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预测比较中的不确定性量化AI 解读

Skill scores, which measure the relative improvement of a forecasting method over a benchmark via consistent scoring functions and proper scoring rules, are a standard tool in forecast evaluation, yet their sampling uncertainty is rarely rigorously quantified. With modern forecasting applications being increasingly multivariate and involving evaluations across multiple horizons, variables, spatial locations, and forecasting methods, standard tools like the pairwise…

广义协方差与相关系数AI 解读

The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or thresholds. Deviations from these functionals are defined via generalised errors, typically induced through identification or moment functions. As a normalised measure of dependence, a generalised correlation is constructed. Replacing the…

自相关系数的同时推断带AI 解读

Sample autocorrelograms typically come with significance (non-rejection) bands for the null hypothesis of no temporal correlation. These bands have three shortcomings. First, they build on pointwise intervals and suffer from joint undercoverage (overrejection) under the null hypothesis. Second, in cases where this null is clearly violated one would rather prefer to see confidence bands to quantify estimation uncertainty. Third, they are invalid under conditional…

秩相关系数的渐近推断AI 解读

Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in particular for discrete random variables and in the time series case, and concerning variance estimation in general. Consequently, asymptotic confidence intervals are not available. We provide a comprehensive treatment of asymptotic inference for…

基于评分规则的多元预测分布校准检验AI 解读

Calibration tests based on the probability integral transform (PIT) are routinely used to assess the quality of univariate distributional forecasts. However, PIT-based calibration tests for multivariate distributional forecasts face various challenges. We propose two new types of tests based on proper scoring rules, which overcome these challenges. They arise from a general framework for calibration testing in the multivariate case, introduced in this work. The new tests…

分位数预测最优性的检验AI 解读

Quantile forecasts made across multiple horizons have become an important output of many financial institutions, central banks and international organisations. This paper proposes misspecification tests for such quantile forecasts that assess optimality over a set of multiple forecast horizons and/or quantiles. The tests build on multiple Mincer-Zarnowitz quantile regressions cast in a moment equality framework. Our main test is for the null hypothesis of autocalibration, a…