An Introduction to Long-memory Time Series Models and Fractional Differencing

Abstract It has become standard practice for time series analysts to consider differencing their series ‘to achieve stationarity’. By this they mean that one differences to achieve a form of the series that can be identified as an ARMA model. If a series does need differencing to achieve this, it means that strictly the original, undifferenced series has infinite variance. There clearly can be problems when a variable with infinite variance is regressed on another such variable, using least squares techniques, as illustrated by Granger and Newbold (1974).

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