Testing Cointegrating Relationships Using Irregular and Non‐Contemporaneous Series with an Application to Paleoclimate Data

Abstract

Time series that are observed neither regularly nor contemporaneously pose problems for most multivariate analyses. Common and intuitive solutions to these problems include interpolation and other types of imputation to a higher, regular frequency. However, interpolation is known to cause serious problems with the size and power of statistical tests. Due to the difficulty in dating paleoclimate data such as CO2 concentrations and surface temperatures, time series of such measurements are observed neither regularly nor contemporaneously. This article presents large‐ and small‐sample analyses of the size and power of cointegration tests of time series with these features and supports the robustness of cointegration of these two series found in the extant literature. Compared to linear or higher‐order polynomial interpolation, step interpolation results in the least size distortion and is therefore recommended.