A Sales Forecasting Model for the Consumer Goods with Holiday Effects
 DOI
 https://doi.org/10.2991/jracr.k.200709.001How to use a DOI?
 Keywords
 Consumer goods; sales forecasting; holiday effects; seasonal decomposition; ARIMA model; seasonal factor
 Abstract
In reality, there are socalled holiday effects in the sales of many consumer goods, and their sales data have the characteristics of double trend change of time series. In view of this, by introducing the seasonal decomposition and ARIMA model, this paper proposes a sales forecasting model for the consumer goods with holiday effects. First, a dummy variable model is constructed to test the holiday effects in consumer goods market. Second, using the seasonal decomposition, the seasonal factor is separated from the original series, and the seasonally adjusted series is then obtained. Through the ARIMA model, a trend forecast to the seasonally adjusted series is further carried out. Finally, according to the multiplicative model, refilling the trend forecast value with the seasonal factor, thus, the final sales forecast results of the consumer goods with holiday effects can be obtained. Taking the cigarettes sales in G City, Guizhou, China as an example, the feasibility and effectiveness of this new model is verified by the example analysis results.
 Copyright
 © 2020 The Authors. Published by Atlantis Press B.V.
 Open Access
 This is an open access article distributed under the CC BYNC 4.0 license (http://creativecommons.org/licenses/bync/4.0/).
1. INTRODUCTION
Sales forecasting refers to the estimation of sales quantity and sales amount of all products or specific products in a specific time in the future [1]. Sales forecasting is based on the full consideration of various influence factors in the future, combined with the actual sales performance of enterprises, through certain analysis methods to put forward practical sales objectives. Through sales forecasting, the initiative of sales staff can be mobilized, and the products can be sold as soon as possible, so as to complete the transformation from use value to value. Meanwhile, the enterprises can set production by sales, arrange production according to sales forecasting data, and avoid overstock of products. It can be seen that the accurate and reliable sales forecasting is of great significance to the formulation of enterprises marketing plan, safety inventory, normal operation of cash flow and so on.
At present, the commonly used qualitative forecasting methods in sales forecasting include: senior manager’s opinion method, salesperson’s opinion method, buyer’s expectation method and Delphi method, etc. In addition, the commonly used quantitative forecasting methods in sales forecasting include: time series analysis method [1], regression and correlation analysis method [1], artificial intelligence technology represented by neural network [2] and support vector regression machine [3], etc. The qualitative forecasting method is simple and easy, but it has strong subjectivity. It is difficult to make an accurate explanation for the future change trend, to make a quantitative explanation for the interaction degree between various forecasting objectives, to estimate the error of the forecasting results and to evaluate the reliability of the forecasting results. The quantitative forecasting method is less affected by subjective factors, which overcomes the shortcomings of qualitative forecasting method. However, there are socalled holiday effects in the sales of many consumer goods in reality, and their sales data have the characteristics of double trend change of time series, that is, the overall trend variability and seasonal volatility [4,5], which leads to the decrease of prediction accuracy and the increase of prediction risk of quantitative forecasting method.
The socalled holiday effects originally refer to the abnormal phenomenon of stock index return rate in the preholiday trading days and postholiday trading days compared with other trading days due to the change of people’s mood and behavior caused by the holiday in the stock market [6]. With the deepening of research, some scholars found that the holiday effects widely exist in consumer goods, tourism, film and television and many other fields. In terms of theoretical research on the holiday effects in consumer goods market, Hua [7] thought that for the phenomenon of holiday shopping, the economists call it “the period of consumption function mutation”, the sociologists call it “the period of consumption behavior impulse”, and the business counselors call it “holiday effects”. Chen [8] summed up the main characteristics of holiday economy, the impact of holiday economy on economic life, the consumption potential of holiday economy and its development countermeasures. In terms of empirical research on the holiday effects in consumer goods market, Li [9] made a sample analysis on the sales volume of social science books in Jingdong Mall in recent 3 years, which shows that there are holiday and weekend negative effects in book online sales. Gui and Han [10] took the monthly data of total retail sales of consumer goods from January 2000 to December 2009 as the research object, and used Bayes seasonal adjustment model to measure the holiday effects of household consumption. 곽영식 et al. [11] demonstrated empirically that replacement intervals of mobile phones sold in China online B2C are influenced by purchase points such as holidays. Cheng et al. [12] analyzed the fluctuations of the three fresh cut flower yields of roses, gypsophila and gerbera before and after the festival, which had the largest trading volume in Kunming International Flower Trading Center, the festival trading rules of fresh cut flowers in the auction market were then determined basically. Cai et al. [13] proposed an oracally efficient estimation for dense functional data with holiday effects, and applied it to analysis the sporting goods sales data.
In view of the sales forecast problem of the consumer goods with holiday effects, in Xie et al. [14], the time series of cigarettes sales was divided into trend component and cycle component. Based on the circular back propagation network model, the two components were predicted respectively, and the overall predicted value of cigarettes sales volume was obtained through combination. In Zou [15], according to the seasonal volatility of cigarettes sales, the paper selected the seasonal index prediction model as the basic prediction model of cigarettes sales, by introducing the lunar date, the prediction process and its system implementation method based on the lunar date were proposed. However, the former is limited by the defects of BP neural network, such as “black box”, difficulty in structure determination, low training efficiency and so on [16]; the latter assumes that the yearonyear growth rate of sales in the forecast month is equal to the yearonyear growth rate of total sales in the previous 12 months in trend prediction, its rationality is worth discussing.
Seasonal decomposition is to decompose the components of time series into four kinds: longterm trend factor (T), seasonal change factor (S), cycle change factor (C) and random fluctuation factor (I), etc. These components are then separated from time series to study their influence on the change of time series [17]. At present, the seasonal decomposition has been widely used in tax analysis and prediction, tourism passenger flow analysis and prediction, automobile sales analysis, agricultural product price prediction and other fields [17–20]. In addition, the ARIMA model not only considers the dependence of economic phenomena on time series, but also considers the interference of random fluctuation in the process of economic prediction, so that the ARIMA model has a relatively high prediction accuracy for the shortterm trend of economic operation [21,22]. In view of this, by introducing the seasonal decomposition and ARIMA model, this paper proposes a sales forecasting model for the consumer goods with holiday effects.
This paper is structured as follows: Section 2 constructs a dummy variable model to test the holiday effects in consumer goods market. Section 3 proposes a new model to forecast the sales of consumer goods with the holiday effects. Section 4 describes the example analysis results and Section 5 concludes this paper.
2. A TEST MODEL OF HOLIDAY EFFECTS IN CONSUMER GOODS MARKET
According to the connotation of holiday effects in consumer goods market and the test principle of holiday effects in stock market, the following dummy variable model is constructed to test the holiday effects in consumer goods market.
where, S(i)_{t} is the sales volume of the ith consumer goods in the tth period (month or day);
In this paper, the weighted least square method is used for parameter estimation, where the weight W is the reciprocal of the estimated value of residual obtained by ordinary least square method.
3. A SALES FORECASTING MODEL FOR THE CONSUMER GOODS WITH HOLIDAY EFFECTS
3.1. Seasonal Decomposition
Generally speaking, the information of time series can come from the following four aspects [17]: (1) Longterm trend refers to the continuous change of phenomena in a certain direction over a long period of time. The longterm trend is the result of the influence of some fixed and fundamental factors. (2) Seasonal change refers to the regular change with the change of seasons in a year under the influence of nature and other factors. (3) Cycle change refers to the regular period change with several years (months and quarters) as a certain period. The cycle change is different from the oneway continuous change of longterm trend and the fixed period rule of seasonal fluctuation, which is difficult to identify. (4) Random fluctuation refers to the irregular change of phenomena influenced by accidental factors.
Seasonal decomposition can subjectively decompose time series into four kinds of factors: longterm trend factor (T), seasonal change factor (S), cycle change factor (C) and random fluctuation factor (I), i.e. time series can be considered as a function of these four factors, it can be expressed as:
where, Y_{t} represents the time series, T_{t} represents the longterm trend factor (may be linear trend, may also be periodic fluctuation or long period fluctuation), S_{t} represents the seasonal factor (refers to the fluctuation with fixed amplitude and period, for example, the calendar effect is the common seasonal factor), C_{t} represents the cycle change factor and I_{t} represents the random fluctuation factor (may be regarded as error). The function f includes the additive model Y_{t} = T_{t} + S_{t} + C_{t} + I_{t} and the multiplicative model Y_{t} = T_{t} + S_{t} + C_{t} + I_{t} Where, the multiplicative model is often used [23].
In the sales of consumer goods with holiday effects, the quantity of each period is affected by many different factors. For example, the monthly sales volume will be affected by some factors, such as residents’ purchasing power, commodity price, commodity quality, customers’ preferences, seasonal change and so on. According to the historical sales data of consumer goods with holiday effects, the sales of consumer goods with holiday effects have the characteristics of double trend change of time series, that is, the overall trend variability and seasonal volatility [5]. In view of this feature, using the seasonal decomposition, the seasonal factor is separated from the original series, and the seasonally adjusted series is then obtained.
3.2. Trend Forecast
ARIMA model is a time series analysis model put forward by Box et al. in the 1970s. Its basic idea is as follows [21,22]: some time series are a group of random variables depending on time t, although the single series value of time series has uncertainty, the change of the whole series has certain regularity, therefore, which can be approximately described by the corresponding mathematical model. Time series model is a model based on its past value and random disturbance term. Its concrete form is
The above formula shows that a random time series can be generated by an autoregressive moving average process, that is, it can be interpreted by its own past or lag values and random interference terms. If the time series is stable, that is, its behavior will not change with the passage of time, the future can be predicted according to the past behavior of the series.
ARIMA(p, d, q) model is called differential autoregressive moving average model, where AR is autoregressive, p is the number of autoregressive terms; MA is the moving average, q is the number of moving average terms; I is single integer, d is the number of difference times (order) to make time series become stable series. The specific modeling steps of ARIMA(p, d, q) model include [21,22]: stability test and processing, model recognition, model order determination and model test, etc.
The characteristics of double trend prediction are the importance of the ranking of observation values, and the correlation between the frontback observation values and the same period ratio, that is, the correlation between the prediction point and the observation point close to each other is strong, while the correlation between the prediction point and the observation point far away from each other is weak [14]. Therefore, the ARIMA(p, d, q) model is established to predict the trend of the seasonally adjusted series in Subsection 3.1, and the trend prediction value in the prediction period is then obtained.
3.3. Sales Forecast of the Consumer Goods with Holiday Effects
According to the multiplicative model of the seasonal decomposition, refilling the trend forecast value obtained in Subsection 3.2 with the seasonal factor separated out in Subsection 3.1, that is, the corresponding seasonal factor is multiplied by the trend prediction value of the seasonally adjusted series in the prediction period, thus, the final sales forecast results of the consumer goods with holiday effects can be obtained.
4. EXAMPLE ANALYSIS
4.1. Sample Data
The original series of total monthly sales volume of cigarettes in G City, Guizhou, China from 2007 to 2010 was shown in Figure 1. The original data were from G City Branch, Guizhou Tobacco Company of China (see Table 1).
Time (monthyear)  Original series (Box)  Moving average series (Box)  Ratio of original series to moving average series (%)  Seasonal factor (%)  Seasonally adjusted series (Box)  Smoothed trendcycle series (Box)  Irregular (error) component 

JAN2007  20242.14  —  —  146.3  13839.430  14024.348  0.987 
FEB2007  13116.56  —  —  91.3  14365.099  14122.436  1.017 
MAR2007  13955.97  —  —  98.5  14162.779  14318.610  0.989 
APR2007  14054.03  —  —  96.7  14534.791  14498.119  1.003 
MAY2007  13811.13  —  —  93.7  14739.944  14628.354  1.008 
JUN2007  14045.40  —  —  95.5  14708.150  14707.775  1.000 
JUL2007  14883.09  14615.6077  101.8  100.7  14786.690  14750.661  1.002 
AUG2007  14433.64  14516.1466  99.4  98.5  14657.462  14760.819  0.993 
SEP2007  17377.90  14585.9138  119.1  116.4  14924.713  14852.390  1.005 
OCT2007  12893.89  14601.8745  88.3  87.5  14744.025  14932.850  0.987 
NOV2007  14535.67  14686.0441  99.0  95.0  15307.709  14826.872  1.032 
DEC2007  12037.88  14896.2546  80.8  80.0  15041.271  14645.788  1.027 
JAN2008  19048.61  14980.3642  127.2  146.3  13023.418  14375.738  0.906 
FEB2008  13953.76  15134.6609  92.2  91.3  15281.998  14580.863  1.048 
MAR2008  14147.50  15310.2532  92.4  98.5  14357.145  15027.746  0.955 
APR2008  15064.06  15469.7871  97.4  96.7  15579.378  15707.082  0.992 
MAY2008  16333.66  15598.9116  104.7  93.7  17432.113  16218.742  1.075 
JUN2008  15054.72  15727.3979  95.7  95.5  15765.091  16420.960  0.960 
JUL2008  16734.65  15838.1249  105.7  100.7  16626.259  16556.047  1.004 
AUG2008  16540.75  16429.4141  100.7  98.5  16797.244  16562.548  1.014 
SEP2008  19292.31  16409.1248  117.6  116.4  16568.869  16654.500  0.995 
OCT2008  14443.38  16632.9389  86.8  87.5  16515.855  16671.881  0.991 
NOV2008  16077.51  16768.1978  95.9  95.0  16931.437  16852.494  1.005 
DEC2008  13366.60  16763.3228  79.7  80.0  16701.505  16805.299  0.994 
JAN2009  26144.08  16901.4492  154.7  146.3  17874.548  16785.723  1.065 
FEB2009  13710.29  16926.9555  81.0  91.3  15015.350  16546.676  0.907 
MAR2009  16833.27  16918.0162  99.5  98.5  17082.714  16782.121  1.018 
APR2009  16687.17  17051.2879  97.9  96.7  17258.007  17021.664  1.014 
MAY2009  16275.16  17202.2155  94.6  93.7  17369.680  17293.307  1.004 
JUN2009  16712.23  17187.1725  97.2  95.5  17500.818  17227.649  1.016 
JUL2009  17040.72  17318.4606  98.4  100.7  16930.352  17164.595  0.986 
AUG2009  16433.48  17374.2949  94.6  98.5  16688.309  17322.005  0.963 
SEP2009  20891.57  17811.1228  117.3  116.4  17942.366  17561.015  1.022 
OCT2009  16254.51  17956.3201  90.5  87.5  18586.865  17831.815  1.042 
NOV2009  15896.99  18068.2965  88.0  95.0  16741.333  17890.310  0.936 
DEC2009  14942.06  18050.0652  82.8  80.0  18670.030  18389.016  1.015 
JAN2010  26814.09  18155.8828  147.7  146.3  18332.632  18826.967  0.974 
FEB2010  18952.23  18306.9824  103.5  91.3  20756.256  19328.173  1.074 
MAR2010  18575.64  18439.0649  100.7  98.5  18850.901  18981.047  0.993 
APR2010  18030.89  18467.9041  97.6  96.7  18647.690  18611.562  1.002 
MAY2010  16056.38  18346.4800  87.5  93.7  17136.192  18216.417  0.941 
JUN2010  17982.04  18648.9966  96.4  95.5  18830.546  18352.578  1.026 
JUL2010  18853.92  18587.4788  101.4  100.7  18731.804  18425.337  1.017 
AUG2010  18018.47  —  —  98.5  18297.878  18287.517  1.001 
SEP2010  21237.64  —  —  116.4  18239.582  18272.450  0.998 
OCT2010  14797.42  —  —  87.5  16920.699  18268.385  0.926 
NOV2010  19527.19  —  —  95.0  20564.345  18410.893  1.117 
DEC2010  14203.85  —  —  80.0  17747.637  18482.148  0.960 
Seasonal decomposition
It can be seen from Figure 1 that from 2007 to 2010, the original series shows the general characteristics of rising the bottom gradually and emerging two seasonal peaks in January and September every year. Therefore, it can be preliminarily judged that the total monthly sales volume of cigarettes in G City have the characteristics of double trend change of time series.
4.2. Test of the Holiday Effects
In this paper, the Spring Festival and National Day were selected as the holidays to investigate the holiday effects of cigarettes sales in G City. In order to facilitate comparison, the sample data were divided into two subgroups: the last month before the holiday (referred to as preholiday) and all other months (referred to as other). We used Excel software to make descriptive statistical analysis of sample data, and used Eviews7.2 software to do regression analysis of sample data.
The descriptive statistical analysis results of the original series were shown in Table 2. It can be seen from Table 1 that the preholiday average value is 21381.04 boxes, which is far higher than the other average value of 15631.69 boxes, reaching 1.3678 times. This preliminary shows that the cigarettes sales in G City have obvious preholiday effects. In addition, from the standard deviation point of view, the preholiday standard deviation is 3371.942 boxes, which is much higher than the other standard deviation of 1843.548 boxes, reflecting the greater preholiday volatility. Therefore, the followup needs to carry on the regression analysis to get the general conclusion.
Subgroups  Average value/Box  Maximal value/Box  Minimal value/Box  Standard deviation/Box  Sample sizes  Multiple of average value 

Preholiday  21381.04  26814  17378  3371.942  8  1.3678 
Other  15631.69  19527  12038  1843.548  40  1.0000 
Multiple of average value, preholiday average value/other average value.
Descriptive statistical analysis results
Using Equation (1), a dummy variable model was constructed, and the preholiday effects of cigarettes sales in G City were then test. The test results were shown in Table 3.
Variable  Coefficient  Std. Error  tStatistic  Prob. 

c  15645.03  141.3023  110.7203  0.0000 

5585.926  145.6055  38.36343  0.0000 
Test results of the preholiday effects
Table 3 shows that the constant term c is 15645.03 and the regression coefficient α is 5585.926 in this model. The tstatistic of α is 38.36343, and the corresponding probability pvalue is 0.0000, which shows that the regression coefficient α is significant at the 1% significance level. The goodnessoffit (R^{2}) of the model is 0.9696, and the adjusted goodnessoffit (Adjusted R^{2}) is 0.9690, which shows that the fitting effect of the model is good, and the independent variable can explain 96.96% difference of the dependent variable. The observed value of Fstatistic is 1471.753, which is higher than the critical value (7.220) of Ftest at the 1% significance level. Therefore, the hypothesis of zero is rejected, which shows that the linear relationship between dependent variable and independent variable is very significant, and a linear model can be established. The above results show that the cigarettes sales in G City have the statistically significant positive preholiday effects.
4.3. Seasonal Decomposition Results
According to Subsection 3.1, using the seasonal decomposition function provided by SPSS18.0 software, we selected “Multiplicative” model (system default option) in the “Model Type” option group, and selected “All points equal” in “Moving Average Weight”, thus, we can get the seasonal decomposition table, as shown in Table 1.
Based on the original series, according to the specified moving average method and period, we obtained the moving average series. Its purpose was to eliminate the seasonal factors in the original series and get the trend value of the original series. According to the multiplicative model, the trend factors were removed from the original series, and the ratio of original series to moving average series was then obtained. We averaged the ratio of the same month in each year to get 12 averages, and then divided the 12 averages by the total ratio average, therefore, the seasonal factor for each month can be obtained. After removing the seasonal component from the original series, we got the seasonally adjusted series, and then smooth it to get the smoothed trendcycle series. Finally, the irregular (error) component was obtained by eliminating the cyclic fluctuation factors from the seasonally adjusted series [23]. The original series and seasonally adjusted series were shown in Figure 2.
In Figure 2, it can be seen that the original series shows the characteristics of fluctuating growth in annual cycle, and the seasonally adjusted series (i.e. the corrected monthly effects series) shows a steady growth trend in four years. The seasonal factor was shown in Figure 3.
In Figure 3, the seasonal factor fluctuates regularly in a 12month period. It can be found that the sales volume of cigarettes in January and September are larger than that in other months. Figures 2 and 3 further verify the observations in Subsection 4.1.
4.4. Trend Forecast Results
According to Subsection 3.2, we used SPSS18.0 software to build the ARIMA(p, d, q) model and forecast the trend of the seasonally adjusted series.
 (1)
Stability test and processing. The Augmented Dickey–Fuller (ADF) test results shown that the seasonally adjusted series was a firstorder stationary series, i.e. d = 1.
 (2)
Model recognition. Because the Partial Autocorrelation Function (PACF) graph and ACF graph of the stationary series were tailed, it can be determined that the stationary series was suitable for the ARMA model.
 (3)
Model order determination. The determining order method based on the optimal criterion function was used to determine the order of the model [24], i.e. we selected the group of orders minimizing the Akaike’s information criterion as the ideal order. Through the comparative test, the ARIMA(1, 1, 1) model was selected.
 (4)
Model test. Through observing the ADF test, ACF graph and PACF graph of the residual series of the ARIMA(1, 1, 1) model, it was confirmed that the residual series was the white noise series. Thus, the ARIMA(1, 1, 1) model was the best prediction model for the stationary series.
In the “Criteria” option group, we selected the “Nonseasonal ARIMA”, “None Transformation” and “Include constant in model”; selected the “Display forecasts” in the “Statistics” option group; set January to March 2011 as the forecast period in the “Selection” option group; and other items adopted the default options. The trend forecast results of the seasonally adjusted series were shown in Table 4.
Months  2011–01  2011–02  2011–03 

Forecast value/Box  19426.1  19430.3  19547.5 
Upper limit value/Box  21313.2  21319.1  21436.5 
Lower limit value/Box  17539.0  17541.5  17658.6 
The trend forecast results of the seasonally adjusted series
4.5. Sales Forecast Results
According to Subsection 3.3, refilling the trend forecast value in Table 4 with the seasonal factor in Table 1, i.e. the seasonal factor of the corresponding month was multiplied by the trend forecast value of the seasonally adjusted series, thus, the forecast results of the total monthly sales volume of cigarettes in G City from January to March 2011 were obtained, as shown in Table 5.
Months  Actual value/Box  Forecast value/Box  Error/%  Upper limit value/Box  Error/%  Lower limit value/Box  Error/% 

2011–01  30756.98  28420.36  −7.60  31181.21  1.38  25659.50  −16.57 
2011–02  18614.07  17739.86  −4.70  19464.35  4.57  16015.38  −13.96 
2011–03  19315.71  19254.33  −0.32  21114.98  9.32  17393.69  −9.95 
Error = (forecast value − actual value)/actual value.
The forecast results of the total monthly sales volume of cigarettes in G City from January to March 2011
Table 5 shows the relative error between the forecast value obtained by our model and the actual value of the total monthly sales volume of cigarettes in G City. The absolute average error after calculation is 4.20%, which shows that our model can better predict the change trend of the total monthly sales volume of cigarettes in G City, and can effectively simulate the seasonal, periodic and random characteristics of cigarettes sales. In addition, our model also gives the upper and lower limits of the forecast value, which provide a space for the empirical adjustment of the forecast value.
4.6. Comparative Analysis
In order to facilitate comparison, based on the original series, we also adopted respectively the nonseasonal ARIMA model, product seasonal ARIMA model [25] and seasonal exponential smoothing method  Winters multiplicative model to forecast the total monthly sales volume of cigarettes in G City from January to March 2011, the results were shown in Table 6. Where, the nonseasonal ARIMA (2, 1, 1) model and the product seasonal ARIMA(1, 1, 1)(1, 0 ,1) model were finally determined as the best prediction models for the stationary series after the modeling steps of stability test and processing, model recognition, model order determination and model test.
Months  Actual value/Box  Nonseasonal ARIMA(2, 1, 1)  Product seasonal ARIMA(1, 1, 1) (1, 0, 1)  Winters multiplicative model  Our model  

Forecast value/Box  Error/%  Forecast value/Box  Error/%  Forecast value/Box  Error/%  Forecast value/Box  Error/%  
2011–01  30756.98  20631.91  −32.92  26933.74  −12.43  27552.18  −10.42  28420.36  −7.60 
2011–02  18614.07  18583.61  −0.16  18669.34  0.30  17834.00  −4.19  17739.86  −4.70 
2011–03  19315.71  19305.21  −0.05  19465.53  0.78  18958.20  −1.85  19254.33  −0.32 
Absolute Average Error/%  —  11.05  —  4.30  —  5.49  —  4.20 
Error = (forecast value − actual value)/actual value.
Comparative analysis results
It can be seen from Table 6 that the absolute average error of our model is only 4.20%, which is lower than 5.49% of the Winters multiplicative model and 11.05% of the nonseasonal ARIMA(2, 1, 1) model, which is also slightly lower than 4.30% of the product seasonal ARIMA(1, 1, 1)(1, 0, 1) model. Especially in January 2011, when the seasonal fluctuation is prominent, the prediction error of our model is only −7.60%, which is significantly lower than the other three models. Which means that the prediction accuracy of our model is better, which shows good applicability in the double trend prediction and can meet the needs of practical application.
5. DISCUSSION
From the results and analysis of the previous section, we observed that our model was able to obtain the slightly higher prediction accuracy than the product seasonal ARIMA(1, 1, 1)(1, 0, 1) model [our method was 95.8%, and the product seasonal ARIMA(1, 1, 1)(1, 0, 1) model was 95.7%], and the higher prediction accuracy than the Winters multiplicative model and the nonseasonal ARIMA(2, 1, 1) model [the Winters multiplicative model was 94.51%, and the nonseasonal ARIMA(2, 1, 1) model was 88.95%].
Compared with the product seasonal ARIMA, Winters multiplicative model and the nonseasonal ARIMA model, our method can obtain the slightly higher or higher prediction accuracy. Since our model divides the sales forecasting into three stages. First, using the seasonal decomposition, the seasonal factor is separated from the original series, and the seasonally adjusted series is then obtained. Second, using the ARIMA model, a trend forecast to the seasonally adjusted series is further carried out. Finally, according to the multiplicative model, refilling the trend forecast value with the seasonal factor, thus, the final sales forecast results of the consumer goods with holiday effects can be obtained.
In addition, compared with literature [14], our model avoids the limitation of BP neural network in trend prediction. Compared with literature [15], our model overcomes the irrationality of hypothesis premise in trend prediction. Obviously, the advantage of our model is that it can give full play to the advantages of seasonal decomposition in dealing with seasonal change factor, and the advantages of ARIMA model in trend prediction at the same time. Therefore, our model has high prediction accuracy and low prediction risk in sales forecasting of the consumer goods with holiday effects. It should be noticed that the time span of the original series in this paper is from 2007 to 2010, and there are only 48 sample data, which may weaken the persuasiveness of the example analysis results. However, due to the trade secrets involved, the data problem cannot be solved temporarily.
6. CONCLUSION
There are socalled holiday effects in the sales of many consumer goods in reality, and their sales data have the characteristics of double trend change of time series, which leads to the decrease of prediction accuracy and the increase of prediction risk of quantitative prediction method. In view of this, by introducing the seasonal decomposition and ARIMA model, this paper proposed a sales forecasting model for the consumer goods with holiday effects. Taking the cigarettes sales in G City, Guizhou, China as an example, the feasibility and effectiveness of this new model was verified by the example analysis results. This paper provides a new method and idea for improving the sales forecasting accuracy of the consumer goods with holiday effects, which has high practical value.
The basic law of prediction is that the shorter the prediction period, the stronger the prediction ability of quantitative prediction method; the longer the prediction period, the weaker the prediction ability of quantitative prediction method. Therefore, in practical application, it is necessary to establish a sales forecasting system based on our model to make realtime dynamic sales forecast for the consumer goods with holiday effects.
It should be noticed that the seasonal decomposition artificially decomposes time series into four fixed components; however, its scientific nature needs to be further verified. In addition, since the information used in a single prediction method is limited, only one method is used to predict the same problem, the prediction accuracy is often not high, and the prediction risk is large [26]. Therefore, in order to improve the forecast effect, it is worth further study to establish a sales combination forecasting model for the consumer goods with holiday effects [27].
CONFLICTS OF INTEREST
The authors declare they have no conflicts of interest.
AUTHORS’ CONTRIBUTION
MZ contributed in conceived and designed the experiments. CY contributed in performed the experiments. XH contributed in analyzed the data. MZ and XH contributed in paper drafting and final revision.
ACKNOWLEDGMENTS
To the Regional Project of National Natural Science Foundation of China (71861003) and the Innovative Exploration and New Academic Seedlings Project of Guizhou University of Finance and Economics (GuizhouScience Cooperation Platform Talents [2018] 5774016) for their support.
REFERENCES
Cite this article
TY  JOUR AU  Mu Zhang AU  Xiaonan Huang AU  Changbing Yang PY  2020 DA  2020/07/15 TI  A Sales Forecasting Model for the Consumer Goods with Holiday Effects JO  Journal of Risk Analysis and Crisis Response SP  69 EP  76 VL  10 IS  2 SN  22108505 UR  https://doi.org/10.2991/jracr.k.200709.001 DO  https://doi.org/10.2991/jracr.k.200709.001 ID  Zhang2020 ER 