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Macroeconomic Forecasting and Variable Ordering in Multivariate Stochastic Volatility Models

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Abstract
We document five novel empirical findings on the well-known potential ordering drawback associated with the time-varying parameter vector autoregression with stochastic volatility developed by Cogley and Sargent (2005) and Primiceri (2005), CSP-SV. First, the ordering does not affect point prediction. Second, the standard deviation of the predictive densities implied by different orderings can differ substantially. Third, the average length of the prediction intervals is also sensitive to the ordering. Fourth, the best ordering for one variable in terms of log-predictive scores does not necessarily imply the best ordering for another variable under the same metric. Fifth, the best ordering for variable x in terms of log-predictive scores tends to put the variable x first while the worst ordering for variable x tends to put the variable x last. Then, we consider two alternative ordering invariant time-varying parameter VAR-SV models: the discounted Wishart SV model (DW-SV) and the dynamic stochastic correlation SV model (DSC-SV). The DW-SV underperforms relative to each ordering of the CSP-SV. The DSC-SV has an out-of-sample forecasting performance comparable to the median outcomes across orderings of the CSP-SV.

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  • Jonas E. Arias & Juan F. Rubio-Ramirez & Minchul Shin, 2021. "Macroeconomic Forecasting and Variable Ordering in Multivariate Stochastic Volatility Models," Working Papers 21-21, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:92355
    DOI: 10.21799/frbp.wp.2021.21
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    Cited by:

    1. Joshua C. C. Chan & Gary Koop & Xuewen Yu, 2024. "Large Order-Invariant Bayesian VARs with Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 825-837, April.
    2. Chan, Joshua C.C. & Yu, Xuewen, 2022. "Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    3. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino & Elmar Mertens, 2024. "Addressing COVID-19 Outliers in BVARs with Stochastic Volatility," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1403-1417, September.
    4. Joshua Chan & Eric Eisenstat & Xuewen Yu, 2022. "Large Bayesian VARs with Factor Stochastic Volatility: Identification, Order Invariance and Structural Analysis," Papers 2207.03988, arXiv.org.
    5. Florian Huber & Gary Koop & Massimiliano Marcellino & Tobias Scheckel, 2024. "Bayesian modelling of VAR precision matrices using stochastic block networks," Papers 2407.16349, arXiv.org.
    6. Wu, Ping & Koop, Gary, 2023. "Estimating the ordering of variables in a VAR using a Plackett–Luce prior," Economics Letters, Elsevier, vol. 230(C).
    7. Botelho, Vasco & Foroni, Claudia & Renzetti, Andrea, 2023. "Labour at risk," Working Paper Series 2840, European Central Bank.

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    More about this item

    Keywords

    Vector Autoregressions; Time-Varying Parameters; Stochastic Volatility; Variable Ordering; Cholesky Decomposition; Wishart Process; Dynamic Conditional Correlation; Out-of-sample Forecasting Evaluation;
    All these keywords.

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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