## 2 Methodology
### Data Collection and Preprocessing for Labeling
#### 2.1.2 Labeling of Car Sales Movement Directions  
As mentioned in Section 1, this research selected the sales movement direction as the response variable of car sales prediction models. Hence, the monthly sales movement directions were labeled with the collected monthly sales volumes for six car brands. The three types of sales movement directions, Up (U), Flat (F), and Down (D) are defined in Equation (1). Since the intent of this research was to predict the car sales movement direction of the next month at this month, this equation indicates that the \(i\)th month's label \(l_{i}\) is determined by the \(i+1\)th month's monthly sales growth rate \((S_{i+1}-S_{i})/S_{i}\) and the predefined threshold \(h\).  
\[l_{i}=\left\{\begin{array}{rl}U,\ if\ (S_{i+1}-S_{i})/S_{i}>h\\ F,\ if\ -h\leq(S_{i+1}-S_{i})/S_{i}\leq h\\ D,\ if\ (S_{i+1}-S_{i})/S_{i}<-h\end{array}\right. \tag{1}\]  
Assume that the threshold \(h\) is set at 10%. The results of Equation (1), in Table 3, show the labeling results of each month from 2014 to 2019 based on the collected historical car sales volumes shown in Table 1.  
For example, the \(l_{1}\) (i.e., the label of 2014/1) of BMW is determined by the 2 nd month's (i.e., 2014/2's) monthly sales growth rate \((624\ -\ 1437)/1437=-56.58\%\) and the predefined threshold \(h=10\%\). As the 2 nd month's monthly sales growth rate, \(-56.58\%\), is smaller than \(-10\%\) (i.e., \(-h\)), the \(l_{1}\) of BMW is labeled as the Down direction \"D\". As mentioned in Section 2.1.1, for labeling the sales movement direction of 2019/12, i.e., \(l_{72}\), the car sales volume of 2020/1 must be collected. For the example of the \(l_{72}\) of Lexus, the 73 rd month's monthly sales growth rate \((2687-2348)/2348=14.44\%\) is greater than the threshold \(h=10\%\); the \(l_{72}\) of Lexus should be labeled with an Up direction \"U\" according to Equation (1).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & & \\ \cline{3-8}
**No** & **Month** & **BMW** & **Lexus** & **Mazda** & **Benz** & **Toyota** & **VW** \\ \cline{3-8}  & & **Sales** & **Sales** & **Sales** & **Sales** & **Sales** & **Sales** \\ \hline
1 & 2014/1 & 1437 & 1207 & 691 & 1815 & 2471 & 897 \\
2 & 2014/2 & 624 & 806 & 231 & 1033 & 957 & 551 \\
3 & 2014/3 & 1294 & 971 & 477 & 1588 & 1653 & 1053 \\
4 & 2014/4 & 1393 & 1039 & 452 & 1692 & 1943 & 1154 \\
5 & 2014/5 & 1284 & 1310 & 466 & 1518 & 1783 & 1113 \\
6 & 2014/6 & 1424 & 1131 & 319 & 1620 & 2220 & 1414 \\
7 & 2014/7 & 1469 & 1481 & 618 & 1616 & 2631 & 959 \\
8 & 2014/8 & 1190 & 593 & 325 & 1389 & 983 & 914 \\
9 & 2014/9 & 1454 & 1193 & 444 & 1784 & 1615 & 1438 \\
10 & 2014/10 & 1630 & 1334 & 298 & 1695 & 1645 & 1313 \\
11 & 2014/11 & 1565 & 1094 & 434 & 1754 & 2031 & 795 \\
12 & 2014/12 & 2135 & 1148 & 517 & 1796 & 2805 & 1329 \\
13 & 2015/1 & 2040 & 787 & 1970 & 2086 & 2468 & 1095 \\
14 & 2015/2 & 1016 & 1193 & 609 & 1219 & 1575 & 720 \\ \hline
24 & 2015/12 & 1718 & 1634 & 1859 & 2024 & 2721 & 773 \\
25 & 2016/1 & 2045 & 1379 & 1697 & 2554 & 2003 & 980 \\ \hline
70 & 2019/10 & 1658 & 2233 & 1418 & 3037 & 5712 & 1118 \\
71 & 2019/11 & 1461 & 2556 & 1553 & 2555 & 5120 & 1103 \\
72 & 2019/12 & 1927 & 2348 & 1857 & 2721 & 4405 & 1399 \\
* & 2020/1 & 1355 & 2687 & 1122 & 2490 & 5686 & 1232 \\ \hline \hline \end{tabular} \({}^{*}\) The record of 2020/1 is for ensuing labeling.  
\end{table}
Table 1: The collected historical monthly car sales volumes.