Modeling time-varying parameters using artificial neural networks: a GARCH illustration

We propose a new volatility process in which parameters vary over time according to an artificial neural network (ANN). We prove the process’s stationarity as well as the global identification of the parameters. Since ANNs require economic series as input variables, we develop a shrinkage approach to select which explanatory variables are relevant to forecast volatility. Empirically, the proposed model favorably compares with other flexible processes in terms of in-sample fit on six financial returns. It also delivers accurate short-term volatility predictions in terms of root mean squared errors and the predictive likelihood criterion. For long-term forecasts, it can be competitive with the Markov-switching generalized autoregressive conditional heteroskedastic (MS-GARCH) model if appropriate exogenous variables are used. Since our new type of time-varying parameter (TVP) process is based on a universal approximator, the approach can readily revisit and potentially improve many standard TVP applications.