Introduction
Planning is an important aspect of managing any business. Planning sometimes involves prediction of the future conditions. Forecasting sales is significant in profit planning among other strategic decisions. Several methods are used in forecasting sales. A business should apply the method that most accurately estimates the future sales. Excellent Consulting Group wants to identify the best method to forecast its sales for year two. A forecast has already been made using the regression analysis method. The technique involved developing an equation which gives the monthly sales figure as a function of the number of customers in each month. The regression equation has been used to forecast year two sales since the data on the number of customers is available. The manager wants a different method to be used in forecasting year two sales. Exponential smoothing has been proposed at alphas of 0.15 and 0.90. This report gives the forecasts using the exponential smoothing and analyses the two methods to determine the most reliable. The techniques will be compared suing measures such as the mean percentage error, mean absolute percentage error and the mean error.
Description of exponential smoothing method
The technique gives a forecast as the weighted average of past observations. Under the method, it is assumed that past observations have different impacts on the future values (Yaffee & McGee, 2000). Thus, the most recent observations are given more weights than the older values. Thus, the weights decrease exponentially from the most recent observation to the older observations. The smoothing coefficient determines the relative weight assigned to a past observation. The alpha (smoothing coefficient) ranges from zero to one (Yaffee & McGee, 2000). The first value is usually a naive forecast which is taken as the actual figure for the last period. In this case, data for the last one year is available. The forecast for January year 2 is a naïve forecast and is given by the sales for December year 1.
The exponential smoothing forecast formula is as shown below:
Forecast = (Most recent month’s sales × Alpha) + (most recent forecast × (1 – alpha)
Regression analysis gives an equation of the monthly sales in terms of the number if customers. The sales forecast, in this case, is determined by substituting the number of customers in the regression equation (Tsay, 2010). The difference between this technique and the exponential smoothing is that it gives equal weights to all past observations (Tsay, 2010). Thus, the previous month’s sales and the sales 12 months ago have equal weights in determining the monthly sales for the next period.
Evaluating the techniques
Mean Error
This is the average of the variations or deviations of the forecast value from the actual value. This measure helps in determining the accuracy and reliability of the forecast and the forecasting technique (Fildes & Allen, 2011). A good forecast is one that is closest to the actual value. Thus, the most suitable technique is one which minimizes the mean error (Fildes & Allen, 2011).
As shown in the spreadsheet, the mean error for the regression forecast is -16.953. This means that a regression forecast of the monthly sales is likely to deviate from the actual monthly sales by -16.953. The exponential smoothing forecast with an alpha of 0.15 has a mean error of 16.884 indicating that if the technique is used, it is likely that the forecast will deviate from the actual sales value by 16.884 (Fildes & Allen, 2011). If a smoothing coefficient of 0.9 is used, the mean error is 2.322. The forecast monthly sales figure is likely to be less than the actual sales by $2,322.
The exponential smoothing with a coefficient of 0.90 gives the least mean error, followed by the regression forecast and the exponential smoothing forecast with a coefficient of 0.15. This shows that the exponential smoothing technique is the most accurate based on the mean error. It further shows that more accurate forecasts can be obtained if greater weights are assigned to the most recent observation.
The mean error, however, is not a reliable measure of the accuracy of a forecast. Both negative and positive deviations are summed up to determine the mean error (Fildes & Allen, 2011). This implies that a technique can give a smaller mean error since positive deviations offset negative deviations. This can be misleading as it does not give the true reflection of the deviations from the actual forecast.
Mean Percentage Error
The measure gives the average f the percentage deviations of the forecasts from eth actual values. Mean percentage error is determined by expressing the deviation as a percentage of the actual sales (Black, 2009). The use of percentages makes this a relative measure hence it is more suitable than the mean error when assessing the accuracy of a forecast.
The mean percentage error for the linear regression forecast is -7.840% implying that the forecast is likely to be less than the actual sales by -7.840%. The exponential smoothing forecast with a smoothing coefficient of 0.15 has a mean percentage error of 3.86% indicating that the forecast is likely to deviate from the actual value by 3.86%. Finally, the exponential smoothing forecast at an alpha of 0.90 has a mean percentage error of -0.50%
As shown above, the exponential smoothing technique has the lowest mean percentage error. This implies that it gives the most accurate forecast of the three options. If it is used, it is likely to give a forecast that is closest to the actual sales value than the forecast of the two other alternatives.
Mean Absolute Percentage Error
It is the average of the absolute percentage deviations of the forecasts from the actual monthly sales values (Black, 2009). All the deviations, both positive and negative, are treated as positive deviations. The regression forecast has a mean absolute percentage deviation of 11.594% while the exponential smoothing with a coefficient of 0.15 has a MAPE of 14.78%. The exponential smoothing forecast with a 0.90 coefficient has a MAPE of 13.49%. Based on this measure, the regression forecast is the most accurate since it has the lowest mean absolute percentage error.
Conclusion
The company needs a technique that will give the most accurate forecast of the sales figures for year 2. When evaluating the techniques, factors such as the availability of data, ease of use, accuracy, among other factors, should be considered. Accuracy is the most important aspect. It ensures that the forecast is closer to the actual sales thus reducing the error. As shown in the above analysis, the techniques have different levels of accuracy. The exponential smoothing forecast with a coefficient of 0.15 has the least mean error and mean percentage error. This implies that it is the most accurate forecast if the methods are assessed on the basis of mean error. However, the regression forecast has the least mean absolute percentage error. Owing to the limitations of the MAPE discussed above, we should assess the techniques using the mean error and mean percentage error. Thus, the exponential smoothing is more accurate than the linear regression. Comparative analysis of the forecasts using coefficients of 0.90 and 0.15 shows that the forecast is more accurate if the smoothing coefficient is higher than when it is lower. This further implies that the most recent observations are relatively more important in determining the next period’s values than the earlier observations. Thus, Excellent Consultant Group should apply the exponential smoothing technique to estimate monthly sales for year 2.
References
Black, K. (2009). Business Statistics: Contemporary Decision Making (2nd ed.). Hoboken,
NJ: Wiley.
Fildes, R. & Allen, P. (2011). Forecasting (1st ed.). Los Angeles, Calif.: SAGE.
Tsay, R. (2010). Analysis of financial time series (1st ed.). Hoboken, NJ.: Wiley.
Yaffee, R. & McGee, M. (2000). Introduction to time series analysis and forecasting (1st
ed.). San Diego: Academic Press.
