## 3 Materials and Methods  
### Data  
#### 3.1.1 Data Collection and Observations  
The dataset used in the proposed method was extracted from a database of the sales volume of about 3000 items sold in the POS (point of sale) system of a local food retail store in Wanju, South Korea. The time-series data of five items (WelshOnion, Lettuce, ChineseMallow, Onion, and JujubeMiniTomato) that showed the least number of missing dates were chosen. The sales period for the five items was from June 2014 to December 2019, so each sales time-step was around T = 2000 days or more, where T is the total number of time-steps. Table 1 presents the sales periods and the sales days of the five items.  
The difference between the number of days (T) and the sales days in Table 1 is due to the fact that the data contains missing values for various reasons, such as holidays at the Wanju local food retail store and a lack of supply of certain products. Figure 1 shows the sales volume data of the five items.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Item** & **Sales Days** & **Period** & **T** \\ \hline
1 & WelshOnion & 2014 & 1 June 2014–31 December 2019 & 2040 \\
2 & Lettuce & 2014 & 1 June 2014–31 December 2019 & 2040 \\
3 & ChineseMallow & 2012 & 1 June 2014–31 December 2019 & 2040 \\
4 & Onion & 2009 & 1 June 2014–31 December 2019 & 2040 \\
5 & JujubeMiniTomato & 2011 & 1 June 2014–31 December 2019 & 2040 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The sales periods and the sales dates of the five items.  
Figure 1: Cont.  
Figure 2 shows the distribution of the values in the dataset for the five items. We noticed the presence of outliers in Figure 2. Outliers result from mistakes in sales volume input, such as numerical unit errors or decimal point notation errors in sales volume.  
Figure 3 shows the correlation between each pair of the five items, and all correlations show weak relationships. The top-two most correlated pairs are Onion-Lettuce (0.36) and JujubeMiniTomato-ChineseMallow (0.35), while the least correlated pair is the JujubeMiniTomato- WelshOnion (0.00011). Figure 4 shows the average sales volumes by day, month, and quarter of Lettuce sales data from 1 June 2014 to 31 December 2019. Figure 3(a) shows that the average sales volume is the highest on Saturday, followed, in order, by Sunday and Friday. In Figure 3(b), it can be seen that average sales are highest in March, followed, in order, by April and August. Figure 3(c) shows that average sales are in descending order of the first, third, second, and fourth quarters. Average sales in the second and third quarters are similar. As it shows a high degree of seasonality, embedding the seasonality information in the prediction models as weekly, monthly, and quarterly features is expected to improve prediction accuracy.  
Figure 1: Sales volumes of five items (WelshOnion (**a**), Lettuce (**b**), ChineseMallow (**c**), Onion (**d**), and JujubeMiniTomato (**e**)). Note that the y-axis scale of each plot is different. The first 60% was used for the training subset (blue line), the next 20% was used for the validation subset (orange line), and the most recent 20% was used for the test subset (green line).  
Figure 2: Boxplot of sales volumes of five items (WelshOnion (WO), Lettuce (L), ChineseMallow (CM), Onion (O), and JujubeMiniTomato (JMT)).