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Order Invariant Tests for Proper Calibration of Multivariate Density Forecasts

Author

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  • Jonas Dovern

    (Alfred-Weber-Institute for Economics, Heidelberg University)

  • Hans Manner

    (University of Graz, Austria)

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," Graz Economics Papers 2018-09, University of Graz, Department of Economics.
    • Handle: RePEc:grz:wpaper:2018-09
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    Cited by:

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    2. 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.
    3. Hertrich, Daniel, 2023. "Carry and conditional value at risk trend: Capturing the short-, intermediate-, and long-term trends of left-tail risk forecasts," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 82(C).
    4. Lena S. Bjerkander & Jonas Dovern & Hans Manner, 2024. "Testing with Vectors of Statistics: Revisiting Combined Hypothesis Tests with an Application to Specification Testing," CESifo Working Paper Series 11027, CESifo.

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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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