Dynamic Copula-Based Markov Time Series

This article examines a test procedure for checking the constancy of serial dependence via copulas for Markov time series data. It also provides a copula-based modeling approach for the dynamic serial dependence. Various parametric families of copulas offering different dependent structures are investigated. A score test is proposed for checking the constancy of a copula parameter. The score test is constructed and its asymptotic null distribution established under a two-stage estimation procedure. The test does not require specification of the probability distribution for the copula parameter. To capture the dynamics of dependence structure over time, autoregressive moving average and exponential type models are proposed. Illustrations are given based on simulated data and historic coffee prices data.     

Semiparametric score test for varying copula parameter in Markov time series

This article examines a semiparametric test for checking the constancy of serial dependence via copula models for Markov time series. A semiparametric score test is proposed for testing the constancy of the copula parameter against stochastically varying copula parameter. The asymptotic null distribution of the test is established. A semiparametric bootstrap procedure is employed for the estimation of the variance of the proposed score test. Illustrations are given based on simulated series and historic interest rate data.     

Modeling statistical dependence of Markov chains via copula models

Conditional probability distributions have been commonly used in modeling Markov chains. In this paper we consider an alternative approach based on copulas to investigate Markov-type dependence structures. Based on the realization of a single Markov chain, we estimate the parameters using one- and two-stage estimation procedures. We derive asymptotic properties of the marginal and copula parameter estimators and compare performance of the estimation procedures based on Monte Carlo simulations. At low and moderate dependence structures the two-stage estimation has comparable performance as the maximum likelihood estimation. In addition we propose a parametric pseudo-likelihood ratio test for copula model selection under the two-stage procedure. We apply the proposed methods to an environmental data set.     

An alternative parameterization of Bayesian logistic hierarchical models for mixed treatment comparisons

Mixed treatment comparison (MTC) models rely on estimates of relative effectiveness from randomized clinical trials so as to respect randomization across treatment arms. This approach could potentially be simplified by an alternative parameterization of the way effectiveness is modeled. We introduce a treatment‐based parameterization of the MTC model that estimates outcomes on both the study and treatment levels. We compare the proposed model to the commonly used MTC models using a simulation study as well as three randomized clinical trial datasets from published systematic reviews comparing (i) treatments on bleeding after cirrhosis, (ii) the impact of antihypertensive drugs in diabetes mellitus, and (iii) smoking cessation strategies. The simulation results suggest similar or sometimes better performance of the treatment‐based MTC model. Moreover, from the real data analyses, little differences were observed on the inference extracted from both models. Overall, our proposed MTC approach performed as good, or better, than the commonly applied indirect and MTC models and is simpler, fast, and easier to implement in standard statistical software. Copyright © 2015 John Wiley & Sons, Ltd.