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The Power of Cointegration Tests versus Data Frequency and Time Spans

2001; Wiley; Volume: 67; Issue: 4 Linguagem: Inglês

10.2307/1061577

2325-8012

Su Zhou,

Economic, financial, and policy analysis

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