Making Density Forecasting Models Statistically Consistent
نویسندگان
چکیده
We propose a new approach to density forecast optimisation and apply it to Value-at-Risk estimation. All existing density forecasting models try to optimise the distribution of the returns based solely on the predicted density at the observation. In this paper we argue that probabilistic predictions should be optimised on more than just this accuracy score and suggest that the statistical consistency of the probability estimates should also be optimised during training. Statistical consistency refers to the property that if a predicted density function suggests P percent probability of occurrence, the event truly ought to have probability P of occurring. We describe a quality score that can rank probability density forecasts in terms of statistical consistency based on the probability integral transform (Diebold et al., 1998b). We then describe a framework that can optimise any density forecasting model in terms of any set of objective functions. The framework uses a multi-objective evolutionary algorithm to determine a set of trade-off solutions known as the Pareto front of optimal solutions. Using this framework we develop an algorithm for optimising density forecasting models and implement this algorithm for GARCH (Bollerslev, 1986) and GJR models (Glosten et al., 1993). We call these new models Pareto-GARCH and Pareto-GJR. To determine whether this approach of multi-objective optimisation of density forecasting models produces better results over the standard GARCH and GJR optimisation techniques we compare the models produced empirically on a Value-at-Risk application. Our evaluation shows that our Pareto models produce superior results out-of-sample.
منابع مشابه
The Benefits of Using a Complete Probability Distribution when Decision Making: An Example in Anticoagulant Drug Therapy
In this paper we aim to show how probabilistic prediction of a continuous variable could be more beneficial to a medical practitioner than classification or numeric/point prediction of the same variable in many scenarios. We introduce a probability density forecasting model that produces accurate estimates and achieves statistically consistent predicted distributions. An empirical evaluation of...
متن کاملThe Proposed Mathematical Models For Decision- Making And Forecasting On Euro- Yen In Foreign Exchange Market
متن کامل
Forecasting the Stock Return Distribution Using Macro-Finance Variables
This paper proposes a new method to forecast S&P 500 return distribution by combining quantile regression models using macro-finance variables with volatility-based models including various standard EGARCH and stochastic volatility specifications. 30 density forecasting models are compared and combined in an out-of-sample forecasting exercise. Using macro-finance variables is found to help subs...
متن کاملUsing a Fuzzy Auto Regressive Integrated Moving Average Model for Exchange Rate Forecasting
Forecasting models have wide applications in decision making. In the real world, rapid changes normally take place in different areas, specifically in financial markets. Collecting the required data is a main problem for forecasters in such unstable environments. Forecasting methods such as Auto Regressive Integrated Moving Average (ARIMA) models and also Artificial Neural Networks (ANNs) need ...
متن کاملUsing a Fuzzy Auto Regressive Integrated Moving Average Model for Exchange Rate Forecasting
Forecasting models have wide applications in decision making. In the real world, rapid changes normally take place in different areas, specifically in financial markets. Collecting the required data is a main problem for forecasters in such unstable environments. Forecasting methods such as Auto Regressive Integrated Moving Average (ARIMA) models and also Artificial Neural Networks (ANNs) need ...
متن کامل