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I want to compare the performance of various volatility models like GARCH, eGARCH, and gjrGARCH from actual volatility (computed using high frequency data). I found three common performance evaluation measures used profoundly in literature, i.e. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). But I found conflicting results from the above three criteria, like I found RMSE is minimum for GARCH model, MAE is minimum for eGARCH model, and MAPE is minimum for gjrGARCH model.
I want to know which one is the best measure for evaluating performance and which results should I report? If all three are equally valid then how can I interpret the results? Is there any other way to compare the performance of various volatility models other than performance measures?