Nonparametric inference for unbalanced time series data

This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data are unbalanced or incomplete. In this case, one can work with only the common sample, to which a standard HAC/ bootstrap theory applies, but at the expense of throwing away data and perhaps losing efficiency. An alternative is to use some sort of imputation method, but this requires additional modeling assumptions, which we would rather avoid. We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss efficiency and power. Unbalanced data of the type we consider are quite common in financial panel data; see, for example, Connor and Korajczyk (1993, Journal of Finance 48, 1263–1291). These data also occur in cross-country studies.