Final Report Summary - MODEL_PREDICTABILITY (Volatility Forecasting Evaluation Framework)
The project proposes an enhanced volatility forecasting evaluation framework which combines the state-of-the-art findings in financial and statistical literature with the assumption that the forecast errors are non-normally distributed.
We developed the appropriate framework for defining realized (intra-day) volatility as the quantity for appropriate measuring integrated volatility and simulated data generated realized volatility series from an ARFIMA-GARCH framework assuming that the forecast errors are conditionally leptokurtotic or/and asymmetrically distributed.
We estimated a set of models for forecasting realized volatility under the assumptions that the innovations are i) symmetrically, ii) leptokurtically, and ii) leptokurtically and asymmetrically distributed. We computed the forecast errors from the estimated models and investigated whether the data-generated model achieves the lowest value of the standardized prediction error criterion (SPEC); the sum of the squared standardized forecast errors. The data-generated model does have the lowest value of the SPEC criterion under a model specification with i) symmetric distribution, i.e. z~N(0,1) , ii) leptokurtic distribution, i.e. z~t(0,1;v) and z~Ged(0,1;v) as well as iii) leptokurtic and asymmetric distribution, i.e. z~skT(0,1;v,g) . The SPEC loss function picks the data-generated model as the most accurate for one-point-in-time-ahead realized volatility forecasts. Thus, the usage of the SPEC as a predictability criterion in not limited to models with normally distributed residuals. The sum of the squared standardized forecast errors is an accurate criterion for evaluating predictability for realized volatility models with leptokurtically and asymmetrically distributed residuals as well.
In the sequel, the models were applied in estimating and forecasting the realized volatility of the major European Union’s stock market indices (FTSE100, DAX30, CAC40) and the exchange rates of Euro to the Great Britain Pound, the United States Dollar and the Japanese Yen. Each one of the models was re-estimated for each trading day, based on a rolling sample of constant size of 1000 trading days. The predictability of the estimated models was evaluated according to the SPEC criterion; i.e. we investigate which model achieves the lowest value of the SPEC loss function. In general, the ARFIMA(1,d,1)-GARCH(1,1) model achieves the lowest value of the sum of the squared standardized forecast errors for the vast majority of the cases. For the 6 realized volatility series and the 4 distributional assumptions, in total 24 cases, there were just two exceptions; the HAR-RV-GARCH(1,1) model for the Euro/Pound rate under the normal distribution and the ARFIMA(0,d,1)-GARCH(1,1) model for the DAX30 index under the Student t distribution.
The project benefits fellow's career by offering him an opportunity to continue his research in the field of evaluating model's forecasting accuracy and strengthening his professional affiliation. The fellowship has transferred researcher's knowledge previously acquired to the host institution. The Marie Curie Fellowship gave the opportunity to the academic staff of both University of Portsmouth and Athens University of Economics and Business for joining and advancing research efforts as well as for developing a skilled academic network. The fellowship gave the opportunity to the researcher to develop strong research collaborations with researchers in academia as well as in industry. With the completion of the project the fellow has the perspective to obtain a stable, promising long term position.
We developed the appropriate framework for defining realized (intra-day) volatility as the quantity for appropriate measuring integrated volatility and simulated data generated realized volatility series from an ARFIMA-GARCH framework assuming that the forecast errors are conditionally leptokurtotic or/and asymmetrically distributed.
We estimated a set of models for forecasting realized volatility under the assumptions that the innovations are i) symmetrically, ii) leptokurtically, and ii) leptokurtically and asymmetrically distributed. We computed the forecast errors from the estimated models and investigated whether the data-generated model achieves the lowest value of the standardized prediction error criterion (SPEC); the sum of the squared standardized forecast errors. The data-generated model does have the lowest value of the SPEC criterion under a model specification with i) symmetric distribution, i.e. z~N(0,1) , ii) leptokurtic distribution, i.e. z~t(0,1;v) and z~Ged(0,1;v) as well as iii) leptokurtic and asymmetric distribution, i.e. z~skT(0,1;v,g) . The SPEC loss function picks the data-generated model as the most accurate for one-point-in-time-ahead realized volatility forecasts. Thus, the usage of the SPEC as a predictability criterion in not limited to models with normally distributed residuals. The sum of the squared standardized forecast errors is an accurate criterion for evaluating predictability for realized volatility models with leptokurtically and asymmetrically distributed residuals as well.
In the sequel, the models were applied in estimating and forecasting the realized volatility of the major European Union’s stock market indices (FTSE100, DAX30, CAC40) and the exchange rates of Euro to the Great Britain Pound, the United States Dollar and the Japanese Yen. Each one of the models was re-estimated for each trading day, based on a rolling sample of constant size of 1000 trading days. The predictability of the estimated models was evaluated according to the SPEC criterion; i.e. we investigate which model achieves the lowest value of the SPEC loss function. In general, the ARFIMA(1,d,1)-GARCH(1,1) model achieves the lowest value of the sum of the squared standardized forecast errors for the vast majority of the cases. For the 6 realized volatility series and the 4 distributional assumptions, in total 24 cases, there were just two exceptions; the HAR-RV-GARCH(1,1) model for the Euro/Pound rate under the normal distribution and the ARFIMA(0,d,1)-GARCH(1,1) model for the DAX30 index under the Student t distribution.
The project benefits fellow's career by offering him an opportunity to continue his research in the field of evaluating model's forecasting accuracy and strengthening his professional affiliation. The fellowship has transferred researcher's knowledge previously acquired to the host institution. The Marie Curie Fellowship gave the opportunity to the academic staff of both University of Portsmouth and Athens University of Economics and Business for joining and advancing research efforts as well as for developing a skilled academic network. The fellowship gave the opportunity to the researcher to develop strong research collaborations with researchers in academia as well as in industry. With the completion of the project the fellow has the perspective to obtain a stable, promising long term position.
