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Order‐invariant tests for proper calibration of multivariate density forecasts
Author(s) -
Dovern Jonas,
Manner Hans
Publication year - 2020
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.2755
Subject(s) - multivariate statistics , autoregressive model , econometrics , heteroscedasticity , bayesian vector autoregression , bayesian probability , calibration , probability integral transform , invariant (physics) , mathematics , monte carlo method , vector autoregression , statistics , marginal distribution , random variable , mathematical physics
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.