LAG WINDOW ESTIMATION OF THE DEGREE OF DIFFERENCING IN FRACTIONALLY INTEGRATED TIME SERIES MODELS

Abstract. In this paper we consider the estimation of the degree of differencing d in the fractionally integrated autoregressive moving-average time series model ARFIMA ( p, d, q ). Using lag window spectral density estimators we develop a regression type estimator of d which is easy to calculate and does not require prior knowledge of p and q. Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provided.     

On t and EWMA t charts for monitoring changes in the process mean

The performance of an X‐bar chart is usually studied under the assumption that the process standard deviation is well estimated and does not change. This is, of course, not always the case in practice. We find that X‐bar charts are not robust against errors in estimating the process standard deviation or changing standard deviation. In this paper we discuss the use of a t chart and an exponentially weighted moving average (EWMA) t chart to monitor the process mean. We determine the optimal control limits for the EWMA t chart and show that this chart has the desired robustness property. Copyright © 2009 John Wiley & Sons, Ltd.