Sales Forecasting Using Statistical Analysis

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Sales Data

Table 1. Company sales data and forecast sales for 36 months.

Month Sales ($ Million) Alpha Beta SE AD
1 400.00 190.16 304.921 3.528
2 440.00 400.00 209.17 135.413 43.528
3 206.00 416.00 97.93 -50.966 190.472
4 590.00 332.00 280.48 283.759 193.528
5 330.00 435.20 156.88 33.960 66.472
6 290.00 393.12 137.86 24.508 106.472
7 323.00 351.87 153.55 70.288 73.472
8 480.00 340.32 228.19 195.744 83.528
9 350.00 396.19 166.39 68.709 46.472
10 410.00 377.72 194.91 123.686 13.528
11 570.00 390.63 270.97 239.198 173.528
12 290.00 462.38 137.86 -10.121 106.472
13 374.00 393.43 177.80 88.388 22.472
14 280.00 385.66 133.11 20.617 116.472
15 410.00 343.39 194.91 140.847 13.528
16 390.00 370.04 185.40 112.280 6.472
17 508.00 378.02 241.50 198.239 111.528
18 450.00 430.01 213.93 128.030 53.528
19 380.00 438.01 180.65 70.671 16.472
20 450.00 414.80 213.93 135.634 53.528
21 410.00 428.88 194.91 98.103 13.528
22 480.00 421.33 228.19 155.241 83.528
23 530.00 444.80 251.96 181.622 133.528
24 380.00 478.88 180.65 50.236 16.472
25 410.00 439.33 194.91 92.881 13.528
26 430.00 427.60 204.42 113.992 33.528
27 499.00 428.56 237.22 166.110 102.528
28 290.00 456.73 137.86 -7.299 106.472
29 350.00 390.04 166.39 71.786 46.472
30 265.00 374.02 125.98 14.998 131.472
31 278.00 330.41 132.16 46.713 118.472
32 299.00 309.45 142.14 73.204 97.472
33 321.00 305.27 152.60 92.065 75.472
34 380.00 311.56 180.65 133.894 16.472
35 490.00 338.94 232.94 204.060 93.528
36 540.00 399.36 256.71 211.963 143.528
Mean value
396.4722222
MSE
111.483
MAD
75.583

The figure below presents the time series of the company sales for a period of 3 years (36 months).

Time series 
Figure 1: Time series 
Time series analysis of company sales data using SE and AD
Figure 2. Time series analysis of company sales data using SE and AD

Discussion

The company sales have fluctuated from time to time, as seen in the figure above. The reason for the variation is not discussed in this paper. However, alpha and beta analyses were employed to predict sales over the proposed period. Although alpha and beta are used in forecasting, they play two different roles, hence the distinct difference in their results (Calle, 2019). Alpha is concerned with smoothing the time series curve by calculating the best coefficient for that particular purpose. On the other hand, beta forecasting is focused on smoothing the trend. Both forecasts use coefficients to achieve the purposes mentioned above. The analysis was carried out with an alpha= 0.4 and beta= 0.475394027.

Based on figure 1 above, the beta forecast is identical to the compare sales except that the two have a huge difference. The difference between the actual sales and the beta forecast sales is 207.991696. Statistically, such a colossal error value could significantly affect the validity of the results obtained. It implies that relying on this forecast strategy is ineffective and could potentially mislead the company in making financial forecasts and extensive budgeting processes.

The alpha forecast curve is almost similar to that of the actual company sales. However, the values differ from month to month, which clearly indicates the reliability of the alpha coefficient in forecasting company sales. As seen in the figure above, the alpha curve lags behind the actual sales curve. A rise or decline in the actual sales is followed by a subsequent rise or decline in the alpha forecasts, respectively. The average error in the alpha forecasts is 14.9734236, which is far much smaller than the earlier beta forecast error. The small error value can be attributed to higher levels of accuracy of the alpha forecast. Concerning the MAD and MSE, there is a significant discrepancy in the trends of the results obtained. Both analyses lie below the actual sales, with AD producing the lowest curve. The SE curve is congruent to the actual sales, which gives a good indication of foreseeably accurate predictions. The mean monthly sales were $ 396.4722222, MSE was $111.483, while the MAD was $75.583. The above discussion focused on the alpha and beta analysis, where alpha produced the best forecasts. In the second case, the squared error presents a more accurate prediction than the absolute deviation. The absolute deviation overlooks the potential variations caused by ignoring the negative values that arise from calculations.

With respect to the results obtained, the Alpha forecast is the best approach that the company can use to predict its future sales and financial performance. The results have shown that this approach has a small error value as compared to the beta approach. Besides, the visual presentation of the actual sales and respective forecasts shown in figure 1 is clear evidence of the reliability of the alpha approach. The values of the alpha forecast are almost the same as those of the actual sales, which makes it highly reliable. With reference to Mean absolute deviation (MAD) and mean square error (MSE), MSE is the better choice as it produces close and congruent results to the actual values.

References

Calle, M. Luz. “Statistical analysis of metagenomics data.” Genomics & informatics 17.1 (2019). Web.

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BusinessEssay. 2023. "Sales Forecasting Using Statistical Analysis." January 3, 2023. https://business-essay.com/sales-forecasting-using-statistical-analysis/.

1. BusinessEssay. "Sales Forecasting Using Statistical Analysis." January 3, 2023. https://business-essay.com/sales-forecasting-using-statistical-analysis/.


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