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MANAGEMENT SCIENCE Vol. 31, No. 10, October 1985 Printed in U.S.A.
FORECASTING TRENDS IN TIME SERIES*
EVERETTE S. GARDNER, JR. AND ED. McKENZIE OperationsAnalysis Department,Navy Fleet Material SupportOffice, P.O. Box 2010, Mechanicsburg,Pennsylvania 17055 Mathematics Department, Universityof Strathclyde, Glasgow GI 1XW, Scotland, United Kingdom Most time series methods assume that any trend will continue unabated, regardless of the forecast leadtime. But recent empirical findings suggest that forecast accuracy can be improved by either damping or ignoring altogether trends which have a low probability of persistence. This paper develops an exponential smoothing model designed to damp erratic trends. The model is tested using the sample of 1,001 time series first analyzed by Makridakis et al. Compared to smoothing models based on a linear trend, the model improves forecast accuracy, particularly at long leadtimes. The model also compares favorably to sophisticated time series models noted for good long-range performance, such as those of Lewandowski and Parzen. (FORECASTING-TIME SERIES)
1. Introduction Research in time series analysis and forecasting has traditionally been concerned with modelling the autocorrelation structure in a stationary time series. However, as discussed in Fildes (1983), recent empirical work has shown this to be a relatively unimportant problem compared to the modelling of trends. For example, Makridakis et al. evaluated the post-sample accuracy of 21 automatic forecasting methods on a collection of 1,001 time series. The accuracy of all methods deteriorated badly at leadtimes more than a few steps ahead. This was particularly true of methods based on a linear trend which typically overshot the data at long leadtimes. Makridakis also examined a subset of 111 time series taken from the 1,001. Several sophisticated methods were tested in this subset in addition to the 21 automatic methods. The sophisticated methods included the Box-Jenkins approach, the FORSYS system of Lewandowski (1982), and the ARARMA methodology of Parzen (1979, 1982). Like the automatic methods, Box-Jenkins did badly at long leadtimes. However, Lewandowski and Parzen were the most accurate at long leadtimes among all methods tested. Lewandowski's FORSYS system is widely used in European companies. The distinguishing feature of FORSYS is that it damps the trend as the forecast leadtime increases. The rate of damping increases with the level of noise in the series. The rationale is that the more noise in the series the greater the risk in trend extrapolation. It is difficult to say more than this about FORSYS because the system is proprietary. Parzen's approach attempts to classify the "memory" of the time series. "Shortmemory" series are covariance-stationary and are modelled by conventional ARMA schemes. "Long-memory" series contain trends modelled by nonstationary autoregression. This approach produced models robust at...