Cointegration and sampling frequency

Abstract

This paper analyses the effects of sampling frequency on the properties of ordinary least squares (OLS) and fully modified least squares (FM‐OLS) regression estimators of cointegrating parameters. Large sample asymptotic properties are derived under three scenarios concerning the span of data and sampling frequency, each scenario depending on whether span or frequency (or both) tends to infinity. In cases where span tends to infinity the OLS estimators are consistent but their limiting distributions suffer from second‐order bias effects arising from serial correlation and endogeneity; the OLS estimators are not even consistent when the span is fixed and sampling frequency increases. In contrast, the FM‐OLS estimators are shown to have limiting mixed normal distributions when span tends to infinity and associated Wald statistics have limiting chi‐square distributions. The finite sample performance of the estimators and test statistics is explored in a simulation study in which the superiority of the FM‐OLS estimator in terms of bias and mean square error is demonstrated and the Wald statistics are found to generally have good size and power properties. Directions in which the model can be extended, and the effects of such extensions, are also discussed.

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