Category Archives: Forecasting

Sources of Error

Sources of Error

Errors can come from a variety of sources. One common source of which many forecasters' are unaware is caused by the projection of pa t trends into the future. For example, when we talk about statistical errors in regression analysis. we are referring to the deviations of observation from our regression line. It is common to attach a confidence band to the regression
line to reduce the unexplained error. However. when we subsequently use this regression line as a forecasting device by projecting it into the future. the error may not be correctly defined by the projected confidence band. This is because the confidence interval is based on past data; consequently it mayor may not be totally valid for projected data points and therefore cannot be used with the same confidence. In fact experience has shown that the actual errors tend to be greater than those predicted from forecasting  models.

Errors can be classified as either bias or random. Bias errors occur when a consistent mistake is made, that is. the forecast is always too high or always too low. Sources of bias include (a) failing to include the right variables. (b) using the wrong relationships among variables. (c) employing the wrong trend line. (d) mistakenly shifting the seasonal demand from where it normally occurs. and (e) the existence of some undetected trend. Random errors can be defined simply a those that cannot be explained by the forecast model being used. These random errors are often referred to as "noise" in the model.

FORECASTING MODEL SAVES L.L. BEAN $300,000 IN LABOR ANNUALLY

FORECASTING MODEL SAVES L.L. BEAN $300,000 IN LABOR ANNUALLY

L.l. Bean, the outdoor mail-order company located in Free port, Maine, depends on customer telephone orders for 72 percent of its business. Scheduling telephone operators at its call centers is therefore a critical element in its success. Having too few operators results in long customer waiting times and the real possibility of losing ·customers to competitors. On the other hand, having too many telephone operators results in unnecessary labor costs, which impacts negatively on profits. The key to scheduling the proper number of operators to be on duty at any given time depends on the ability to accurately-to recast
the number and type of customer calls that will occur in a given time period. Using a time-series forecasting, model developed by professors at the University of Southern Maine, L.L. Bean has been able to save approximately $300,000 annually in labor costs by scheduling their operators more efficiently. This has been done without incurring any decrease in service quality!

Forecasting Errors in Time-Series Analysis

Forecasting Errors in Time-Series Analysis

When we use the word error we are referring to the difference between the forecast value and what actually occurred. So long as the forecast value is within the confidence limits as we discuss below in Measurement of Error this is not really an error. However common u age refers to the difference as an error. Demand generated through the interaction of a number of factors that are either too complex to describe accurately in a model or are not readily identifiable. Therefore, all
forecasts contain some degree of error. In discussing forecast errors. it is important to distinguish between sources of error and the measurement of error:

Determining Alpha (a) with Adaptive Forecasting

Determining Alpha (a) with Adaptive Forecasting

A key factor to accurate forecasting with exponential smoothing is the selection of the proper value of alpha (a). As stated previously, the value of alpha can vary between 0 and 1. If the actual demand appears to be relatively stable over time, then we would select a relatively small value for alpha, that is, a value closer to zero. On the other hand, if the actual demand  ends to fluctuate rapidly, as in the case of a new product that is experiencing tremendous growth then we would select a relatively large value of alpha that is nearer one. Regardless of the initial value selected a will have to be adjusted periodically to ensure that  is providing accurate forecasts. This is often referred to as adaptive forecasting. There are two approaches for adjusting the value of alpha. One uses various values of alpha and the other uses a tracking signal (which is discussed later in the chapter).

1. Two or more predetermined values of alpha. The amount of error between the forecast and the actual demand is measured. Depending on the degree of error different values of alpha are used. For example, if the error is large alpha is 0.8 if the error is small alpha is 0.2.

2. Computed values of alpha. A tracking signal computes whether the forecast is keeping pace with genuine upward or downward changes in demand (as opposed to random changes). The tracking signal is defined here as the exponentially smoothed actual error divided by the exponentially smoothed absolute error. Alpha is set equal to this tracking signal and therefore changes from period to period within the possible range of 0 to 1.

In logic computing alpha seems simple. In practice, however it is quite prone to error. There are three exponential equations one for the single exponentially smoothed forecast as done in the previous section of this chapter one to compute an exponentially smoothed actual error and the third to compute the exponentially smoothed absolute error Thus the user must keep three equations running in sequence for each period. Further assumptions must be made during the initial time periods until the technique has had a chance to start computing values. For example, alpha must be given a value for the first two periods until actual data are available. Also, the user must select a second smoothing constant in addition to alpha, that is used in the actual and absolute error equations. Clearly, those who use adaptive forecasting on a regular basis rely on technology for the calculations.

Trend Effects in Exponential Smoothing

Trend Effects in Exponential Smoothing

As . tared earlier an upward or downward trend in data collected over a eloquence of time periods causes the exponential forecast to always lag behind (that is to be above or below) the actual amount. Exponentially smoothed forecasts can be corrected some hat b including a trend adjustment. To correct for the trend we now need two smoothing constants. In addition to the smoothing constant a the trend equation also require a trend smoothing constant delta (0). Like alpha. delta is limited to values between 0 and  The delta reduces the impact of the error that occurs1.1

between the actual and the forecast. If both alpha and delta are not included, the trend would overreact to errors.
To initiate the trend equation. the trend value must be entered manually. This first trend value can be an educated guess or computed from past data. The equation to compute the forecast including trend (FIT) is

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