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Order Invariant Tests for Proper Calibration of Multivariate Density Forecasts

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  • Jonas Dovern
  • Hans Manner

Abstract

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 GARCH-based multivariate density forecasts for a vector of stock market returns.

Suggested Citation

  • Jonas Dovern & Hans Manner, 2018. "Order Invariant Tests for Proper Calibration of Multivariate Density Forecasts," CESifo Working Paper Series 7023, CESifo.
    • Handle: RePEc:ces:ceswps:_7023
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    3. Julia Kielmann & Hans Manner & Aleksey Min, 2022. "Stock market returns and oil price shocks: A CoVaR analysis based on dynamic vine copula models," Empirical Economics, Springer, vol. 62(4), pages 1543-1574, April.

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    More about this item

    Keywords

    density calibration; goodness-of-fit test; predictive density; Rosenblatt transformation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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