579). Hakkio and Rush's point is similar to the one made by Shiller and Perron (1985), that the length of the time series is far more important than the frequency of observation when testing for unit roots. While those who criticize the collection of high frequency data to deal with the short time span problem advocate the use of long spans of data to test properly for cointegration, their suggestion is sometimes misinterpreted as a support for using a small number of annual data.' For instance, Bahmani-Oskooee (1996, p. 481) borrows Hakkio and Rush's (1991, p. 572) "testing a long-run property of the data with 120 monthly observations is no different than testing it with ten annual observations" to defend his use of annual data by saying that, using annual data of over 30 years "is as good as using quarterly or monthly data over the same period." Taylor (1995, p. 112) claims that the deficiency of using less than 50 annual observations "should be compensated by the fact that the data set spans nearly half a century." I would like to point out that Hakkio and Rush's study has several limitations, and therefore it may not be appropriate to cite the conclusions of the study for the cases beyond its limitations. Their study only allows the cointegrating residual to be a pure first-order autoregressive (ARC[1]) process and is limited to the single-equation method of cointegration tests. They show the results only for some extreme cases where the cointegrating residual for the monthly data is either very highly serially correlated (nearly nonstationary and thus all the cointegration tests would have very low test power regardless of the frequency of the data) or with a quite low coefficient of serial correlation (thus all the cointegration tests can easily reject the null of no cointegration regardless of the frequency of the data). The present paper is motivated by seeking the answers to the following questions: (i) Does the frequency of observation play a very minor role in exploring a cointegration relationship in the cases where the cointegrating residual is not nearly nonstationary? (ii) Can the validity of the conclusions of Hakkio and Rush (1991) based on a single-equation method be extended to other popular cointegration tests and to more realistic cases, where the models with higher lag orders are required when the cointegrating residual is generated with more noise than a pure first-order autoregressive process? (iii) While testing cointegration with 120 monthly observations could be no different than testing it with 10 annual observations as both cases are subject to very low test power, does this warrant that using annual data of 30 to 40 years is as good as using quarterly or monthly data over the same period? (iv) How serious would the problem of size distortion be for the use of a small number of annual observations? This paper examines the power of cointegration tests versus frequency of observation and time spans, as well as the small-sample size distortions of the tests, through the Monte Carlo experiments. …