Testing for Unit Roots With Missing Observations

This paper considers unit root testing of time-series data with missing observations. Three procedures for dealing with the gaps are discussed. These include: ignoring the gaps, replacing the gaps with the last available observation, and filling the gaps with a linear interpolation method. The tests for the first two procedures yield test statistics which have the same asymptotic distribution as that tabulated by Dickey and Fuller (1979) for the complete data situation. The remaining procedure yields a test statistic that has an asymptotic distribution that differs from Dickey and Fuller’s tabulated distribution by an adjustment factor. In addition, models that include an ARIMA (0,1,q) error and augmented Dickey-Fuller tests are also considered in this paper. A simulation experiment is performed for the above models using the A-B sampling scheme. The results show that ignoring gaps in time- series data with missing observations produces unit root tests that are more powerful than the other two approaches that are considered.