Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models

Abstract

A number of ARCH models are considered in the framework of evaluating the performance of a method for model selection based on a standardized prediction error criterion (SPEC). According to this method, the ARCH model with the lowest sum of squared standardized forecasting errors is selected for predicting future volatility. A number of statistical criteria, that measure the distance between predicted and inter-day realized volatility, are used to examine the performance of a model to predict future volatility, for forecasting horizons ranging from one day to 100 days ahead. The results reveal that the SPEC model selection procedure has a satisfactory performance in picking that model that generates 'better' volatility predictions. A comparison of the SPEC algorithm with a set of other model evaluation criteria yields similar findings. It appears, therefore, that it can be regarded as a tool in guiding the choice of the appropriate model for predicting future volatility, with applications in evaluating portfolios, managing financial risk and creating speculative strategies with options.

Backtesting VaR Models: An Expected Shortfall Approach

“…We choose to set 1 = = q p , given that in the majority of empirical volatility forecasting studies, the order of one lag has proven to work effectively. So and Yu (2006) concluded that "the best fitted model according to AIC (Akaike, 1973) and SBC (Schwarz, 1978) criteria does not necessarily lead to better VaR estimates", whereas Degiannakis and Xekalaki (2006) demonstrated that in the volatility forecasting arena, the best-performing model could not be selected according to any in-sample model selection criterion.…”

Volatility forecasting: Intra-day versus inter-day models

“…A representative example of the inability of the in-sample model selection methods to suggest models with superior volatility forecasting ability is given byDegiannakis and Xekalaki (2007). They showed that the commonly used in-sample methods of model selection such as AIC, SBC, and mean squared error (MSE), among others, did not lead to the selection of a model that tracks close future volatility.…”

Simulated evidence on the distribution of the standardized one-step-ahead prediction errors in ARCH processes

“…The algorithm allows switching from the model used at time 1  t for forecasting volatility to another model for use at time t and, in particular, to the model with the minimum value of the average squared standardized prediction error. As indicated by the results obtained by Degiannakis and Xekalaki (2005b), the SPEC model selection procedure appears to have a satisfactory performance in selecting the model that generates better volatility predictions. Moreover, the SPEC algorithm exhibited a satisfactory performance on a simulated options market (Xekalaki and Degiannakis 2005) as well as on trading S&P500 options on a daily basis (Degiannakis and Xekalaki 2001).…”