For local and average kernel based estimators, smoothness conditions ensure that the kernel order determines the rate at which the bias of the estimator goes to zero and thus allows the econometrician to control the rate of convergence. In practice, even with smoothness the estimation errors may...

Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for...

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...

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...

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,...

The pattern of decay of forecast content (or skill) with increasing horizon is well known for many types of meteorological forecasts; by contrast, little generally accepted information about these patterns or content horizons is available for economic variables. In this paper we estimate content...