[Paper Review] A Flexible Mixed-Frequency Vector Autoregression with a Steady-State Prior

Sebastian Ankargren, Måns Unosson+1 more|arXiv (Cornell University)|Nov 20, 2019

Monetary Policy and Economic Impact52 references4 citations

TL;DR

This paper proposes a Bayesian mixed-frequency vector autoregression (VAR) model that incorporates a steady-state prior for unconditional means and stochastic volatility to improve macroeconomic forecasting. By modeling monthly and quarterly variables within a state-space framework with missing data imputation, the approach enhances forecast accuracy—especially for quarterly variables—while leveraging prior knowledge on long-run means and time-varying volatility.

ABSTRACT

We propose a Bayesian vector autoregressive (VAR) model for mixed-frequency data. Our model is based on the mean-adjusted parametrization of the VAR and allows for an explicit prior on the 'steady states' (unconditional means) of the included variables. Based on recent developments in the literature, we discuss extensions of the model that improve the flexibility of the modeling approach. These extensions include a hierarchical shrinkage prior for the steady-state parameters, and the use of stochastic volatility to model heteroskedasticity. We put the proposed model to use in a forecast evaluation using US data consisting of 10 monthly and 3 quarterly variables. The results show that the predictive ability typically benefits from using mixed-frequency data, and that improvements can be obtained for both monthly and quarterly variables. We also find that the steady-state prior generally enhances the accuracy of the forecasts, and that accounting for heteroskedasticity by means of stochastic volatility usually provides additional improvements, although not for all variables.

Motivation & Objective

• Address the loss of information when aggregating high-frequency data to quarterly frequency in standard VAR models.
• Incorporate prior knowledge about long-run unconditional means (steady states) of macroeconomic variables to improve forecast stability and accuracy.
• Enhance model flexibility by allowing time-varying volatility through stochastic volatility modeling.
• Evaluate the predictive performance of the proposed model against standard VARs using mixed-frequency data in a real-world macroeconomic setting.

Proposed method

• Formulate a mean-adjusted VAR using a state-space representation to handle mixed-frequency data with missing intra-quarterly observations.
• Introduce a steady-state prior that explicitly models the unconditional mean of each variable, enabling direct incorporation of theoretical or empirical long-run expectations.
• Apply a hierarchical shrinkage prior to the steady-state parameters, allowing automatic shrinkage toward hyperpriors while maintaining flexibility.
• Incorporate common stochastic volatility via the model of Carriero et al. (2016) to allow time-varying error covariance matrices.
• Use Markov Chain Monte Carlo (MCMC) methods, including Gibbs sampling, to estimate the intractable posterior distributions under the Bayesian framework.
• Estimate the model on a dataset of 10 monthly and 3 quarterly US macroeconomic variables, comparing predictive performance across multiple horizons.

Experimental results

Research questions

• RQ1 Does incorporating mixed-frequency data through a state-space model improve forecast accuracy compared to single-frequency VARs?
• RQ2 To what extent does including a steady-state prior enhance forecast performance, particularly for quarterly variables?
• RQ3 How does the hierarchical shrinkage prior on steady-state parameters compare to the standard steady-state prior in terms of predictive accuracy?
• RQ4 Does modeling time-varying volatility via stochastic volatility lead to improved forecast density and point predictions?
• RQ5 Are the gains from the proposed model robust across different data vintages and forecast horizons?

Key findings

• The mixed-frequency VAR with missing data imputation significantly improves forecast accuracy for both monthly and quarterly variables compared to single-frequency benchmarks.
• The steady-state prior consistently enhances forecast accuracy, with models using this prior outperforming those without it across all horizons and evaluation metrics.
• The hierarchical steady-state prior, which allows for automatic shrinkage, performs as well as or better than the standard steady-state prior in most cases.
• Stochastic volatility improves forecast density accuracy, particularly for unemployment and federal funds rate, though its impact on point forecasts is more variable.
• The model with all three components—mixed-frequency handling, steady-state prior, and stochastic volatility—achieves the best overall performance, dominating all alternatives in predictive ability.
• Results remain robust when evaluated against the second available data vintage, confirming that findings are not driven by data revision effects.