Los instrumentos populares árabes

To test how the model actually performs, one can estimate the model without all values of dependable variable. For example, in this analysis the model is estimated until the end of 2016. After that, one can then “forecast” next 12 months but using the regression coefficients that would have been estimated at the end of 2016. With this is shortcut one will have the correct coefficients, which one would have had back in 2016. From statistical perspective, there is no bias for the test since the future actual values will not affect the regression coefficients. The forecast is easy to process since all the explanatory variables have data. One extra aspect of testing the model in this way is to benchmark against operations personnel’ budget forecast. As previously, the forecast is done with parameter uncertainty to have varying standard error for forecasts and not only one static error.

One issue comparing to budget might be incentive-based manipulation for the budget. Walker and McClelland (1991) found that sales operatives might boost the sales budget in order to balance between two different and conflicting objectives. First, the sales organization must have high sales to justify their allocated costs; the profitability of the part of organization must be high enough. Secondly they must motivate and encourage personnel via incentive plans to perform better, the targets must be able to achieve, i.e., the target sales cannot be too high. (Walker & McClelland 1991, 379.)

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Figure 9. 90 % profitability distribution for 2017 forecasts. Forecast for 01/2017 is the index level 100 (estimated by the author).

From the figure 9, one will immediately notice the same August effect that was visible in the forecast for 2018. In addition, one will notice the increasing year-end sales effect, so called hockey stick – effect (Chen 2000, 186). From figure 9, the difficult start for the year is clearly visible; probably customers will not need new forklift trucks in the middle of winter. Naturally, there are areas in EMEA that do not suffer from winter but there are many highly snow sensitive areas, e.g., Sweden, Finland and even Germany occasionally. These snowy areas are a small proportion based on count but do present important part of the total sales and the winter is due to that a plausible factor to explain the dropping sales in addition to the hockey stick effect (Chen 2000, 186) in December.

Table 7. Mean and standard error for the forecasted periods

Horizon Forecast SE Actual Error t-value -2SE +2SE

January 104.32 100.00 100.00 -4.32 -0.175 64.31 169.20

February 77.64 101.82 100.00 22.36 1.028 47.44 127.03

March 71.9 99.88 100.00 28.10 1.366 44.36 116.54

April 145.22 98.97 100.00 -45.22 -1.559 89.99 234.35

May 110.6 101.99 100.00 -10.60 -0.409 67.54 181.13

June 91.35 100.33 100.00 8.65 0.373 56.22 148.41

July 128.36 100.29 100.00 -28.36 -1.030 79.03 208.5

90%

95%

100%

105%

110%

115%

Jan-17 Feb-17 Mar-17 Apr-17 May-17 Jun-17 Jul-17 Aug-17 Sep-17 Oct-17 Nov-17 Dec-17 90 - 95 % 85 - 90 % 75 - 85 % 25 - 75 % 15 - 25 % 10 - 15%

5 - 10 % Forecast Actual Budget

53 November is April, where the actual barely stays with-in the 90% probability mass. T-value for the forecast for April is -1.559 and with two-tailed t-distribution, the lower 5 % t-value is -1.645, the corresponding t-probability for the forecast is 6.11 %.

To determinate, what value the external fundamentals based forecast model will bring to everyday business life, it is important to benchmark against the operations personnel’ budget. From table 8, one will see that the first half of the year, the forecast and budget are aligned and both are as much right as are wrong. The largest difference appears after July when the holiday season starts in the Central Europe and in some cases, people return to work in the Northern Europe. The budget is a lot larger than the forecast model implies the sales to be and during the autumn and early winter, the forecast model is performing much better than the budget does. One must remember that the budget is one year old, when the August actually comes but still, the performance of the budget is not adequate. The forecast model has better performance in the challenging part of the year and in fact in overall terms. Forecast model has a twelve-month forecast accuracy of 99.67 % and the budget has 89.86 % respectively. The deviation between forecast and the actual is roughly one unit of medium forklift trucks or two light forklift trucks.

Table 8. Comparison between forecasted, actual and budgeted sales Horizon Forecast

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To evaluate the performance of the forecast model, following key statistics are introduced. These are mean of the error term, standard deviation of the error term, mean square error (MSE), root mean square error (RMSE) and mean absolute percentage error (MAPE). (Mendenhall & Reinmuth 1993, 668-669.) Mean of the error indicates whether the residual has a mean of zero or not. One normal assumption in time economics is assuming normal distribution with zero mean and standard deviation of one. The residual of the model has a bit zero deviating mean, -0.02. This do not require further actions but is informative that the mean of the probability distribution is not exactly at zero. The standard error of the model is 0.20. To evaluate the performance of the forecast model, one could calculate following statistics:

where 𝑦_𝑡 is the actual value from the series and 𝑦̂_𝑡 is the corresponding estimated value for the period.

Mean absolute error (MAD) (equation 33) has a caveat for extreme deviations and due to this; mean

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square error (MSE) (equation 34) is introduced. MSE (equation 34) and the square rooted version RMSE (equation 35) will punish of the extreme deviations between the actual and forecasted value.

The usefulness of this punishment or penalizing comes from the cost of wrong estimated value. If the result of incorrect estimate will endanger the organization then the model should be selected which has the best forecast capability. With mean absolute error (MAPE) (equation 36), one will have an issue of inflating the statistic. Since there is a quotient in the formula and the statistic is shown as percent, extremely low denominator values will increase the value of the MAPE (equation 36) extensively. (Mendenhall & Reinmuth 1993, 668-669.) Test statistics for the 2017 forecast are RMSE

= 0.20473 and MAPE = 1.9217. Since the test values are to determine which model to choose, the test values itself do not imply that much information. In order to benchmark the values against a counterpart, corresponding test statistics are presented for 2016 forecast.

To test one-year forecast, the model is estimated up-to 2015 and then forecasted one year forward.

Test statistics are RMSE = 0.23257 and MAPE = 2.0726. With same process is done for a two-year forecast and following test statistics are observed RMSE = 0.21768 and MAPE = 1.9738. With these test statistics, one will quickly see that the performance of the 2016 forecast was below the forecast accuracy for 2017. The forecast accuracy for two years is between 2016 and 2017 forecasts, which will imply the great performance of the model to forecast the 2017 sales. For further reading of the key statistic, one will find about MSE, e.g., Nahmias (2009), Hanke and Wichern (2009), Silver, Pyke and Peterson. (1998) and about the MAPE, e.g., Hanke and Wichern (2009).