2016 Joint International Conference on Economics and Management Engineering (ICEME 2016) and International Conference on Economics and Business Management (EBM 2016) ISBN: 978-1-60595-365-6 Sales Forecast for Amazon Sales Based on Different Statistics Methodologies Jian-hong YU 1,*, Xiao-juan LE 2 1 Business School, Jianghan University, Wuhan, Hubei 430056, China 2 China General Nuclear Power Corporation, Futian District, Shenzhen, Guangdong 518120, China *Corresponding author Keywords: Forecasting, Winters exponential smoothing, Time-series decomposition, ARIMA. Abstract. Accurate sales forecast plays an important role in reducing costs and improving customer service levels, especially for B2C e-commerce. This paper tries to forecast future sales at Amazon based on historical sales data. Firstly, it proposes three possible forecasting approaches according to the historical data pattern, that is Winters exponential smoothing, time-series decomposition and ARIMA. Secondly, it specifies three relatively accurate and suitable approaches. Then, a sensitivity analysis will be conducted on the three methods, considering the suitability of the forecast methods will be judged by whether or not they produce random residuals. Finally the three methods will be implemented to forecast Amazon s quarterly sales in 2014. The result can help Amazon well manage its future operation especially for the season sales at Christmas. Introduction For an online retailer, the special online shopping festival, such as the Black Friday and Cyber Monday in USA, and the NOV 11 in China, makes up a substantial percentage of sales. This is especially true for Amazon.com. In the Black Friday of 2013, Amazon sold four million items, at a rate of around 41 items per second. In order to provide better service during the holiday shopping season, Amazon hired 15,000 temporary staff and 2,300 extra permanent employees. During this season, it is a major challenge for Amazon to allocate resources such as employees, the third part logistics and items, to attain higher customer satisfaction. Therefore, it is useful to forecast future quarterly net sales, which can help Amazon prepare for future Black Fridays and Cyber Mondays. There are some methods that usually used to forecast the demand in short time, such as Winters [1], Time series analysis [2-3] and ARIMA [4-5]. J.N. Xue and Z.K. Shi [6] adopts chaos time series theory to forecast short-time traffic flow. P. Zhou et. al. use ARIMA-BP combination model [7] to forecast the traffic demand of civil aviation tourism. L. Zhou and X.L. Yong [8] establish ARIMA(0, 2, 2) model using stationary data of historical electricity consumption, and make an empirical case on Beijing City. Nowadays, some researchers use different methods to forecast the e-commerce demand. Y.F. Tang [9] uses RBF neural network and SVM (support vector machine) to construct a dynamic demand forecasting system of fresh agricultural products for e-commerce, and analyzes the forecasting system with application of MATLAB simulation software to compare their effectiveness. Y.Y. Fan [10] uses the brief elaboration regarding coalition analysis method to forecast the product demand of demand chain in e-commerce, and states the coalition analysis method on the case of MP3 production. The result indicates that the coalition analysis may improve the accuracy of product demand forecast. However, these papers doesn t consider the special shopping festival of online shopping, such as Double 11 and Double 12. As we know, only Q. Zheng [11] try to forecast the e-commerce demand on Double 11. Q. Zheng [11] forecasts the demand of Taobao in NOV 11 with linear regression, exponential regression, logarithm regression, power multiply regression, and polynomial regression models, and points out that the polynomial regression model is better than others.
In this paper, we will try to use different forecasting methodologies to forecast Amazon s future quarterly net sales, based on its historic quarterly data. First, we will use three different methods to forecast the quarterly net sales in 2013. Then we will test and justify different approaches by comparing forecasting data with the actual net sales in 2013, and find the best approach suitable for forecasting future quarterly net sales at Amazon. Finally, we will conduct a sensitivity analysis and implement the best method to forecast Amazon s quarterly sales in 2014. Data Collection and Forecasting Methodologies In this paper, we will try to forecast the quarterly net sales in 2013 and then compare the actual and forecasting data. Usually, there is seasonality present in a retailer s sales, resulting from the holiday shopping season. Thus, it is important to collect data continuously. We obtained Amazon s net sales of the first quarter to the third quarter from 2000 to 2013, then we attained the fourth quarter on the website of Amazon, which amounted to a total of 56 observations (actual net sales data). There is seasonality present in the sales of Amazon. Sales were the highest in the fourth quarter of each year throughout the data. This is typical for a retailer since the fourth quarter encompasses the holiday shopping season that typically runs from late November through the end of December. In addition, sales have been increasing over time. The deseasonlized sales chart shows that sales have been rising at an increasing rate. Based on the analysis of the data pattern, we can use Winters exponential smoothing, time-series decomposition and ARIMA (Autoregressive Integrated Moving Average model) to forecast Amazon s quarterly net sales. The comparison of different forecasting approaches can be categorized as shown in Table 1. Table 1. Comparison of different forecasting method. Approach Data pattern Number of observations Forecasting Horizon Winters Trend and Seasonality At least 4 to 5 per season Short to medium Time series Trend, seasonal and cyclical Enough to see two peaks patterns and troughs in the cycle Short, medium and long ARIMA Stationary or transferred to stationary Minimum 50 Short, medium and long Sales Forecasting and Residual Analysis Winters Exponential Smoothing Winters Exponential Smoothing allows for both trend and seasonal patterns of the data to be taken into account as the smoothing process is applied. A Winters Exponential Smoothing forecast model is created using sales as the dependent variable, time as the independent variable, and a seasonality of four. The forecast result attained from STATGRAPHIC Centurion using Winters Exponential Smoothing is shown in Fig 1 and Table 2. Figure 1. Plot for forecasting sales ($000) of Amazon using Winters Exponential Smoothing.
Table 2. Quarterly forecasting sales in 2013 using winters exponential smoothing. Period Forecast($000) Lower 95.0% Limit Lower 95.0% Limit Q1/13 15,796,700 14,993,700 16,599,800 Q2/13 14,771,000 13,867,900 15,674,200 Q3/13 16,005,800 14,859,600 17,152,000 Based on calculation, the RMSE equals 803,296, accounting for 3.14% of the actual average sales in 2013. Intuitionally, the method of Winters Exponential Smoothing can be applied to this forecast. The residuals of this forecast are random (for the non-zero P-values ) and thus Winters Exponential Smoothing method can be applied to the quarterly sales forecasting of Amazon in 2013. Time Series Decomposition (Improved) The time series decomposition model is used by finding the linear trend of the data, along with a seasonality index and a cyclical factor. To use this method, the centered moving average, and the centered moving average trend need to be found. In this model, a central moving average trend is established using the central moving averages of the past four quarters. This trend will then be multiplied by a seasonal index for each quarter, as well as a cyclical factor in order to forecast sales for 2013. However, after testing we found the residuals are not random. To use time series decomposition, the Box Jenkins methodology will have to be used to adjust the forecast. To do this, the residuals will be forecasted for 2013 using an ARIMA model, and these forecasted residuals will be added to the previous forecast to obtain the new forecast for 2013. The adjusted forecasts and residuals using the Box Jenkins methodology are shown in Table 3. Table 3. Quarterly forecasting sales in 2013 using improved time series decomposition ($000). Date Previous Forecast Box Jenkins Adjustment Updated Forecast Q1/13 11,211,000 5,179,360 16,390,360 Q2/13 10,205,300 5,621,420 15,826,720 Q3/13 10,437,300 6,186,300 16,623,600 Q4/13 16,854,700 8,005,830 24,860,530 Based on calculation, the RMSE equals 464,986, accounting for 1.82% of the actual average sales in 2013, and indicating a small forecasting deviation. Intuitionally the method of ARIMA can be applied to this forecasting for the smaller RMSE and forecasting deviation. We can find that the residuals are random based on residual-randomness testing result (for the non-zero P-values ). Thus, ARIMA is a good model that can be used to forecast Amazon quarterly sales in 2013. ARIMA In ARIMA model, a number of ARIMA models will be compared, and the model that produces random residuals with the lowest RMSE for the 2000 to 2012 sales will be used to forecast the 2013 sales. From the data pattern, we can find that the data is non-stationary because of the upward trend. From the data pattern, we can find that the data is non-stationary because of the upward trend. Thus, we can use the Box-Jenkins method can be used to deal with the data and then a best model will be identified. Then ARIMA model, with chosen p, q and d, can be used to forecast the Amazon quarterly sales in 2013. After testing by Box-Jenkins, we can identify ARIMA (0,1,1)*(2,0,2) model is possible for this data series. The forecasting result attained from STATGRAPHIC Centurion using ARIMA (0,1,1)*(2,0,2) is show in Table 4 and Fig 2.
Table 4. Quarterly forecasting sales in 2013 using ARIMA($000). Period Forecast Lower 95% Limit Upper 95% Limit Q1/13 16,062,400 15,518,200 16,606,700 Q2/13 15,648,300 14,878,600 16,418,000 Q3/13 17,192,800 16,250,100 18,135,400 Q4/13 27,423,500 26,335,000 28,512,000 Figure 1. Plot for forecasting sales ($000) of Amazon using ARIMA. Based on calculation, the RMSE equals 920,062, accounting for 3.60% of the actual average sales in 2013, indicating a small forecasting deviation. Intuitionally the method of ARIMA can also be applied to this forecasting for the smaller RMSE and forecasting deviation. We can find that the residuals are random based on residual randomness testing result (for the non-zero P-values). Accordingly, ARIMA is a good model that can be used to forecast Amazon quarterly sales in 2013. Sensitivity Analysis Before selecting which model to adopt, Amazon will also want to know which of these forecasts are more sensitive to small changes in the data. This is important because Amazon will want to know how their chosen forecast method will react to slight changes in sales. For this section, the 2013 sales will adjust upward and downward slightly. The forecast methods that return a greater variance for future forecasts based on the adjustments to the sales in 2013, which will be judged to be more sensitive to changes in the data. Specifically, Amazon s sales will be forecasted for 2014 to 2016 for three cases: 1) after decreasing sales by 2 percent for each quarter of 2013, 2) after increasing sales by 2 percent for each quarter of 2013, and 3) after keeping 2013 sales the same, which will be referred to as the base forecasts. To accomplish this, 12 forecasts will be taken. The first four forecasts will be summed to determine the forecasted annual sales for 2014, and so on. The variance between forecasts for the two percent decrease and increase will be used to determine the sensitivity of the forecast. Sensitivity Analysis of Winters Model Table 5 shows the annual forecasts for 2014 through 2015 using Winters Exponential Smoothing. The total variance in sales between the 2 percent decrease and increase is $26.8 billion. Table 5. Annual forecasts for 2014 through 2015 using Winters Model ($000). 2014 2015 2016 2014-2016 -2% 84,530,400 95,791,000 107,051,500 287,372,900 Base 87,477,400 100,330,500 113,183,800 300,991,700 2% 90,334,000 104,727,900 119,121,800 314,183,700 Variance 5,803,600 8,936,900 12,070,300 26,810,800
Sensitivity Analysis of Time-Series Decomposition Model Table 6 shows the annual forecasts for 2014 through 2015 using Time-Series Decomposition with a Box Jenkins Adjustment. The total variance in sales between the 2 percent decrease and increase is $32.7 billion. Table 6. Annual forecasts for 2014 through 2015 using Time-Series Model ($000). 2014 2015 2016 2014-2016 -2% 84,946,660 94,957,460 102,482,220 282,386,340 Base 88,305,940 100,491,520 110,507,360 299,304,820 2% 91,489,970 105,655,830 117,995,200 315,141,000 Variance 6,543,310 10,698,370 15,512,980 32,754,660 Sensitivity Analysis of ARIMA Model Table 7 shows the annual forecasts for 2014 through 2015 using the ARIMA model. The total variance in sales between the 2 percent decrease and increase is $32.9 billion. Table 7. Annual forecasts for 2014 through 2015 using ARIMA Model ($000). 2014 2015 2016 2014-2016 -2% 86,175,800 102,635,900 122,829,900 311,641,600 Base 89,617,800 108,076,000 130,473,100 328,166,900 2% 93,059,900 113,497,500 138,063,500 344,620,900 Variance 6,884,100 10,861,600 15,233,600 32,979,300 Overall, it appears that the Winters Exponential Smoothing forecast is the least sensitive to changes in the data, while the Time-Series Decomposition with the Box Jenkins adjustment forecast and the ARIMA model forecast are similarly sensitive to changes. We found the Time-Series Decomposition with a Box Jenkins Adjustment and the ARIMA model were more sensitive to changes in the data, they may be more likely to pick up on small changes in the data that do impact future sales, and therefore, possibly provide more accurate forecasts. However, as mentioned above, if the small changes will not impact future sales, then these models are less likely to be accurate. Since the Winters Exponential Smoothing model is less sensitive to changes, it may be less quick to react to changes in the data. However, since it is less sensitive, it may also be the best model to predict sales at Amazon for more than a couple of years in advance. Implementation for Amazon Three methods were used to forecast the quarterly sales of Amazon in 2013, then we compared the forecasting results with the actual data and find the three best methods to do the sales forecasting for Amazon Winters, Time-Series and ARIMA, among which improved Time-Series is strongly recommended to do the forecast for the smallest RMSE. The result of above three methods to forecast quarterly sale of Amazon in 2014 is shown in the Table 8. Table 8. Quarterly sales forecasts for Amazon in 2014 ($000). Winters' Time Series ARIMA Q1/14 19,251,800 18,578,000 19,925,600 Q2/14 18,300,500 17,576,700 19,024,300 Q3/14 19,688,400 18,779,200 20,597,600 Q4/14 30,236,700 28,614,100 31,859,200 Actually, we found the real sale in different quarter in 2014 is $19,741million, 19,340 million, 20,579 million and $29,328 million in Amazon web site, which demonstrate above three methods can all be used for the sale forecasting for Amazon due to small deviations.
However, from the practical operation management of Amazon, it s very much important to forecast the sales in the fourth quarter, because of the greatly expanded demand compared with other three quarters. In this respect, after comparing we found the improved Time Series approach is more suitable because the forecasting deviation is only 2.4% compared with the real sales. Thus this result reflects the same forecasting accuracy as show in the forecasting part, in which the RMSE is the smallest under the method of Time Series Decomposition (Improved). Conclusion In this paper, we analyze three methods to forecast sales for Amazon based on the historical data. The results show that all above three methods can be put into practice to forecast sales for Amazon, and the sensitivity of Winters Exponential Smoothing is less than the other two methods. Based on the forecasting result, Amazon can have a big picture of the demand and then to take relevant measures to arrange resources, such as hiring more employees, storing more items or expanding shipping capacity, and thus to offer good service to improve customer satisfaction. Though, the forecasting error (RMSE) of the above three methods is very small and can be applied to the forecast of Amazon sales, there are still some obstacles to using these methods as follows. One major obstacle impeding the implementation of the forecast is the necessary data to precisely carry out the forecast. Amazon s quarterly sales are influenced by many diverse factors, such as population, disposable household income, interest rate, macroeconomic trend and so on. Acknowledgement This research was financially supported by the National Science Foundation (71471084). References [1] D.Y. He, L. Luo, An improved winters model for airline demand forecast. Journal of Transportation Systems Engineering and Information Technology, 6(2006), 103-107. [2] S.G. Makridakis, S.C. Wheelwright, Forecasting Methods for Management, 5th Edition, Wiley, (1989). [3] E. Bouding, Times Series Analysis: Forecast and Control. New York: Prentice Hall Inc, (1994). [4] P.A. Butler, Prior information and ARIMA forecasting. Journal of Forecasting, 1(1982), 375-383. [5] L. Bianchi, R.C. Hanumara, Improving forecasting for telemarketing centers by ARIMA modeling with intervention. International Journal of Forecasting, 14(1998), 497-504. [6] J.N. Xue, Z.K. Shi, Short-time traffic flow prediction based on chaos time series theory. Journal of Transportation Systems Engineering and Information Technology, 8(2008), 68-72. [7] Zou P, Yang J S, Fu J R, et al. Artificial neural network and time series models predicting soil salt and water content [J]. Agricultural Water Management, 2010, 97(12): 2009-2019. [8] L. Zhou, X.L. Yong, Electricity demand forecasting based on ARIMI model and linear neural network. Journal of Ludong University (Natural Science Edition), 31(2015), 277-282. [9] Y.Y. Fan, Research on product demand forecasting model for demand chain under e-business. Harbin Institute of Technology, (2008). [10] Y.F. Tang, Dynamic demand forecasting of fresh agricultural products in e-commerce circumstance. Nanjing University, (2014). [11] Q. Zheng, Taobao how to deal with the shopping event of NOV 11 of 2015. The Journal of ideological front, 41(2015), 26-28.