International Journal of Forecasting 7 (1991) 317-330 North-Holland 317 zyxwvuts Exponential smoothing: The effect of initial values and loss functions on post-sample forecasting accuracy Spyros Makridakis and Mich6le Hibon INSEAD, 77305 Fontainebleau Cedex, France zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract: This paper describes an empirical investigation aimed at measuring the effect of different initial values and loss functions (both symmetric and asymmetric) on the post-sample forecasting accuracy. The 1001 series of the M-competition are used and three exponential smoothing methods are employed. The results are compared over various types of data and forecasting horizons and validated with additional data. The paper concludes that contrary to expectations, post-sample forecasting accuracies are not affected by the type of initial values used or the loss function employed in the great majority of cases. Keywords: Forecasting, Time series, Exponential smoothing, Accuracy, M-competition. 1. Introduction Exponential smoothing methods are widely used in many industrial applications including produc- tion planning, production scheduling and inven- tory control [Brown (1959); Brown (1963); Brown (1967); Gardner (1985); Holt et al. (1960); John- son and Montgomery (1974); Makridakis and Wheelwright (1989); Winters (1960)]. Although extremely simple and easy to model, such methods have been found by many studies to be as accu- rate as more complex and statistically sophisti- cated alternatives [Groff (1973); Chatfield (1978); Koehler and Murphree (1988); Makridakis and Hibon (1979); Makridakis et al. (1982); Martin and Witt (1989)]. Furthermore exponential smoothing methods are robust, easy to program, require a minimum of historical data while the cost of running them on the computer is the smallest of all available alternatives. The purpose of this paper is to empirically investigate the effect of various initial values and loss functions on the post-sample forecasting ac- curacy of three of the most widely used (Single, Holt’s and Dampened) exponential smoothing methods. The fourth widely used method (Win- ters’) was not utilized as empirical findings have shown it to produce forecasts very similar to those of Holt’s [see Makridakis et al. (1982)]. Section 2 of the paper reviews the literature and provides the reasoning for undertaking this study. Section 3 describes the methodology used and formulates various hypotheses to be studied. Section 4 pre- sents and analyses the results. There is a conclud- ing section which discusses the implications of the findings, validates such findings with another set of data provided by Fildes (1989) and presents possible avenues for further research. 2. Literature review and reasons for undertaking this study Since the introduction of exponential smooth- ing methods the question of how to initialize the first smoothed value(s) has always been posed [Cogger (1973); McClain (1981); Taylor (1981); Wade (1967)]. Several alternatives have been pro- posed in the literature, but there is little advice on 0169-2070/91/$03.50 0 1991 - Elsetier Science Publishers B.V. All rights reserved