## 3 Problem Formulation and System Model  
In this paper, the home appliance sales forecasting problem is formalized as an end-to-end time series prediction task, with the objective of predicting future sales within a specific time frame based on the sequence of historical sales volume data. The core goal is to identify and learn patterns within the historical sales data and apply these patterns to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Methods** & **Contributions** & **Drawbacks** \\ \hline
[13] & Clustering + ML & \
\begin{tabular}{c} Improving the accuracy of household \\ appliance sales forecasting \\ \end{tabular} &
\begin{tabular}{c} Increased complexity, \\ computationally intensive \\ \end{tabular} \\ \hline
[10] & CNN & \
\begin{tabular}{c} Learning effective features from the \\ historical sales data automatically \\ and predicting household \\ appliance sales \\ \end{tabular} &
\begin{tabular}{c} Low prediction accuracy, high data \\ requirements \\ \end{tabular} \\ \hline
[15] & LSTM & \
\begin{tabular}{c} Exploiting the temporal correlation \\ among the historical sales data \\ \end{tabular} &
\begin{tabular}{c} Low prediction accuracy, longer \\ training time \\ \end{tabular} \\ \hline
[16] & LSTM + PSO & \
\begin{tabular}{c} Enhanced performance of sales \\ forecasting with hyperparameter \\ optimization \\ \end{tabular} &
\begin{tabular}{c} Risk of overfitting, potential local \\ optima \\ \end{tabular} \\ \hline
[17] & ARIMA + RNN &
\begin{tabular}{c} Capturing both linear and nonlinear \\ relationships of time series data \\ \end{tabular} & Complex implementation \\ \hline
[18] & CNN + LSTM &
\begin{tabular}{c} Using spatiotemporal information to \\ improve prediction accuracy \\ \end{tabular} & High computational cost \\ \hline
[19] & CNN + LSTM + Attention & \
\begin{tabular}{c} Addressing the limitations of \\ traditional LSTM, particularly in \\ scenarios influenced by small weights \\ \end{tabular} &
\begin{tabular}{c} Higher complexity and \\ computationally expensive \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Related studies on sales forecasting. forecast future sales trends. Therefore, we establish a functional model that is capable of learning and representing the patterns in sales data. Mathematically, this process can be defined as a mapping function \(f(\cdot)\), which takes the historical sales data \(X=\{x_{1},\ x_{2},\ \ldots,\ x_{t-1},x_{t}\}\) as the input and outputs the predicted sales volume \(Y=\{y_{1},y_{2},\ldots,y_{k}\}=\{x_{t+1},\ x_{t+2},\ \ldots,\ x_{t+k}\}\) for a given time length \(k\). This process is shown as follows:  
\[Y=f(X;\theta), \tag{1}\]  
where \(\theta\) represents the parameters of the model, which are learned through the training process. We introduce the TransTLA model, a novel forecasting approach for home appliance sales volumes, leveraging DL and TL technologies. The model integrates TCN, LSTM, and attention mechanisms, along with a custom loss function that incorporates TL mechanisms. The TCN-LSTM structure extracts the features from both source and target domains, while the attention mechanism refines these features to improve the predictive performance. After a round of training, the TL mechanism incorporates the distance between the features of both domains into a composite loss function. Once the model is trained, it can be used for forecasting the sales volume of home appliance products. The TransTLA model is shown in Figure 1, which contains the input layer, TCN layer, LSTM layer, attention layer, and output layer. Firstly, the TCN layer extracts local features by using two stacked residual blocks. Secondly, the LSTM layer captures the temporal features of sequence data with two stacked LSTM units. Then, the attention mechanism layer refines these features by assigning weights based on relevance, and thus, the model's predictive focus can be improved.