This paper applies new diagnostics to the Bank of England's pioneering density forecasts (fan charts). We compute their implicit probability forecast for annual rates of inflation and output growth that exceed a given threshold (in this case, the target inflation rate and 2.5% respectively.)...

This paper uses estimation techniques related to those of Galbraith and Zinde-Walsh (2000) for ARCH and GARCH models, based on realized volatility (Andersen and Bollerslev 1998, and others), to estimate the conditional quantiles of daily volatility in samples of equity index and foreign exchange...

A probabilistic forecast is the estimated probability with which a future event will satisfy a specified criterion. One interesting feature of such forecasts is their calibration, or the match between predicted probabilities and actual outcome probabilities. Calibration has been evaluated in the...

Financial returns typically display heavy tails and some skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures...

We consider estimates of the parameters of GARCH models of daily financial returns, obtained using intra-day (high-frequency) returns data to estimate the daily conditional volatility.Two potential bases for estimation are considered. One uses aggregation of high-frequency Quasi- ML estimates,...

This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in...

This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA (p,d,q) models, based on autoregressive approximation. We demonstrate consistency of the estimator for -1/2 d 1, and in the stationary case we provide a Normal approximation to the finite-sample...

Using the tail index of returns on US equities as a summary measure of extreme behaviour, we examine changes in the equity markets surrounding the development of program trading for portfolio insurance, the crash of 1987, and the subsequent introduction of circuit breakers and other changes in...

The growth rates of real output and real investment are two macroeconomic time series which are particularly difficult to forecast. This paper considers the application of diffusion index forecasting models to this problem. We begin by characterizing the performance of standard forecasts, via...

Using realized volatility to estimate daily conditional volatility of financial returns, we compare forecasts of daily volatility from standard QML-estimated GARCH models, and from projections on past realized volatilities obtained from high-frequency data. We consider horizons extending to...