Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy

Jochmann, Markus; Koop, Gary; Leon-Gonzalez, Roberto; Strachan, Rodney W.

doi:10.1002/jae.1238

Cited by 20 publications

(17 citation statements)

References 39 publications

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“…t s β = − ′ In models with larger n, there will typically be many more. For instance, in the 9-variable VECM of Jochmann et al (2013) In short, with regime switching cointegration it is very easy for the number of models to become very large very quickly. In this paper, we estimate and calculate the marginal likelihood in every model using posterior simulation methods.…”

Section: Model Spacementioning

confidence: 99%

“…With such a large model space, the methods used in this paper would not be computationally feasible. In such cases, the researcher must either restrict the model space in some way or use methods which do not explicitly calculate the marginal likelihood in each model (e.g., the stochastic search variable selection approach of Jochmann et al 2013).…”

Section: Model Spacementioning

confidence: 99%

“…The second case (b = 1) assumes a cointegration rank of one but does not constrain the cointegration space: 2 Note that an alternative to imposing the restriction on the cointegration space directly is to use a prior that is tightly centered over the restriction (see Jochmann et al 2013, for details and justification of this approach). We followed this strategy in an earlier version of this paper and obtained similar results.…”

Section: Application: the Fisher Effectmentioning

confidence: 99%

“…The researcher will typically consider models with different cointegrating ranks, different restrictions imposed on the cointegrating relationships, different lag lengths, different treatment of deterministic terms, etc. In previous work (see Koop, Potter, and Strachan 2008;Jochmann et al 2013), we have developed Bayesian methods to navigate through such high-dimensional model spaces in the constant coefficient VECM. In this paper, we work with models with regime change and, in these, the dimension of the model space is greatly increased.…”

Section: Introductionmentioning

confidence: 99%

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Regime-switching cointegration

Jochmann

Koop

2015

Studies in Nonlinear Dynamics &Amp; Econometrics

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Abstract:We develop methods for Bayesian inference in vector error correction models which are subject to a variety of switches in regime (e.g., Markov switches in regime or structural breaks). An important aspect of our approach is that we allow both the cointegrating vectors and the number of cointegrating relationships to change when the regime changes. We show how Bayesian model averaging or model selection methods can be used to deal with the high-dimensional model space that results. Our methods are used in an empirical study of the Fisher effect.

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Section: Model Spacementioning

confidence: 99%

Section: Model Spacementioning

confidence: 99%

Section: Application: the Fisher Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Regime-switching cointegration

Jochmann

Koop

2015

Studies in Nonlinear Dynamics &Amp; Econometrics

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“…When stationarity conditions are met for the latent processes the prior distributions for the state equation coefficients can be specified as proposed in Lopes, Salazar and Gamerman (2008). For the cointegration case, since the formulation given in equation (11) is quite general, and many plausible restricted models can be envisaged, Stochastic Search Variable Selection (SSVS) priors [see Jochmann et al (2013)] are used for the parameters of the state equations. Note that these plausible models may differ in the choice of the restrictions on the cointegration space, the number of exogenous and endogenous latent variables, and the lag length allowed for the autoregression.…”

Section: Cointegrated Latent Factorsmentioning

confidence: 99%

Modeling US housing prices by spatial dynamic structural equation models

Valentini¹,

Ippoliti²,

Fontanella³

2013

Ann. Appl. Stat.

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This article proposes a spatial dynamic structural equation model for the analysis of housing prices at the State level in the USA. The study contributes to the existing literature by extending the use of dynamic factor models to the econometric analysis of multivariate lattice data. One of the main advantages of our model formulation is that by modeling the spatial variation via spatially structured factor loadings, we entertain the possibility of identifying similarity "regions" that share common time series components. The factor loadings are modeled as conditionally independent multivariate Gaussian Markov Random Fields, while the common components are modeled by latent dynamic factors. The general model is proposed in a state-space formulation where both stationary and nonstationary autoregressive distributed-lag processes for the latent factors are considered. For the latent factors which exhibit a common trend, and hence are cointegrated, an error correction specification of the (vector) autoregressive distributed-lag process is proposed. Full probabilistic inference for the model parameters is facilitated by adapting standard Markov chain Monte Carlo (MCMC) algorithms for dynamic linear models to our model formulation. The fit of the model is discussed for a data set of 48 States for which we model the relationship between housing prices and the macroeconomy, using State level unemployment and per capita personal income.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS613 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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High-dimensional VAR with low-rank transition

et al. 2020

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We propose a vector auto-regressive (VAR) model with a low-rank constraint on the transition matrix. This new model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. We study estimation, prediction, and rank selection for this model in a very general setting. Our method shows excellent performances on a wide variety of simulated datasets. On macro-economic data from Giannone et al. (2015), our method is competitive with state-of-the-art methods in small dimension, and even improves on them in high dimension.(1995); Francq and Zakoian (2019). In this paper, we propose a vector auto-regressive (VAR) model that is suitable to predict high-dimensional series that are strongly correlated, or that are driven by a reasonable number of hidden factors. These features are captured by imposing a low-rank constraint on the transition matrix. The coefficients can be efficiently computed by convex optimization techniques.Let us briefly describe the motivation for this model. Assume we deal with an R M -valued process (X t ) t≥0 withfor a very large M . For examples, think of daily sales of items on Amazon, where an item might be iPhone 7 128Go black, Lord of the Rings -Harper Collins Box Set, 1991 or Estimation of Dependences Based on Empirical Data: Second Edition, by Vladimir Vapnik, Springer.Then it is obvious that even with a few years of observations, we observe at most X t for a few thousands of days t while M is probably of the order or 10 5 or 10 6 . Thus the estimation of the M 2 coefficients of the matrix A is impossible. Some constraints are necessary to reduce the dimension of the problem. We believe that the sparsity of A, studied by Davis et al. (2016) in another context, does not make sense here.On the other hand, it is clear that a few factors, like the current economic conditions, the period of the year, have a strong influence on the series. Assuming these factors H t are linear functions of X t , we can write them asThen, assuming that X t+1 can be linearly predicted by H t , we can predict X t+1 by U H t = U V X t for some M × r matrix U . At the end of the day, we indeed predict X t+1 by (U V )X t = AX t , but the rank of A is r M . Note that the assumption that the coefficient matrix A is low-rank in a multivariate regression model Y i = AX i +ξ i where Y i ∈ R s and X i ∈ R t was studied in Econometric theory as early as in the 50's Anderson (1951);Izenman (1975). It was referred to as RRR (reduced-rank regression). We refer the reader to Koltchinskii et al. (2011); Suzuki (2015); Alquier et al. (2017); Klopp et al. (2017a,b); Moridomi et al. (2018) for state-of-the-art results. Low-rank matrices were actually used to model high-dimensional time series by De Castro et al. (2017) and Alquier and Marie (2019), however, the models described in these papers cannot be straightforwardly used for prediction purposes. Here, we study estimation and prediction for the model (1).The paper is designed as follows. In the end of the in...

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Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy

Cited by 20 publications

References 39 publications

Regime-switching cointegration

Regime-switching cointegration

Modeling US housing prices by spatial dynamic structural equation models

High-dimensional VAR with low-rank transition

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