# Lecture 7 - Exponential Smoothing Models1 Professor Thomas...

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1 Exponential Smoothing Models 1 Professor Thomas B. Fomby Department of Economics Southern Methodist University Dallas, TX June 2008 Introduction The formulation of exponential smoothing forecasting methods arose in the 1950’s from the original work of Brown (1959, 1962) and Holt (1960) who were working on creating forecasting models for inventory control systems. One of the basic ideas of smoothing models is to construct forecasts of future values as weighted averages of past observations with the more recent observations carrying more weight in determining forecasts than observations in the more distant past. By forming forecasts based on weighted averages we are using a “smoothing” method . The adjective exponential derives from the fact that some of the exponential smoothing models not only have weights that diminish with time but they do so in an exponential way, as in j j where 1 1 and , 2 , 1 j represents the specific period in the past. At least three major points can be raised about exponential smoothing models: As a methodology, exponential smoothing methods suffer from not having an objective statistical identification and diagnostic system for evaluating the “goodness” of competing exponential smoothing models . For example, the smoothing parameters of the smoothing models are determined by fit and are not based on any statistical criteria like tests of hypotheses concerning parameters or tests for white noise in the errors produced by the model. In this sense, exponential smoothing models are ad hoc models, statistically speaking. Of course, if one continues to monitor the forecasting performance of a given exponential smoothing model, and, if the model’s forecasts become more and more inaccurate over time, then one has, in a sense, an ex post evaluation method for picking and choosing between competing exponential smoothing models. The 1 The discussion here draws heavily from the SAS manual SAS/ETS Software: Time Series Forecastin g System , Version 6, First Edition, Cary, NC. SAS Institute Inc., 1995, 225-235.

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2 only problem is that this approach comes with a cost. Bad forecasting for a certain amount of time while learning can be expensive when, for example, dealing with inventories that run into the millions of dollars. But instead of pursuing this ex post monitoring approach , one can attempt to make a good choice of exponential smoother before hand by using out-of-sample forecasting experiments . In this approach, the forecaster reserves some of the available data for a “horse race” between competing exponential smoothing methods. To carry these horse races out, one divides the data into two parts: the in-sample data set (say 60% of the first part of the available time series data) and with the remaining latter part of the time series assigned to the out-of-sample data set. Then one “runs” the competing exponential smoothing methods through the out -of-sample data while forecasting h-steps ahead each time (we assume h is the forecast
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