A weighted symmetric cointegration test

Weighted symmetric estimation is employed to develop a new test for cointegration. Using Monte Carlo simulation, the resulting test is shown to possess greater power than alternative existing tests.     

Bias correction and improved residuals for non-exponential family nonlinear models

In this paper we derive general formulae for the biases to order n ^?1 of the parameter estimates in a general class of nonlinear regression models, where n is the sample size. The formulae are related to those of Cordeiro and McCullagh (1991) and Paula (1992) and may be viewed as extensions of their results, Correction factors are derived for the score and deviance component residuals in these models. The practical use of such corrections is illustrated for the log-gamma model.     

Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions

The main goal in this paper is to develop and apply stochastic simulation techniques for GARCH models with multivariate skewed distributions using the Bayesian approach. Both parameter estimation and model comparison are not trivial tasks and several approximate and computationally intensive methods (Markov chain Monte Carlo) will be used to this end. We consider a flexible class of multivariate distributions which can model both skewness and heavy tails. Also, we do not fix tail behaviour when dealing with fat tail distributions but leave it subject to inference.     

A simulation study of estimators for generalized linear measurement error models

The purpose of this paper is to examine the properties of several bias-corrected estimators for generalized linear measurement error models, along with the naive estimator, in some special settings. In particular, we consider logistic regression, poisson regression and exponential-gamma models where the covariates are subject to measurement error. Monte Carlo experiments are conducted to compare the relative performance of the estimators in terms of several criteria. The results indicate that the naive estimator of slope is biased towards zero by a factor increasing with the magnitude of slope and measurement error as well as the sample size. It is found that none of the biased-corrected estimators always outperforms the others, and that their small sample properties typically depend on the underlying model assumptions.     

Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models

Inference, quantile forecasting and model comparison for an asymmetric double smooth transition heteroskedastic model is investigated. A Bayesian framework in employed and an adaptive Markov chain Monte Carlo scheme is designed. A mixture prior is proposed that alleviates the usual identifiability problem as the speed of transition parameter tends to zero, and an informative prior for this parameter is suggested, that allows for reliable inference and a proper posterior, despite the non-integrability of the likelihood function. A formal Bayesian posterior model comparison procedure is employed to compare the proposed model with its two limiting cases: the double threshold GARCH and symmetric ARX GARCH models. The proposed methods are illustrated using both simulated and international stock market return series. Some illustrations of the advantages of an adaptive sampling scheme for these models are also provided. Finally, Bayesian forecasting methods are employed in a Value-at-Risk study of the international return series. The results generally favour the proposed smooth transition model and highlight explosive and smooth nonlinear behaviour in financial markets.     

Estimation and inference for exponential smooth transition nonlinear volatility models

A family of threshold nonlinear generalised autoregressive conditionally heteroscedastic models is considered, that allows smooth transitions between regimes, capturing size asymmetry via an exponential smooth transition function. A Bayesian approach is taken and an efficient adaptive sampling scheme is employed for inference, including a novel extension to a recently proposed prior for the smoothing parameter that solves a likelihood identification problem. A simulation study illustrates that the sampling scheme performs well, with the chosen prior kept close to uninformative, while successfully ensuring identification of model parameters and accurate inference for the smoothing parameter. An empirical study confirms the potential suitability of the model, highlighting the presence of both mean and volatility (size) asymmetry; while the model is favoured over modern, popular model competitors, including those with sign asymmetry, via the deviance information criterion.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.     

A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao-Cramer lower bound) in the limit of small noise.     

A unified approach to estimation of nonlinear mixed effects and Berkson measurement error models

Mixed effects models and Berkson measurement error models are widely used. They share features which the author uses to develop a unified estimation framework. He deals with models in which the random effects (or measurement errors) have a general parametric distribution, whereas the random regression coefficients (or unobserved predictor variables) and error terms have nonparametric distributions. He proposes a second-order least squares estimator and a simulation-based estimator based on the first two moments of the conditional response variable given the observed covariates. He shows that both estimators are consistent and asymptotically normally distributed under fairly general conditions. The author also reports Monte Carlo simulation studies showing that the proposed estimators perform satisfactorily for relatively small sample sizes. Compared to the likelihood approach, the proposed methods are computationally feasible and do not rely on the normality assumption for random effects or other variables in the model.     

A fiducial-based approach to the one-way ANOVA in the presence of nonnormality and heterogeneous error variances

In this study, we propose a new test for testing the equality of the treatment means in one-way ANOVA when the usual normality and the homogeneity of variances assumptions are not met. In developing the proposed test, we benefit from the Fisher's fiducial inference [1–3]. Distribution of the error terms is assumed to be long-tailed symmetric (LTS) which includes the normal distribution as a limiting case. Modified maximum likelihood (MML) estimators are used in the test statistics rather than the traditional least squares (LS) estimators, since LS estimators have very low efficiencies under nonnormal distributions, see Tiku [4] for the details of MML methodology. An extensive Monte Carlo simulation study is done to compare the efficiency of the proposed test with the corresponding test based on normal theory, see Li et al. [5]. Finally, we give a real life example to show the applicability of the proposed methodology.     

A model averaging approach for the ordered probit and nested logit models with applications

This paper considers model averaging for the ordered probit and nested logit models, which are widely used in empirical research. Within the frameworks of these models, we examine a range of model averaging methods, including the jackknife method, which is proved to have an optimal asymptotic property in this paper. We conduct a large-scale simulation study to examine the behaviour of these model averaging estimators in finite samples, and draw comparisons with model selection estimators. Our results show that while neither averaging nor selection is a consistently better strategy, model selection results in the poorest estimates far more frequently than averaging, and more often than not, averaging yields superior estimates. Among the averaging methods considered, the one based on a smoothed version of the Bayesian Information criterion frequently produces the most accurate estimates. In three real data applications, we demonstrate the usefulness of model averaging in mitigating problems associated with the ‘replication crisis’ that commonly arises with model selection.     

A new estimation procedure for a partially nonlinear model via a mixed‐effects approach

The authors consider the estimation of the parametric component of a partially nonlinear semiparametric regression model whose nonparametric component is viewed as a nuisance parameter. They show how estimation can proceed through a nonlinear mixed‐effects model approach. They prove that under certain regularity conditions, the proposed estimate is consistent and asymptotically Gaussian. They investigate its finite‐sample properties through simulations and illustrate its use with data on the relation between the photosynthetically active radiation and the net ecosystem‐atmosphere exchange of carbon dioxide.     

A new class of multivariate skew distributions with applications to bayesian regression models

Abstract: The authors develop a new class of distributions by introducing skewness in multivariate elliptically symmetric distributions. The class, which is obtained by using transformation and conditioning, contains many standard families including the multivariate skew‐normal and t distributions. The authors obtain analytical forms of the densities and study distributional properties. They give practical applications in Bayesian regression models and results on the existence of the posterior distributions and moments under improper priors for the regression coefficients. They illustrate their methods using practical examples.     

Stochastic volatility in mean models with scale mixtures of normal distributions and correlated errors: A Bayesian approach

A stochastic volatility in mean model with correlated errors using the symmetrical class of scale mixtures of normal distributions is introduced in this article. The scale mixture of normal distributions is an attractive class of symmetric distributions that includes the normal, Student-t, slash and contaminated normal distributions as special cases, providing a robust alternative to estimation in stochastic volatility in mean models in the absence of normality. Using a Bayesian paradigm, an efficient method based on Markov chain Monte Carlo (MCMC) is developed for parameter estimation. The methods developed are applied to analyze daily stock return data from the São Paulo Stock, Mercantile & Futures Exchange index (IBOVESPA). The Bayesian predictive information criteria (BPIC) and the logarithm of the marginal likelihood are used as model selection criteria. The results reveal that the stochastic volatility in mean model with correlated errors and slash distribution provides a significant improvement in model fit for the IBOVESPA data over the usual normal model.     

A cluster‐sample approach for Monte Carlo integration using multiple samplers

A computational problem in many fields is to estimate simultaneously multiple integrals and expectations, assuming that the data are generated by some Monte Carlo algorithm. Consider two scenarios in which draws are simulated from multiple distributions but the normalizing constants of those distributions may be known or unknown. For each scenario, existing estimators can be classified as using individual samples separately or using all the samples jointly. The latter pooled‐sample estimators are statistically more efficient but computationally more costly to evaluate than the separate‐sample estimators. We develop a cluster‐sample approach to obtain computationally effective estimators, after draws are generated for each scenario. We divide all the samples into mutually exclusive clusters and combine samples from each cluster separately. Furthermore, we exploit a relationship between estimators based on samples from different clusters to achieve variance reduction. The resulting estimators, compared with the pooled‐sample estimators, typically yield similar statistical efficiency but have reduced computational cost. We illustrate the value of the new approach by two examples for an Ising model and a censored Gaussian random field. The Canadian Journal of Statistics 41: 151–173; 2013 © 2012 Statistical Society of Canada