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Estimating Large Mixed-Frequency Bayesian VAR Models
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0003-4415-8734
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We discuss the issue of estimating large-scale vector autoregressive (VAR) models with stochastic volatility in real-time situations where data are sampled at different frequencies. In the case of a large VAR with stochastic volatility, the mixed-frequency data warrant an additional step in the already computationally challenging Markov Chain Monte Carlo algorithm used to sample from the posterior distribution of the parameters. We suggest the use of a factor stochastic volatility model to capture a time-varying error covariance structure. Because the factor stochastic volatility model renders the equations of the VAR conditionally independent, settling for this particular stochastic volatility model comes with major computational benefits. First, we are able to improve upon the mixed-frequency simulation smoothing step by leveraging a univariate and adaptive filtering algorithm. Second, the regression parameters can be sampled equation-by-equation in parallel. These computational features of the model alleviate the computational burden and make it possible to move the mixed-frequency VAR to the high-dimensional regime. We illustrate the model by an application to US data using our mixed-frequency VAR with 20, 34 and 119 variables.

National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-391496OAI: oai:DiVA.org:uu-391496DiVA, id: diva2:1345140
Funder
Swedish National Infrastructure for Computing (SNIC), 2018/8-361Available from: 2019-08-23 Created: 2019-08-23 Last updated: 2019-08-23
In thesis
1. VAR Models, Cointegration and Mixed-Frequency Data
Open this publication in new window or tab >>VAR Models, Cointegration and Mixed-Frequency Data
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of five papers that study two aspects of vector autoregressive (VAR) modeling: cointegration and mixed-frequency data.

Paper I develops a method for estimating a cointegrated VAR model under restrictions implied by the economy under study being a small open economy. Small open economies have no influence on surrounding large economies. The method suggested by Paper I provides a way to enforce the implied restrictions in the model. The method is illustrated in two applications using Swedish data, and we find that differences in impulse responses resulting from failure to impose the restrictions can be considerable.

Paper II considers a Bayesian VAR model that is specified using a prior distribution on the unconditional means of the variables in the model. We extend the model to allow for the possibility of mixed-frequency data with variables observed either monthly or quarterly. Using real-time data for the US, we find that the accuracy of the forecasts is generally improved by leveraging mixed-frequency data, steady-state information, and a more flexible volatility specification.

The mixed-frequency VAR in Paper II is estimated using a state-space formulation of the model. Paper III studies this step of the estimation algorithm in more detail as the state-space step becomes prohibitive for larger models when the model is employed in real-time situations. We therefore propose an improvement of the existing sampling algorithm. Our suggested algorithm is adaptive and provides considerable improvements when the size of the model is large. The described approach makes the use of large mixed-frequency VARs more feasible for nowcasting.

Paper IV studies the estimation of large mixed-frequency VARs with stochastic volatility. We employ a factor stochastic volatility model for the error term and demonstrate that this allows us to improve upon the algorithm for the state-space step further. In addition, regression parameters can be sampled independently in parallel. We draw from the literature on large VARs estimated on single-frequency data and estimate mixed-frequency models with 20, 34 and 119 variables.

Paper V provides an R package for estimating mixed-frequency VARs. The package includes the models discussed in Paper II and IV as well as additional alternatives. The package has been designed with the intent to make the process of specification, estimation and processing simple and easy to use. The key functions of the package are implemented in C++ and are available for other packages to use and build their own mixed-frequency VARs.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 45
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 170
Keywords
vector error correction, small open economy, mixed-frequency data, Bayesian, steady state, nowcasting, state-space model, large VARs, simulation smoothing, factor stochastic volatility, R
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-391500 (URN)978-91-513-0734-3 (ISBN)
Public defence
2019-10-11, Hörsal 2, Kyrkogårdsgatan 10, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2019-09-20 Created: 2019-08-23 Last updated: 2019-10-15

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