Forecasting multidimensional autoregressive time series model with symmetric \(\alpha\)-stable noise using artificial neural networks

Artificial neural networks have been widely studied and applied in time series forecasting. However, the existing studies focus more on the univariate Gaussian data. Here, we extend neural network application to multivariate non-Gaussian data, particularly in time series analysis. In this article, we propose a hybrid methodology that combines symmetric \(\alpha\) $\alpha$ -stable vector autoregressive time series model with artifical neural networks. The methodology is validated through Monte-Carlo simulations. Moreover, the new method is used to model real empirical data thus showing the usefulness of heavy-tailed models supported by artificial neural networks in statistical modelling.