Exponential smoothing This is a widely used forecasting technique in retailing, even though it has not proven to be especially accurate.

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Presentation transcript:

Exponential smoothing This is a widely used forecasting technique in retailing, even though it has not proven to be especially accurate.

Why is exponential smoothing so popular? It's easy—the exotic term notwithstanding. Data storage requirements are minimal (even though this is not the problem it once was due to plunging memory prices). It is very cost effective when forecasts must be made for a large number of items--hence it has extensive use in retailing.

The basic algorithm Where: L t is the forecast for the current period; X t is the most recent observation of the time series variable—such as, for example, sales last month of part # L t-1 is the most recent forecast; and  is the smoothing constant, where 0 <  < 1 (1)

New Forecast =  (New Data) + (1 -  )Most Recent Forecast Equation (1) can be written as follows:

Exponential smoothing is weighted moving average process To demonstrate, let Substitute (2) into (1):

But notice that: Substitute (4) into (3) to obtain: If we continue to substitute recursively, we get: (4)

Notice that are the weights attached to past values of X. Since  < 1, the weights attached to earlier or more remote observations of X are diminishing.

You don’t have to go through this recursive process each time you do a forecast. The process is summarized in the most recent forecast.

Selecting the smoothing constant (  ) The range of possible values is zero and one. If you select a value of  close to 1, that means you are attaching a large weight to the most recent observation. This is not indicated if your series is very erratic (swings widely from period to period). For example, suppose you were forecasting the demand for part #56 in month t. Sales of part #56 Month t-1 t t-2 If you attached too much weight to the observation for t-1, you will have a large forecast error for month t.

We will now forecast sales of liquor and floor covering using this technique. We have monthly data for each variable beginning in January 1999 and running through July of 2007.

Beer, Wine, Liquor Parts, Accessories, Tires Mean Mean Standard Error Standard Error Median2567Median5546 Mode2232Mode5613 Standard Deviation Standard Deviation Sample Variance Sample Variance Kurtosis Kurtosis Skewness Skewness Range2770Range2411 Minimum1818Minimum4503 Maximum4588Maximum6914 Sum273296Sum Count103Count103

The ratio of the standard deviation to the mean gives us a nice measure of the amplitude or volatility of a series month-to-month (or day-to-day, quarter-to- quarter, as the case may be). Beer, Wine, Liquor = Parts, Tires, etc. = 0.099

Pricey time series forecasting software, such as EViews, use an algorithm to select the value of the smoothing constant that minimizes mean square error for in-sample forecasts. If you lack this software, you can use a trial and error process. Selecting the smoothing constant

YearMonthActualSmoothed Auto Parts, Accessories, and Tires (Alpha =.69)

Beer, Wine, and Liquor (Alpha =.1280) YearMonthActualSmoothed

Forecasts for August, 2007 Remember our basic algorithm Hence to parts, accessories, and tire sales (PAT) for August, 2007: To forecast beer, wine, and liquor sales (BWL):