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There is a wide variety of forecasting techniques. How do we choose among them? This article introduces the topic and focuses on the mean absolute deviation (MAD) method, providing some numerical examples.

        1.  Selecting the optimal method

Forecast evaluation is an important part of forecasting exercises, and selecting the optimal forecasting method depends on the case, such that a method appropriate for forecasting in one situation may be inappropriate in another. The decision should be based on factors such as forecast accuracy, cost, analyst expertise, software availability, the properties of the series being forecasted, the way the forecast will be used, and more [1].
For example, the moving average can be suited for a static demand level with irregular pattern and for C Pareto class items; regression analysis is suitable for a continuous trend with irregular pattern; and the exponential model is suitable for variable demand, gradual changing level, and slow-moving spares items [2].

        2.  Measure the forecast accuracy

The optimal forecasting method is often selected by accuracy [1]. Forecasts almost always have an error component, where the usual assessment procedure is to compare the forecast demand to actual demand as soon as it is known [3].
There are different methods to use as criteria for forecasting model selection. These include mean square error (MSE), mean absolute deviation (MAD), mean absolute percentage error (MAPE) [4, 5], mean absolute relative deviation (MARD), and fraction of accurate prediction (FAP) [6].
This article will describe the MAD technique, which is user friendly, easy to understand, and a good measure in practice [2], though when using MAD it may be beneficial to also compute an error measure of bias, such as mean error (ME), which provides the direction of error [7].

        3.  Mean absolute deviation (MAD)

MAD is a simple assessment of demand pattern variance, and is calculated as follows[2]: Mad = sum of absolute deviations from mean/ number of periods included in the sum. It is best explained by examples, as follows.

        3.1  Moving average

Table 2 from article [9], demonstrate a moving average of 3 previous observations. By checking another amount of observations, forecast accuracy can be compared by MAD, as illustrated in Table 1, using two moving averages: 3 and 4 previous observations.

Table 1: Example of three and four moving averages, with MAD testing

Month	Demand (thousands)	Moving average of 3 previous observations	Absolute deviations from mean, 3 previous observation	Moving Average of 4 previous observations	Absolute deviations from mean, 4 previous observation
1	18
2	23
3	33
4	27	24.67	2.33
5	21	27.67	6.67	25.25	4.25
6	26	27.00	1.00	26	0
7	44	24.67	19.33	26.75	17.25
8	32	30.33	1.67	29.5	2.5
9	21	34.00	13.00	30.75	9.75
10	35	32.33	2.67	30.75	4.25
11	36	29.33	6.67	33	3
MAD			6.67		5.86

*Editor's Note: generate your own moving average forecasts and MAD assessments here

The example above illustrates a better result for a 4-period moving average, indicated by MAD. The same way, the moving period may be increased in order to examine the optimal timeframe for the moving average technique.

        3.2  Weighted moving average

Given Table 3 from [9], let’s check the number of observations that best measures accuracy.
Table 2: Example of three and four weighted moving averages, with MAD testing.

Month	Demand (thousands)	Weight	Demand × Weight	Moving average of 3 previous observations	Absolute deviations from mean, 3 previous observation	Moving Average of 4 previous observations	Absolute deviations from mean, 4 previous observation
1	18	0.9	16.2
2	23	0.91	20.93
3	33	0.92	30.36
4	27	0.93	25.11	22.50	4.50
5	21	0.94	19.74	25.47	4.47	23.15	27.00
6	26	0.95	24.7	25.07	0.93	0.93	2.15
7	44	0.96	42.24	23.18	20.82	24.98	1.97
8	32	0.97	31.04	28.89	3.11	27.95	19.02
9	21	0.98	20.58	32.66	11.66	29.43	4.05
10	35	0.99	34.65	31.29	3.71	29.64	8.43
11	36	1	36	28.76	7.24	32.13	5.36
MAD					7.06		9.71

The example above demonstrates a better result for a 3-period moving average, indicated by MAD. The same way, the moving period may be increased in order to obtain the optimal timeframe for the moving average technique.
When comparing the two examples above, the unweighted moving average seems to be better. Therefore, the weight assigned may be changed to achieve a better result.

        3.3  Exponential smoothing

Article [8], provides an example for exponential smoothing forecast with α=1. By choosing different values for α forecast accuracy may be compared with MAD as follows.
Table 3 contains the demand values from Table 2, and measures exponential smoothing forecast with three α values.

Table 3: Measuring exponential smoothing forecast with three α values

Month	Demand (thousands)	Forecast α=0.1	|Forecast-Demand|	Forecast α=0.2	|Forecast -Demand|	Forecast α=0.3	|Forecast-Demand|
1	18	18.00		18.00		18.00
2	23	18.00	5.00	18.00	5.00	18.00	5.00
3	33	18.50	14.50	19.00	14.00	19.50	13.50
4	27	19.95	7.05	21.80	5.20	23.55	3.45
5	21	20.66	0.34	22.84	1.84	24.59	3.58
6	26	20.69	5.31	22.47	3.53	23.51	2.49
7	44	21.22	22.78	23.18	20.82	24.26	19.74
8	32	23.50	8.50	27.34	4.66	30.18	1.82
9	21	24.35	3.35	28.27	7.27	30.73	9.73
10	35	24.01	10.99	26.82	8.18	27.81	7.19
11	36	25.11	10.89	28.46	7.54	29.97	6.03
MAD			8.87		7.80		7.25

Table 3 demonstrates a better result for α=0.3, as indicated by MAD. The same way, the exponential smoothing forecast may be measured with different values for α.
From the three examples, the simple moving average of four previous observations appears to provide the best results.

        4.  Summary

There is a wide range of forecasting methods, and techniques to choose from, some of which require statistical knowledge and expertise. The article presented the topic and provided some in-depth numerical examples for the mean absolute deviation method, a common and easy to understand technique.

This is the forth in the article set of forecasting techniques:
Part 1 introduces the demand forecasting issue, and demonstrated the weighted and unweighted moving average technique
Part 2 demonstrates the simple exponential smoothing technique.
Part 3 presents regression analysis.

        4.1  Some thoughts on processes and leadership responsibility
Forecasting is used in many domains. Today’s competitive environment forces organizations to excel in their domain, and continuously innovate and advance with the aid of technology [10]. The success of companies in implementing promising strategies and new tactics [11, 12], largely depends not only on efficient processes [13], but also on leadership and management style [14-16]. Organization’s leadership and the Top Management Team (TMT) is responsible to work culture in the organization, giving room for social interactions [17], affecting workers happiness [18], which in turn may also affect the company’s stock price [19].

Bibliography

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