Final Report Summary - UHF_M_MODELLING (Volatility forecasting evaluation based on loss function with well-defined multivariate distributional form and ultra-high frequency datasets)
Project context and objectives
The aim of this EU-funded Marie Curie project is the development of a volatility forecasting evaluation framework which combines the state-of-the-art findings in financial and statistical literature. We investigated the advantages and disadvantages of the proposed techniques for the construction of intra-day realised volatility measures. Our intention was to create a realised volatility measure which is accurate and does not suffer from problems such as bias, mis-measurement, but on the other hand can be implemented in a straightforward way, i.e. is not extremely complicated in its construction, or too time consuming in its computation. We reviewed the most broadly used methods of volatility estimation and forecasting. Based on the daily log returns, the ARCH, or Autoregressive Conditionally Heteroskedastic, process is a widely applied method for estimating and forecasting the unobserved asset's volatility. Based on the intra-day realised volatility, the ARFIMA, or Autoregressive Fractionally Integrated Moving Average model is a broadly applied method for estimating and forecasting realised volatility.
Project outcomes
The programmes on which the estimation and forecasting is based have been constructed. Moreover, the most commonly used methods (loss functions) for comparing the forecasting ability of the candidate models were presented. A volatility forecasting evaluation framework which unites the usage of a well-defined loss function with known statistical properties with the simultaneous evaluation of models' forecasting ability has been developed. A loss function is a measure of accuracy, constructed upon the goals of its particular appliance. However, in the majority of cases, the statistical properties of the loss functions are unknown. In financial forecasting literature, the superiority of a loss function against others is not judged on statistical-theoretical grounds but simply from their empirical motivations. The project proposed use of the Standardised Prediction Error Criterion, or SPEC, selection procedure which is based on a loss function whose exact distribution is explicitly derived. The SPEC method is based on the Minimum Multivariate Gamma, or MMG, distribution. The MMG distribution is the cumulative distribution function of the minimum half sum of squared standardised one-step-ahead prediction errors. The realised volatility has been constructed based on ultra-high-frequency data for 17 stock indices and three euro exchange rates. The sampling frequency was selected according to the volatility signature plot, and the realised volatility was adjusted to changes in the prices during the hours that the markets are closed. Three models were estimated with the annualised inter-day adjusted realised daily logarithmic standard deviation as the dependent variable. The models are re-estimated on each trading day based on a rolling sample of constant size of 1000 trading days.
A dynamic evaluation of models' performance was conducted. We supplied empirical evidence that the model with the lowest half sum of squared standardised prediction errors does provide more adequate one-step-ahead forecasts of the dependent variable, i.e. in our case of the annualised inter-day adjusted realised daily logarithmic standard deviation. The majority of the studies about ultra-high-frequency realised volatility modelling are conducted from research institutions in the USA. The proposed project increased the attractiveness of Europe for researchers who are specialised in the topic of volatility estimation and forecasting. The findings of the project would be helpful in strengthening risk management techniques, i.e. regulatory capital requirements in Basel II, which now applies to all banks in Europe. The basic idea of the project is the construction of a robust framework for comparing various forecasting models. A long-term synergy could be the application of the proposed method to other scientific areas, where forecasting evaluation is significant.
The aim of this EU-funded Marie Curie project is the development of a volatility forecasting evaluation framework which combines the state-of-the-art findings in financial and statistical literature. We investigated the advantages and disadvantages of the proposed techniques for the construction of intra-day realised volatility measures. Our intention was to create a realised volatility measure which is accurate and does not suffer from problems such as bias, mis-measurement, but on the other hand can be implemented in a straightforward way, i.e. is not extremely complicated in its construction, or too time consuming in its computation. We reviewed the most broadly used methods of volatility estimation and forecasting. Based on the daily log returns, the ARCH, or Autoregressive Conditionally Heteroskedastic, process is a widely applied method for estimating and forecasting the unobserved asset's volatility. Based on the intra-day realised volatility, the ARFIMA, or Autoregressive Fractionally Integrated Moving Average model is a broadly applied method for estimating and forecasting realised volatility.
Project outcomes
The programmes on which the estimation and forecasting is based have been constructed. Moreover, the most commonly used methods (loss functions) for comparing the forecasting ability of the candidate models were presented. A volatility forecasting evaluation framework which unites the usage of a well-defined loss function with known statistical properties with the simultaneous evaluation of models' forecasting ability has been developed. A loss function is a measure of accuracy, constructed upon the goals of its particular appliance. However, in the majority of cases, the statistical properties of the loss functions are unknown. In financial forecasting literature, the superiority of a loss function against others is not judged on statistical-theoretical grounds but simply from their empirical motivations. The project proposed use of the Standardised Prediction Error Criterion, or SPEC, selection procedure which is based on a loss function whose exact distribution is explicitly derived. The SPEC method is based on the Minimum Multivariate Gamma, or MMG, distribution. The MMG distribution is the cumulative distribution function of the minimum half sum of squared standardised one-step-ahead prediction errors. The realised volatility has been constructed based on ultra-high-frequency data for 17 stock indices and three euro exchange rates. The sampling frequency was selected according to the volatility signature plot, and the realised volatility was adjusted to changes in the prices during the hours that the markets are closed. Three models were estimated with the annualised inter-day adjusted realised daily logarithmic standard deviation as the dependent variable. The models are re-estimated on each trading day based on a rolling sample of constant size of 1000 trading days.
A dynamic evaluation of models' performance was conducted. We supplied empirical evidence that the model with the lowest half sum of squared standardised prediction errors does provide more adequate one-step-ahead forecasts of the dependent variable, i.e. in our case of the annualised inter-day adjusted realised daily logarithmic standard deviation. The majority of the studies about ultra-high-frequency realised volatility modelling are conducted from research institutions in the USA. The proposed project increased the attractiveness of Europe for researchers who are specialised in the topic of volatility estimation and forecasting. The findings of the project would be helpful in strengthening risk management techniques, i.e. regulatory capital requirements in Basel II, which now applies to all banks in Europe. The basic idea of the project is the construction of a robust framework for comparing various forecasting models. A long-term synergy could be the application of the proposed method to other scientific areas, where forecasting evaluation is significant.
