Prediction of Multivariate Chaotic Time Series using GRU, LSTM and RNN

Chaotic systems are identified as nonlinear, deterministic dynamic systems that are exhibit sensitive to initial values. Some chaotic equations modeled from daily events involve time information and generate chaotic time series that are sequential data. Through successful prediction studies conducted on the generated chaotic time series, forecasts can be made about events displaying unpredictable behavior in nature, which have not yet been modeled. This enables preparation for both favorable and unfavorable situations that may arise. In this study, chaotic time series were generated using Lorenz, Chen, and Rikitake multivariate chaotic systems. To enhance prediction accuracy on the generated data, GRU, LSTM and RNN models were trained with different hyperparameters. Subsequently, comprehensive test studies were conducted to evaluate their performance. Predictions were calculated using evaluation metrics, including MSE, RMSE, MAE, MAPE, and R2. In the experimental study, each chaotic system was trained with different hyperparameter combinations on six network models. The experimental results indicate that the utilized models exhibited greater success in predicting chaotic time series compared to some other models in the literature.