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Test Consistency with Varying SamplingFrequency

Published online by Cambridge University Press:  11 February 2009

Pierre Perron
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Abstract

This paper considers the consistency property of sometest statistics based on a time series of data.While the usual consistency criterion is based onkeeping the sampling interval fixed, we let thesampling interval take any equispaced path as thesample size increases to infinity. We consider testsof the null hypotheses of the random walk andrandomness against positive autocorrelation(stationary or explosive). We show that tests of theunit root hypothesis based on the first-ordercorrelation coefficient of the original data areconsistent as long as the span of the data isincreasing. Tests of the same hypothesis based onthe first-order correlation coefficient of thefirst-differenced data are consistent againststationary alternatives only if the span isincreasing at a rate greater thanT½, whereT is the sample size. On theother hand, tests of the randomness hypothesis basedon the first-order correlation coefficient appliedto the original data are consistent as long as thespan is not increasing too fast. We provide MonteCarlo evidence on the power, in finite samples, ofthe tests Studied allowing various combinations ofspan and sampling frequencies. It is found that theconsistency properties summarize well the behaviorof the power in finite samples. The power of testsfor a unit root is more influenced by the span thanthe number of observations while tests of randomnessare more powerful when a small sampling frequency isavailable.

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Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 3 , September 1991 , pp. 341 - 368
Copyright
Copyright © Cambridge University Press 1991

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