## 2 Methodology
### Prediction Model Structure Construction
#### 2.2.1 The Classical Model  
In this research, the classical model was created as the baseline for prediction performance for comparison with the sentimental and the CNN-LSTM models. The classical model adopted the most frequently used predictor variables for sales forecasting, including historical sales data and seasonality data, to predict the car sales movement direction. For example, Table 4 is the dataset prepared for creating the classical model for BMW. The monthly car sales volumes and monthly labeling data were retrieved from Table 3. As for seasonality data, car companies in Taiwan usually start different sales campaigns in specific months to promote sales, so monthly car sales volumes exhibit strong seasonality. In this research, the seasonality data, namely, the month number and the same-month-last-year sales movement direction labels were added, as shown in Table 4, to improve the accuracy of predictions of car sales movement directions. Furthermore, since three types of car sales movement directions (U, F, and D) were defined in this research, the MLR, a generalized logistic regression for solving the problems with more than two classes [22], was selected as the forecasting method of car sales movement directions. Hence, the classical model for forecasting car sales movement directions in Taiwan can be expressed by Equation (2):  
\[y_{i}=\beta_{0}+\beta_{1}x_{i1}+\beta_{2}x_{i2}+\beta_{3}x_{i3}+\epsilon \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Date**} & \multicolumn{3}{c}{**Discussion Forums**} & \multicolumn{3}{c}{**Social Media**} & \multicolumn{3}{c}{**Q&\&A Websites**} & \multicolumn{3}{c}{**Blogs**} & \multicolumn{3}{c}{**News**} \\ \cline{2-13}  & *** P** & **N** & **T** & **P** & **N** & **T** & **P** & **N** & **T** & **P** & **N** & **T** & **P** & **N** & **T** \\ \hline
2014/1/1 & 32 & 18 & 98 & 6 & 1 & 32 & 0 & 0 & 0 & 5 & 2 & 11 & 6 & 1 & 9 \\
2014/1/2 & 31 & 24 & 128 & 4 & 2 & 26 & 0 & 0 & 0 & 4 & 2 & 10 & 19 & 1 & 42 \\
2014/1/3 & 35 & 24 & 101 & 9 & 6 & 50 & 0 & 0 & 0 & 3 & 2 & 15 & 10 & 3 & 29 \\ \hline
2014/1/29 & 23 & 26 & 109 & 4 & 7 & 43 & 3 & 1 & 5 & 2 & 1 & 9 & 3 & 16 & 40 \\
2014/1/30 & 19 & 20 & 87 & 6 & 1 & 27 & 0 & 0 & 0 & 2 & 2 & 9 & 28 & 0 & 42 \\ \hline
2014/1/31 & 40 & 9 & 73 & 27 & 3 & 63 & 2 & 1 & 4 & 0 & 2 & 4 & 13 & 0 & 35 \\
2014/2/1 & 12 & 15 & 59 & 20 & 6 & 56 & 4 & 0 & 7 & 0 & 1 & 4 & 1 & 0 & 12 \\
2014/2/2 & 20 & 18 & 111 & 7 & 2 & 27 & 0 & 0 & 1 & 0 & 1 & 3 & 4 & 0 & 10 \\ \hline
2014/2/28 & 31 & 12 & 91 & 6 & 5 & 29 & 0 & 2 & 4 & 6 & 1 & 13 & 4 & 1 & 12 \\
2014/3/1 & 37 & 18 & 119 & 4 & 12 & 27 & 0 & 1 & 5 & 5 & 1 & 9 & 3 & 0 & 5 \\ \hline
2014/3/2 & 19 & 20 & 85 & 3 & 2 & 16 & 0 & 1 & 4 & 6 & 0 & 11 & 6 & 0 & 11 \\
2014/3/3 & 17 & 17 & 92 & 6 & 12 & 43 & 1 & 1 & 4 & 6 & 0 & 23 & 21 & 24 & 98 \\
2014/3/4 & 33 & 40 & 169 & 8 & 16 & 51 & 0 & 0 & 1 & 6 & 0 & 21 & 16 & 22 & 67 \\ \hline \hline \end{tabular}  
* P: Positive sentiment volume, N: Negative sentiment volume, T: Total sentiment volume including the volume of positive, negative, and neutral sentiments.  
\end{table} 
Table 2: The collected daily online sentiment volume for BMW. where \(y_{i}\) refers to the car sales movement direction (U, F, or D) of the \(i\)th month; \(x_{i1}\) refers to the sales volume of the \(i\)th month; \(x_{i2}\) refers to the same-month-last-year sales movement direction label of the \(i\)th month; \(x_{i3}\) refers to the month number of the \(i\)th month; \(\beta_{0}\) refers to the y-intercept (constant term); \(\beta_{1}\) to \(\beta_{3}\) refer to the slope coefficients for \(x_{i1}\) to \(x_{i3}\); \(\epsilon\) refers to the model's error term (also known as the residuals). In multinomial logistic regression with K classes, one class is chosen as a \"pivot\", and K-1 independent binary logistic regression models are constructed [22].