ESTIMATING D FOR LONG AND SHORT-MEMORY TIME-SERIES

Fractional difference models are a useful extension to ARIMA models as they model longer range dependence. We suggest a simple and efficient way of evaluation the fractional parameter and illustrate this on a series of mud layer measurements. As can be seen, the model we derive is both simple and compelling. The method used can also be used to estimate the differencing parameter for conventional ARIMA models and in addition can be used to find ARMA parameters. For a fractional model, once the fractional parameter is known a simple filtering operation allows us to proceed as for an ARIMA model. While this is not quite as elegant as a full likelihood approach, it is straightforward and uses common software tools. The pile-up effect can also be minimized since we do not make a normal approximation.