Modeling Markov Switching ARMA-GARCH Neural Networks Models and an Application to Forecasting Stock Returns
Table 7
Diebold Mariano equal forecast accuracy test results, out of sample.
Model Group 1: MS-ARMA-GARCH-neural network models
MS-ARMA- GARCH- RNN
MS-ARMA- GARCH- RBF
MS-ARMA- GARCH- ELMAN RNN
MS-ARMA- GARCH- HYBRID MLP
MS-ARMA- GARCH- MLP
MS-ARMA-GARCH- RNN
—
−4.020*** (0.000) [r]
−3.176** (0.002) [r]
−0.645 (0.518) [r]
0.574 (0.566) [c]
MS-ARMA-GARCH- RBF
—
0.585 (0.558) [c]
4.011*** (0.000) [c]
4.142*** (0.000) [c]
MS-ARMA-GARCH-ELMAN RNN
—
3.309*** (0.001) [c]
3.396*** (0.001) [c]
MS-ARMA-GARCH-HYBRID MLP
—
3.355*** (0.01) [c]
MS-ARMA-GARCH- MLP
—
Model Group 2: MS-ARMA-APGARCH-neural network models
MS-ARMA- APGARCH- RNN
MS-ARMA- APGARCH- RBF
MS-ARMA- APGARCH- ELMAN RNN
MS-ARMA- APGARCH- HYBRID MLP
MS-ARMA- APGARCH- MLP
MS-ARMA-APGARCH-RNN
—
−2.932*** (0.003) [r]
3.767*** (0.000) [c]
4.888*** (0.000) [c]
4.805*** (0.000) [c]
MS-ARMA-APGARCH- RBF
—
3.188*** (0.001) [c]
3.251*** (0.001) [c]
3.255*** (0.001) [c]
MS-ARMA-APGARCH-ELMAN RNN
—
2.797*** (0.005) [c]
2.736*** (0.006) [c]
MS-ARMA-APGARCH-HYBRID MLP
—
−1.835** (0.066) [r]
MS-ARMA-APGARCH-MLP
—
Model Group 3: MS-ARMA-FIAPGARCH-neural network models
MS-ARMA-FIAPGARCH- RNN
MS-ARMA-FIAPGARCH- RBF
MS-ARMA- FIAPGARCH- ELMAN RNN
MS-ARMA-FIAPGARCH- HYBRID MLP
MS-ARMA-FIAPGARCH- MLP
MS-ARMA-FIAPGARCH-RNN
—
−2.519** (0.011) [r]
−1.717* (0.086) [r]
−0.588 (0.556) [r]
−0.836 (0.403) [r]
MS-ARMA-FIAPGARCH-RBF
—
2.214** (0.027) [c]
2.608*** (0.009) [c]
2.526** (0.012) [c]
MS-ARMA-FIAPGARCH-ELMAN RNN
—
2.154** (0.031) [c]
−2.214** (0.026) [r]
MS-ARMA-FIAPGARCH-HYBRID MLP
—
−0.716 (0.473) [r]
MS-ARMA-FIAPGARCH-MLP
—
Notes: Statistical significances of the relevant tests are denoted with ***show statistical significance at 1% significance level; while **, and *show significance at 5% and 10%, respectively. D-M test allows for reporting the selected model. Accordingly, [r] shows that the model reported in the “row” is selected over the model in the column. Similarly, [c] stands for the column model being accepted over the row model.
