AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING

Abstract. The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1‐ B ) d . When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long‐memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.