Modeling Markov Switching ARMA-GARCH Neural Networks Models and an Application to Forecasting Stock Returns

The study proposes and a family of regime switching GARCH neural network models to model volatility. The proposed MS-ARMA-GARCH-NN models allow MS type regime switching in both the conditional mean and conditional variance for time series and further augmented with artificial neural networks to achieve improvement in forecasting capabilities. Gray (1996) RS-GARCH model allows within regime heteroskedasticity with markov switching of Hamilton (1989). Firstly, models are extended to fractional integration and asymmetric power GARCH and MS-ARMA-FIGARCH, MS-ARMA-APGARCH, MS-ARMA-FIAPGARCH models are evaluated and discussed. Secondly, in addition to regime swiching type nonlinearity, neural networks based augmentated models are evaluated and discussed. In this respect, MS-ARMA-GARCH models are augmented with Multi Layer Perceptron (MLP), Radial Basis Function (RBF), Elman type Recurrent NN (Elman RNN), Time lag (delay) Recurrent NN (RNN) and Hybrid MLP models. Therefore, the second model group includes MS-ARMA-GARCH-MLP, MS-ARMA-GARCH-RBF, MS-ARMA-GARCH-ElmanRNN, MS-ARMA-GARCH-RNN and MS-ARMA-GARCH-HybridMLP. Thirdly, fractional integrated versions are augmented with neural networks and denoted as MS-ARMA-FIGARCH-MLP, MS-ARMA-FIGARCH-RBF, MS-ARMA-FIGARCH-ElmanRNN, MS-ARMA-FIGARCH-RNN and MS-ARMA-FIGARCH-HybridMLP. Fourth, by allowing asymmetric power transformations, models are further extended to GARCH models. These models are MS-ARMA-APGARCH-RBF, MS-ARMA-APGARCH-ElmanRNN, MS-ARMA-APGARCH-RNN and MS-ARMA-FIGARCH-HybridMLP. Therefore, a total of four group of GARCH models are proposed and evaluated in the study. In the empirical application section, daily stock returns in ISE100 Istanbul Stock Index are modeled and forecasted. Forecast success is evaluated with MAE, MSE and RMSE criteria. Equal forecast accuracy is tested with modified Diebold-Mariano tests. Accordingly, fractional integration and asymmetric power transformation perform better in modeling the daily returns in IMKB100 stock index compared to the simple GARCH and RS-GARCH model of Gray. Hybrid MLP and time lag recurrent architectures (MS-ARMA-FIAPGARCH-HybridMLP and MS-ARMA-FIAPGARCH-RNN) provided the best forecast and modeling performance. In conclusion, the newly proposed GARCH models have significant forecasting improvement and therefore are promising in various economic applications