Integrating Non-Gaussian Autoregressive Processes With Neural Networks for Financial Market Forecasting

The assumption of Gaussian innovations has traditionally been standard in autoregressive integrated moving average (ARIMA) models. However, financial time series frequently exhibit heavy tails, skewness, and outliers, violating the Gaussian assumption and motivating the use of non-Gaussian models, machine learning techniques, and hybrid approaches. To enhance predictive accuracy under such conditions, researchers have explored autoregressive processes with non-Gaussian innovations. This study proposes a new hybrid forecasting model that integrates an autoregressive process with Laplace innovations and a neural network. The autoregressive component captures linear dynamics, whereas the neural network component models nonlinear patterns in the residuals. Replacing Gaussian innovations with Laplace innovations allows the model to better accommodate outliers and heavy-tailed behavior commonly observed in financial data. The modeling procedure involves three steps: (1) estimating the autoregressive model and extracting linear predictions and residuals, (2) training a neural network on the residuals, and (3) combining the linear and nonlinear forecasts to generate final predictions. Simulation experiments based on classic nonlinear time series processes and empirical analyses using leading economic indicators indicate that the proposed hybrid model performs competitively across a variety of settings. Although further extensions may improve general applicability, the results suggest that incorporating non-Gaussian components within a hybrid structure may offer a practical and robust approach for financial time series forecasting.