DETERMINING THE DEGREE OF DIFFERENCING FOR TIME SERIES VIA THE LOG SPECTRUM

Abstract. While many time series require differencing before a model may be fitted it has been shown that 'overdifferencing' may result in a fitted model with poor long term forecasting properties. This may present real problems when the degree of differencing which is appropriate is fractional. We show that the log spectrum is a natural quantity to consider when attempting to determine the degree of differencing required and outline the distribution theory required. The ideas are shown to extend to the seasonal case and can be used to assess whether seasonal differencing is appropriate.