In ARIMA(p,d,q) models, interest lies in establishing the amount of differencing (d) needed to render the process stationary. This is equivalent to testing for unit roots in the characteristic equation of the series. Seasonal versions of the test are also available for testing for unit roots at seasonal frequencies. The distributions are nonstandard even in the limit. Tables of critical values are available for the most common cases such as seasonality 4 quarters or 12 months. If the seasonal period is long, 52 weeks per year for example, it is possible to make some simple adjustments to the test statistics that render them approximately normal. The limit theory for this will be discussed as will some rather substantial simulation results to check finite sample behavior. Examples will illustrate the technique.

Keywords: Unit roots; Seasonality; Time Series; Forecasting

Biography: David Dickey holds a William Neal Reynolds chair in Statistics at North Carolina State University. His research is in time series, especially in the detection of unit roots.