# Prediction and Comparison of In-Vehicle CO\({}_{2}\) Concentration Based on ARIMA and LSTM Models
## 4 Discussion  
The CO\({}_{2}\) concentration in vehicles is affected by factors such as ventilation settings, the number of passengers, driving speed, vehicle characteristics, etc. There are many influencing factors, and they are coupled with each other. Parameters such as the amount of air leakage in a vehicle are difficult to obtain [27], and the accuracy of the model needs to be calibrated with data from multiple studies [13]. Therefore, the utilization of conventional mathematical models for computations encounters certain challenges. When utilizing ARIMA and LSTM for prediction, it is not necessary to deeply explore the impact of various influencing factors on CO\({}_{2}\) concentration. Instead, future trends can be predicted by capturing historical data and analyzing its correlation, seasonal and periodic fluctuations, as well as noise characteristics, leading to accurate prediction results. Additionally, ARIMA and LSTM have demonstrated their reliability in accurately predicting unconventional fluctuations in data [60]. In this research, we utilized ARIMA and LSTM models to build a predictive model for in-vehicle CO\({}_{2}\) concentrations, which yielded accurate forecast results. Predicting in-vehicle CO\({}_{2}\) levels can assist in maintaining a favorable in-vehicle environment, improving traffic safety, and enhancing driving comfort. [PERSON] et al. [28] employed the ARIMA (0, 1, 0) model to forecast the variation in the CO\({}_{2}\) concentration in a vehicle, yielding MAPE and RMSE values of 3.79% and 55.32 ppm, respectively. Compared to this result, the ARIMA model employed in our research yielded more precise prediction outcomes, which may indicate that our model, which considers the autoregressive and moving average items, can better capture the correlations and trends in historical data, whereas ARIMA (0, 1, 0) only performs differential processing on the data and does not consider the correlation with historical data. The prediction principle of ARIMA is to filter the high-frequency noise in the data, detect the linear correlation in the historical data, and use this correlation to predict the future development trend. The prediction principle of RNN involves combining the current input with the previous hidden state to establish temporal dependencies in time series data, which can capture nonlinear relationships within the data. LSTM builds upon this by introducing gating mechanisms that enable memory cells to retain relevant information over longer periods of time, making it particularly effective for large datasets and mitigating issues related to vanishing gradients in traditional RNNs. In our research, the predictive accuracy of LSTM was inferior to that of ARIMA. The possible reasons contributing to this outcome are as follows: (1) The linear relationship of in-vehicle CO\({}_{2}\) concentration data is strong, and there is a clear upward trend in the concentration. ARIMA effectively captures the linear law within time series data, whereas LSTM excels at predicting complex nonlinear patterns. (2) The in-vehicle CO\({}_{2}\) concentration is a one-dimensional time series form of data. Due to the rapid growth process, the amount of data collected at intervals of 5 s within 20 min is only 240 sets. The learning ability of LSTM is restricted by the insufficient amount of data. When predicting data with a limited number of samples and only one dimension, the prediction accuracy of ARIMA may surpass that of LSTM. LSTM requires a large amount of data for training, and the larger the training volume, the higher the prediction accuracy of LSTM. Therefore, using LSTM has a better effect when predicting datasets with a large amount of data [46]. Even though LSTM's prediction accuracy is