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VAR Models, Cointegration and Mixed-Frequency Data
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0003-4415-8734
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 [en]
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: urn:nbn:se:uu:diva-391500ISBN: 978-91-513-0734-3 (print)OAI: oai:DiVA.org:uu-391500DiVA, id: diva2:1345264
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
List of papers
1. Estimating a VECM for a Small Open Economy
Open this publication in new window or tab >>Estimating a VECM for a Small Open Economy
2019 (English)In: Article in journal (Other academic) Submitted
Abstract [en]

In economic theory, the term small open economy refers to an economy that is too small to influence the surrounding world. The surrounding world can, for this reason, be seen as exogenous relative to the economy of this small open economy. The main contribution of this paper is the proposal of how to estimate a vector error correction model with exogeneity restrictions on the long-run parameters, the adjustment parameters as well as on the short-run dynamic parameters between small open economies and the surrounding world. A Monte Carlo simulation study of impulse responses shows that the proposed method is considerably more efficient compared to models that fully or partially ignore the restrictions implied by the small open economy property. Using two Swedish macroeconomic datasets, we find that there are, for some variables, large differences in impulse responses between our proposed method incorporating the restrictions and models using no or partial restrictions. As the small open economy property is in many situations uncontroversial, our method enables the incorporation of indisputable economic theory into the econometric estimation of the model.

National Category
Other Social Sciences not elsewhere specified Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-391493 (URN)
Funder
The Jan Wallander and Tom Hedelius Foundation, P2016-0293:1
Available from: 2019-08-23 Created: 2019-08-23 Last updated: 2019-08-23
2. A Flexible Mixed-Frequency Vector Autoregression with a Steady-State Prior
Open this publication in new window or tab >>A Flexible Mixed-Frequency Vector Autoregression with a Steady-State Prior
2019 (English)In: Article in journal (Other academic) Submitted
Abstract [en]

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.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-391494 (URN)
Funder
The Jan Wallander and Tom Hedelius Foundation, P2016-0293:1Swedish National Infrastructure for Computing (SNIC), 2015/6-117
Available from: 2019-08-23 Created: 2019-08-23 Last updated: 2019-08-23
3. Simulation Smoothing for Nowcasting with Large Mixed-Frequency VARs
Open this publication in new window or tab >>Simulation Smoothing for Nowcasting with Large Mixed-Frequency VARs
2019 (English)In: Article in journal (Other academic) Submitted
Abstract [en]

There is currently an increasing interest in large vector autoregressive (VAR) models. VARs are popular tools for macro-economic forecasting and use of larger models has been demonstrated to often improve the forecasting ability compared to more traditional small-scale models. Mixed-frequency VARs deal with data sampled at different frequencies while remaining within the realms of VARs. Estimation of mixed-frequency VARs makes use of simulation smoothing, but using the standard procedure these models quickly become prohibitive in nowcasting situations as the size of the model grows. We propose two algorithms that alleviate the computational efficiency of the simulation smoothing algorithm. Our preferred choice is an adaptive algorithm, which augments the state vector as necessary to sample also monthly variables that are missing at the end of the sample. For large VARs, we find considerable improvements in speed using our adaptive algorithm. The algorithm therefore provides a crucial building block for bringing the mixed-frequency VARs to the high-dimensional regime.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-391495 (URN)
Available from: 2019-08-23 Created: 2019-08-23 Last updated: 2019-08-23
4. Estimating Large Mixed-Frequency Bayesian VAR Models
Open this publication in new window or tab >>Estimating Large Mixed-Frequency Bayesian VAR Models
(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:nbn:se:uu:diva-391496 (URN)
Funder
Swedish National Infrastructure for Computing (SNIC), 2018/8-361
Available from: 2019-08-23 Created: 2019-08-23 Last updated: 2019-08-23
5. Mixed-Frequency Bayesian VAR Models in R: The mfbvar Package
Open this publication in new window or tab >>Mixed-Frequency Bayesian VAR Models in R: The mfbvar Package
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Time series are often sampled at different frequencies, which leads to mixed-frequency data. Mixed frequencies are often neglected in applications as high-frequency series are aggregated to lower frequencies. In the mfbvar package, we introduce the possibility to estimate Bayesian vector autoregressive (VAR) models when the set of included time series consists of monthly and quarterly variables. The package implements several common prior distributions as well as stochastic volatility methods. The mixed-frequency nature of the data is handled by assuming that quarterly variables are weighted averages of unobserved monthly observations. We provide a user-friendly interface for model estimation and forecasting. The capabilities of the package are illustrated in an application.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-391497 (URN)
Funder
The Jan Wallander and Tom Hedelius Foundation, P2016-0293:1
Available from: 2019-08-23 Created: 2019-08-23 Last updated: 2019-08-23

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