## 4 Experimental Procedure and Analysis of Results
### Experimental Setup
#### 4.1.4 Benchmark Models  
To further demonstrate the effectiveness and superiority of our proposed model, we selected three prediction models and compared them with our proposed model. First, we selected CNN and GRU models and combined them with GARCH-family models to obtain GRU-GARCH-family models and CNN-GARCH-family models as benchmark models. In addition, we also selected the attention-LSTM model, which has an excellent performance in current time series data prediction, to compare with our proposed optimal LSTM-GARCH family model. * GRU has a similar structure to the LSTM and can be regarded as a simple variant of LSTM. Both LSTM and GRU preserve important features through various gate structures and thus ensure they will not be lost even after a long period. GRU improves the complex cell structure of LSTM by merging the input and forgetting gates and merging the cell states and hidden states of LSTM. In the GRU model, the reset gate is used to determine how much past information to forget, and the update gate is used to decide how much input and previous output to pass to the next cell, so the GRU cell can decide how much information to copy from the past to reduce the risk of gradient disappearance. It has often been applied to price prediction in recent years [50]. The performances of LSTM and GRU are slightly different on different data sets. To further verify the superiority of our proposed model, we combined the GRU with the GARCH-family models to obtain the GRU-GARCH-family combined models. The GRU and GRU-GARCH-family models were selected as the benchmark models. We built a stacked GRU model similar to the LSTM model, i.e., with two GRU layers and two fully connected layers. With the hyperparameters adjusted to the optimal case, the optimal LSTM-GARCH-family combined models we obtained in the above experiments were compared with the GRU and GRU-GARCH-family combined models (GRU-G, GRU-GP, and GRU-GEP). * A convolutional neural network (CNN) is suitable for spatial feature extraction and is widely used in the field of image recognition. It mainly includes an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer. We tried to use the CNN model for garlic price prediction work. In this work, the CNN model took garlic price and GARCH-family-related parameters as input data and extracted the correlation between each index and garlic price through convolution operation; then compressed the amount of data and parameters through pooling to avoid overfitting and reduce the complexity of the model; then transformed the data form through flattening layer; and finally fine-tunesd and output the prediction results using a fully connected layer. We combined the CNN with the GARCH-family models to get CNN-GARCH-family combined models to test the ability of the CNN to extract garlic-price series features. We compared the optimal LSTM-GARCH-family models with the combined CNN-GARCH-family models (CNN-G, CNN-GP, and CNN-GEP). We set the CNN to have two convolutional layers, a max pooling layer, a dropout layer, and a fully connected layer ui a grid search method. For the first two convolutional layers, the filter size was 1 and the numbers of filters were selected as 32 and 16, respectively. The filter size for the max pooling layer was 2. In addition, dropout regularization was set to 0.1 to prevent overfitting. * Attention improves the model's ability to select temporal correlations. The attention mechanism is a resource allocation mechanism that mimics human attention, and it can change the level of attention to input information by assigning reasonable weights to different features. Attention-LSTM models are often used in the field of price prediction. Many extant pieces of literature point out that LSTM incorporating the attention mechanism has an advantage over LSTM models in time-series data prediction. Therefore, we selected an attention-LSTM as a benchmark model.