Order‐invariant tests for proper calibration of multivariate density forecasts
针对基于Rosenblatt概率积分变换的多元密度预测校准检验可被变量顺序操纵的问题，提出了顺序不变的检验方法，适用于任意维密度，能处理参数估计不确定性和动态误设，蒙特卡洛模拟显示其功效优于传统方法。
Summary Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order‐invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate generalized autoregressive conditional heteroskedasticity‐based multivariate density forecasts for a vector of stock market returns and macroeconomic forecasts from a Bayesian vector autoregression with time‐varying parameters.