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.

Notes

¹ According to Campbell et al . (1997), ‘The non-synchronous trading or non-trading effect arises when time series, usually asset prices, are taken to be recorded at time intervals of one length when in fact they are recorded at time intervals of other, possible irregular lengths.’ For more details on non-synchronous trading see Scholes and Williams (1977), Dimson (1979), Cohen et al . (1983) and Lo and MacKinlay (1988, 1990).

² For an overview of the Neural Networks (NN) literature, see Poggio and Girosi (1990), Hertz et al . (1991), White (1992), Hutchinson et al . (1994). Plasmans et al . (1998) and Franses and Homelen (1998) investigated the ability of NN on forecasting exchange rates. The non-linearity found in exchange rates is due to ARCH effects. Saltoglu (2003) investigated the forecasting ability of NN on interest rates and noted the importance of modelling both the first and second moments jointly. Jasic and Wood (2004) and Perez-Rodriguez et al . (2005) provided evidence that NN models have a superior ability compared to other model frameworks in predicting stock indices.

³ Brock (1986), Holden (1986), Thompson and Stewart (1986) and Hsieh (1991) review applications of chaotic systems to financial markets. Adrangi and Chatrath (2003) found that the non-linearities in commodity prices are not consistent with chaos but they are explained by an ARCH process. On the other hand, Barkoulas and Travlos (1998) mentioned that even after accounting for the ARCH effect, the evidence is consistent with a chaotic structure of the Greek stock market.

⁴ Priestley (1988), Tong (1990) and Teräsvirta et al . (1994) cover a wide variety of non-linear models. Applications of SETAR and ARFIMA models can be found in Peel and Speight (1996) and Barkoulas et al . (2000), respectively.

⁵ For an overview of the ARCH literature see Bollerslev et al . (1992, 1994), Bera and Higgins (1993), Hamilton (1994), Gourieroux (1997) and Degiannakis and Xekalaki (2004).

⁶ For details, see Taylor (1994), Shephard (1996) and Selcuk (2005).

⁷ Percentage points of the CGR distribution can be found in Xekalaki et al . (2003) and Degiannakis and Xekalaki (2005).

⁸ For details and references about intra-day realized volatility the interested reader is referred to Andersen and Bollerslev (1997, 1998a, b), Barndorff-Nielsen and Shephard (1998), Andersen et al . (1999, 2000a, b, 2001a, b, 2003, 2005).

⁹ Numerical maximization of the log-likelihood function, for the EGARCH(2,2) model, failed to converge in more than 1% of the trading days. So the five EGARCH models for p = q = 2 were excluded.

¹⁰ Here, T = a(b)c denotes .

¹¹ The analysis was also conducted based on giving qualitatively similar results.

¹² These tables are available upon request.