Seemingly Unrelated Time Series Equations and a Test for Homogeneity

Fernández, Francisco Javier Moreno; Harvey, Andrew; Fernández, Francisco Javier

doi:10.2307/1391754

Cited by 14 publications

(11 citation statements)

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“…For the purpose of this paper the discussion is restricted to vector-valued time series; the general description for matrix-valued time series can be found in Salvador et al (2003). We should note that from a frequentist standpoint, MV-DLMs have been developed in Harvey (1986Harvey ( , 1989, Harvey and Snyder (1990), and Fernández and Harvey (1990). Suppose that the p-dimensional response vector y t follows a matrix-variate DLM so that…”

Section: Matrix-variate Dynamic Linear Modelsmentioning

confidence: 99%

Multivariate stochastic volatility with Bayesian dynamic linear models

Triantafyllopoulos

2008

Journal of Statistical Planning and Inference

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This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount the variances element by element and therefore allowing a flexible and pragmatic variance modelling approach. Diagnostic tests and sequential model monitoring are discussed in some detail. The proposed estimation theory is applied to a four-dimensional time series, comprising spot prices of aluminium, copper, lead and zinc of the London metal exchange. The empirical findings suggest that the proposed Bayesian procedure can be effectively applied to financial data, overcoming many of the disadvantages of existing volatility models.

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Section: Matrix-variate Dynamic Linear Modelsmentioning

confidence: 99%

Multivariate stochastic volatility with Bayesian dynamic linear models

Triantafyllopoulos

2008

Journal of Statistical Planning and Inference

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“…To this purpose, we formulate the multivariate dynamic model as a Seemingly Unrelated Time Series Equations (SUTSE) structure, Fernández and Harvey (1990), comprising the six ARIMA models, as in Wilson (1997a,b) and Nyström and Skoglund (2006), among others. Similarly, we assume that e = e 1 , ...,…”

Section: Federalmentioning

confidence: 99%

Linking the Problems of Estimating and Allocating Unconditional Capital

2014

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This paper addresses two problems related to determining the unconditional capital required by a credit portfolio: Estimating it using Monte Carlo simulation and allocating it among the different risk units that form the portfolio. By elaborating on a tractable analytical framework, we propose a new simulation algorithm and a new allocation method. Both contributions rely on the conditional loss distributions and share the same core idea. We discuss their optimality, consistence and practical advantages. In an empirical study based on American data, we show the remarkable gains in efficiency achieved by the former and the improvement in the standard variance-covariance allocation provided by the latter. Estimating it using Monte Carlo simulation and allocating it among the different risk units that form the portfolio. By elaborating on a tractable analytical framework, we propose a new simulation algorithm and a new allocation method. Both contributions rely on the conditional loss distributions and share the same core idea. We discuss their optimality, consistence and practical advantages. In an empirical study based on American data, we show the remarkable gains in efficiency achieved by the former and the improvement in the standard variance-covariance allocation provided by the latter.

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“…Whilst di¤use initial conditions are not explicitly dealt with in this paper, the relevant extensions can be deduced from the algorithms presented in Koopman and Durbin (2000) and Durbin and Koopman (2002). For the proceeding sections, it is convenient to de…ne, for s < t, y s:t = y The form of the SSM in (1) and (2) has been used in a wide range of Bayesian and non Bayesian applications including Fernandez and Harvey (1990), Koopman and Lucas (2005) and Harvey et al (2007), amongst others.…”

Section: Multivariate Linear Gaussian State Space Modelmentioning

confidence: 99%

Efficient Bayesian estimation of multivariate state space models

Strickland

Turner

Denham

et al. 2009

Computational Statistics & Data Analysis

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A Bayesian Markov chain Monte Carlo methodology is developed for the estimation of multivariate linear Gaussian state space models. In particular, an e¢ cient simulation smoothing algorithm is proposed that makes use of the univariate representation of the state space model. Substantial gains over existing algorithms in computational e¢ ciency are achieved using the new simulation smoother for the analysis of high dimensional multivariate time series.The methodology is used to analyse a multivariate timeseries dataset of the Normalised Di¤erence Vegetation Index (NDVI), which is a proxy for the level of live vegetation, for a particular grazing property located in Queensland, Australia.

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Seemingly Unrelated Time Series Equations and a Test for Homogeneity

Cited by 14 publications

References 0 publications

Multivariate stochastic volatility with Bayesian dynamic linear models

Multivariate stochastic volatility with Bayesian dynamic linear models

Linking the Problems of Estimating and Allocating Unconditional Capital

Efficient Bayesian estimation of multivariate state space models

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