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

Meteorological and economic modelling and forecasting have a number of common features, which suggest that it may be interesting to compare their recent progress in forecasting. We concentrate on two aspects of forecasting: first, measures of the value added of forecasts, and the evolution of...

The difference in yields between long-term and short-term securities has been used both as a business cycle leading indicator and as an indicator of the current impact of monetary policy. This paper tests for an asymmetry, in the form of a threshold effect, such that the impact of the yield...

For quantities that are approximately stationary, the information content of statistical forecasts tends to decline as the forecast horizon increases, and there exists a maximum horizon beyond which forecasts cannot provide discernibly more information about the variable than is present in the...

We consider the problem of determining the horizon beyond which forecasts from time series models of stationary processes add nothing to the forecast implicit in the conditional mean. We refer to this as the content horizon for forecasts, and define a forecast content function at horizons s =...

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 book provides a wide-ranging account of the literature on co-integration and the modelling of integrated processes (those which accumulate the effects of past shocks). Data series which display integrated behaviour are common in economics, although techniques appropriate to analysing such...

For a general stationary ARMA(<italic>p,q</italic>) process <italic>u</italic> we derive the <italic>exact</italic> form of the orthogonalizing matrix <italic>R</italic> such that <italic>R</italic>′<italic>R</italic> = Σ⁻¹, where Σ = <italic>E</italic>(<italic>uu</italic>′) is the covariance matrix of <italic>u</italic>, generalizing the known formulae for <italic>AR</italic>(<italic>p</italic>) processes. In a linear regression model with an ARMA(<italic>p,q</italic>) error process,...

Financial returns typically display heavy tails and some degree of 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...