Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models

Jonas E. Arias

doi:10.1016/j.jeconom.2022.04.013

2023-08-01

PRE

Jonas E. Arias

Juan Francisco Rubio-Ramı́rez

Minchul Shin *

DOI：10.1016/j.jeconom.2022.04.013

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摘要

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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). 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 ordering problem becomes exacerbated in conditional forecasting exercises. Then, we consider three alternative ordering invariant models: a canonical discounted Wishart stochastic volatility model and two dynamic stochastic correlation models. When the forecasting performance of these ordering invariant models is compared to Cogley, Primiceri, and Sargent's ordering variant model, the former underperforms relative to all orderings and the latter two have an out-of-sample forecasting performance comparable with the median outcomes across orderings.Published by Elsevier B.V.

Keyword:

Vector autoregressions

Time-varying parameters

Stochastic volatility

Variable ordering

Cholesky decomposition

Wishart process

Dynamic conditional correlation

Out-of-sample forecasting evaluation