A Non‐Parametric tv‐GARCH Model With a Space‐State Representation for Forecasting
Guillermo Ferreira, Jorge A. Muñoz‐Mendoza, Jorge Arratia‐Llancao, Jorge Mateu, Miguel Flores‐Sánchez, Francisco J. Rodríguez‐CortésABSTRACT
We propose a state‐space approach for a non‐parametric tv‐GARCH model. Using a number of non‐parametric techniques, we estimate slowly time‐varying curves for the parameters and combine it with a recursive system based on the Kalman filter as a methodological framework to obtain forecasts from the model. Our results based on Monte Carlo simulations and an application to the Selective Stock Price Index of the Chilean stock market indicate that the non‐parametric tv‐GARCH model shows the best fit and provides the best forecasting performance, compared with the stationary GARCH model and other techniques, such as tv‐GARCH with time‐varying parameters determined by deterministic functions. These results have relevant implications for risk management, portfolio diversification, and asset allocation.