Rank estimation in Cointegrated Vector Auto-Regression models via automated Trans-dimensional Markov chain Monte Carlo (original) (raw)
Model selection and adaptive Markov chain Monte Carlo for Bayesian cointegrated {VAR} models
Bayesian Analysis, 2010
This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorithm of . Developing the adaptive MCMC framework for Bayesian CVAR models allows for efficient estimation of posterior parameters in significantly higher dimensional CVAR series than previously possible with existing griddy Gibbs samplers. For a n-dimensional CVAR series, the matrix-variate posterior is in dimension 3n 2 + n, with significant correlation present between the blocks of matrix random variables. Hence, utilizing a griddy Gibbs sampler for large n becomes computationally impractical as it involves approximating an n × n full conditional posterior using a spline over a high dimensional n × n grid. The adaptive MCMC approach is demonstrated to be ideally suited to learning on-line a proposal to reflect the posterior correlation structure, therefore improving the computational efficiency of the sampler.
Some recent developments in Markov Chain Monte Carlo for cointegrated time series
We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler of Koop et al. [2009] and the Geodesic Hamiltonian Monte Carlo method of Byrne and Girolami [2013]. Then we will propose extensions that can allow the ideas in both methods to be applied for cointegrated time series with non-Gaussian noise. We illustrate the efficiency and accuracy of these extensions using appropriate numerical experiments.
Bayesian Analysis, 2011
We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and α-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of α-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed α-stable models.
Bayesian Analysis of Random Coefficient Autoregressive Models
Model Assisted Statistics and Applications, 2008
Random Coefficient AutoRegressive (RCAR) models are obtained by introducing random coefficients to an AR or more generally ARMA model. These models have second order properties similar to that of ARCH and GARCH models. In this article, a Bayesian approach to estimate the first order RCAR models is considered. A couple of Bayesian testing criteria for the unit-root hypothesis are proposed: one is based on the Posterior Interval, and the other one is based on Bayes Factor. In the end, two real life examples involving the daily stock volume transaction data are presented to show the applicability of the proposed methods.
Bayesian Nonparametric Vector Autoregressive Models
SSRN Electronic Journal, 2015
The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.
A Bayesian approach to modelling graphical vector autoregressions
2006
Abstract. We introduce a Bayesian approach to model assessment in the class of graphical vector autoregressive processes. As a result of the very large number of model structures that may be considered, simulation-based inference, such as Markov chain Monte Carlo, is not feasible. Therefore, we derive an approximate joint posterior distribution of the number of lags in the autoregression and the causality structure represented by graphs using a fractional Bayes approach.
Analysis of Exchange Rates via Multivariate Bayesian Factor Stochastic Volatility Models
Springer Proceedings in Mathematics & Statistics, 2013
Multivariate factor stochastic volatility (SV) models are increasingly used for the analysis of multivariate financial and economic time series because they can capture the volatility dynamics by a small number of latent factors. The main advantage of such a model is its parsimony, as the variances and covariances of a time series vector are governed by a low-dimensional common factor with the components following independent SV models. For high dimensional problems of this kind, Bayesian MCMC estimation is a very efficient estimation method, however, it is associated with a considerable computational burden when the dimensionality of the data is moderate to large. To overcome this, we avoid the usual forward-filtering backward-sampling (FFBS) algorithm by sampling "all without a loop" (AWOL), consider various reparameterizations such as (partial) non-centering, and apply an ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation at a univariate level, which can be applied directly to heteroskedasticity estimation for latent variables such as factors. To show the effectiveness of our approach, we apply the model to a vector of daily exchange rate data.
Bayesian estimation of an autoregressive model using Markov chain Monte Carlo
Journal of Econometrics, 1996
We present a complete Bayesian treatment of autoregressive model estimation incorporating choice of autoregressive order, enforcement of stationarity, treatment of outliers and allowance for missing values and multiplicative seasonality. The paper makes three distinct contributions. First, we enforce the stationarity conditions using a very e cient Metropolis-within-Gibbs algorithm to generate the partial autocorrelations. Second we show how to carry out the Gibbs sampler when the autoregressive order is unknown. Third, we show how to combine the various aspects of tting an autoregressive model giving a more comprehensive and e cient treatment than previous work. We illustrate our methodology with a real example.
Reduced-Rank Covariance Estimation in Vector Autoregressive Modeling
We consider reduced-rank modeling of the white noise covariance matrix in a large dimensional vector autoregressive (VAR) model. We first propose the reduced-rank covariance estimator under the setting where independent observations are available. We derive the reducedrank estimator based on a latent variable model for the vector observation and give the analytical form of its maximum likelihood estimate. Simulation results show that the reduced-rank covariance estimator outperforms two competing covariance estimators for estimating large dimensional covariance matrices from independent observations. Then we describe how to integrate the proposed reduced-rank estimator into the fitting of large dimensional VAR models, where we consider two scenarios that require different model fitting procedures. In the VAR modeling context, our reduced-rank covariance estimator not only provides interpretable descriptions of the dependence structure of VAR processes but also leads to improvement in model-fitting and forecasting over unrestricted covariance estimators. Two real data examples are presented to illustrate these fitting procedures.
Bayesian Estimation and Model Selection for the Weekly Colombian Exchange Rate
Macroeconomics eJournal, 2001
This document reviews and applies recently developed techniques for Bayesian estimation and model selection in the context of Time Series modeling for Stochastic Volatility. After the literature review on Generalized Conditional Autoregressive models, Stochastic Volatility models, and the relevant results on Markov chain Monte Carlo methods (MCMC), an example applying such techniques is shown. The methodology is used with a series of Weekly Colombian - USA Exchange Rate on seven different models. The GARCH model, which uses Type-IV Pearson distribution, is favored for the selecting technique, Reversible Jump MCMC, over other models, including Stochastic Volatility Models with a Student-t distribution.