Anthony S. Tay

Evaluating Density Forecasts with Applications to Financial Risk Management

Density forecasting is increasingly more important and commonplace, for example in financial risk management, yet little attention has been given to the evaluation of density forecasts. The authors develop a simple and operational framework for density forecast evaluation. They illustrate the framework with a detailed application to density forecasting of asset returns in environments with time-varying volatility. Finally, the authors discuss several extensions. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Density forecasting: a survey

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation and evaluation of density forecasts.

Multivariate Density Forecast Evaluation and Calibration In Financial Risk Management: High-Frequency Returns on Foreign Exchange

We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate the adequacy of density forecasts involving cross-variable interactions, such as time-varying conditional correlations. We also provide conditions under which a technique of density forecast calibration can be used to improve deficient density forecasts, and we show how the calibration method can be used to generate good density forecasts from econometric models, even when the conditional density is unknown. Finally, motivated by recent advances in financial risk management, we provide a detailed application to multivariate high-frequency exchange rate density forecasts.

Direction-of-Change Forecasts Based on Conditional Variance,Skewness and Kurtosis Dynamics: International Evidence

Recent theoretical work has revealed a direct connection between asset return volatility forecastability and asset return sign forecastability. This suggests that the pervasive volatility forecastability in equity returns could, via induced sign forecastability, be used to produce direction-of-change forecasts useful for market timing. We attempt to do so in an international sample of developed equity markets, with some success, as assessed by formal probability forecast scoring rules such as the Brier score. An important ingredient is our conditioning not only on conditional mean and variance information, but also conditional skewness and kurtosis information, when forming direction-of-change forecasts.

How should we Interpret Evidence of Time Varying Conditional Skewness

Several recent articles report evidence of predictability in the skewness of equity returns, raising hopes that predictability in third moments will be useful for forecasting the probability of tail events. The evidence is unfortunately difficult to interpret, partly because they were obtained mainly from parametric models of time-varying conditional skewness, and because little is known about the behavior of such models, for instance, when there are outliers. We investigate a non-parametric approach to testing for predictability in skewness. Specifically, we explore the size and power of a Runs tests, and compare this approach with other tests. A re-examination of daily market returns reveals mild evidence of predictability in skewness. Incorporating this conditional heteroskewness into standard volatility models hardly improves out-of-sample forecasts of tail probabilities.

The impact of transaction duration, volume and direction on price dynamics and volatility

We explore the role of trade volume, trade direction, and the duration between trades in explaining price dynamics and volatility using an Asymmetric Autoregressive Conditional Duration model applied to intraday transactions data. Our results suggest that volume, direction and duration are important determinants of price dynamics, while duration is also an important determinant of volatility. However, the impact of volume and direction on volatility is marginal after controlling for duration, and the impact of volume on volatility appears to be confined to periods of infrequent trading.