Forecasting Volatility of Stock Index: Deep Learning Model with Likelihood-Based Loss Function

Table 5

Log likelihoods of the test sample.

	S&P 500	Dow Jones	NASDAQ
LSTM (likelihood-based loss)	11406.25	15448.84	6074.32
DNN (likelihood-based loss)	11346.34	15392.89	6062.46
LSTM (MSE loss)	11348.36	15329.30	6036.95
DNN (MSE loss)	11275.18	15259.39	5999.94
ARMA-GARCH	11291.16	15383.54	6012.85
Simple	11061.59	15123.93	5887.78