Parameterisation and efficient MCMC estimation of non-Gaussian state space models

Strickland, Chris; Martin, Gael M.; Forbes, Catherine

doi:10.1016/j.csda.2007.10.010

Cited by 22 publications

(18 citation statements)

References 24 publications

(34 reference statements)

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“…Although the results highlighted in the paper are particularly relevant to the trade durations literature (see also Engle & Russell 1998;Strickland, Forbes & Martin 2006;Strickland, Martin & Forbes 2008;Bauwens & Hautsch 2009), in which the second moment is of inherent interest as a risk measure, they are also relevant to any setting in which positive, skewed data is the focus. Some contributions to this general literature include Lawrance & Lewis (1980, 1985, Lewis, Mckenzie & Hugus (1989) and Ristic (2005).…”

Section: Introductionmentioning

confidence: 93%

A Quasi‐locally Most Powerful Test for Correlation in the Conditional Variance of Positive Data

McCabe

Martin²,

Freeland

2011

Aus NZ J of Statistics

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A test is derived for short-memory correlation in the conditional variance of strictly positive, skewed data. The test is quasi-locally most powerful (QLMP) under the assumption of conditionally gamma data. Analytical asymptotic relative efficiency calculations show that an alternative test, based on the first-order autocorrelation coefficient of the squared data, has negligible relative power to detect correlation in the conditional variance. Finite-sample simulation results confirm the poor performance of the squares-based test for fixed alternatives, as well as demonstrating the poor performance of the test based on the first-order autocorrelation coefficient of the raw (levels) data. The robustness of the QLMP test, both to misspecification of the conditional distribution and to misspecification of the dynamics, is also demonstrated using simulation. The test is illustrated using financial trade durations data.

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Section: Introductionmentioning

confidence: 93%

A Quasi‐locally Most Powerful Test for Correlation in the Conditional Variance of Positive Data

McCabe

Martin²,

Freeland

2011

Aus NZ J of Statistics

Self Cite

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“…The specification with σ j constant across j and σ T D = 0 is referred to as the basic structural model; see Harvey (1989). The representation used for the components is known as the non-centred (with respect to location and scale) representation; Frühwirth-Schnatter and Wagner (2010) and Strickland et al (2007) discuss its advantages for Bayesian estimation of the model. Notice that the trend component (2) can be written equivalently using the following recursions:…”

Section: Discussionmentioning

confidence: 99%

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

Proietti

Grassi

2014

Empir Econ

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An important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme.The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component: only in 70% of the cases we were able to select at least one stochastic trigonometric cycle out of the six possible cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles.An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects. AbstractAn important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme.The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component: only in 70% of the cases we were able to select at least one stochastic trigonometric cycle out of the six possible cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles.An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects.

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“…The stochastic model specification search methodology proposed by FS-W is based on a reparameterisation of (1), known as the non-centred representation, with respect to location and scale (see also Gelfand et al, 1995;Frühwirth-Schnatter, 2004;Strickland et al, 2007), which is obtained by writing…”

Section: Reparameterisation In Non-centred Formmentioning

confidence: 99%

Characterising economic trends by Bayesian stochastic model specification search

Grassi

Proietti

2014

Computational Statistics & Data Analysis

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Parameterisation and efficient MCMC estimation of non-Gaussian state space models

Cited by 22 publications

References 24 publications

A Quasi‐locally Most Powerful Test for Correlation in the Conditional Variance of Positive Data

A Quasi‐locally Most Powerful Test for Correlation in the Conditional Variance of Positive Data

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

Characterising economic trends by Bayesian stochastic model specification search

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