On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

Theoretical results on the discrete Weibull distribution of Nakagawa and Osaki

In this paper, we discuss some theoretical results and properties of the discrete Weibull distribution, which was introduced by Nakagawa and Osaki [The discrete Weibull distribution. IEEE Trans Reliab. 1975;24:300–301]. We study the monotonicity of the probability mass, survival and hazard functions. Moreover, reliability, moments, p-quantiles, entropies and order statistics are also studied. We consider likelihood-based methods to estimate the model parameters based on complete and censored samples, and to derive confidence intervals. We also consider two additional methods to estimate the model parameters. The uniqueness of the maximum likelihood estimate of one of the parameters that index the discrete Weibull model is discussed. Numerical evaluation of the considered model is performed by Monte Carlo simulations. For illustrative purposes, two real data sets are analyzed.     

A new infinitely divisible discrete distribution with applications to count data modeling

A new discrete distribution involving geometric and discrete Pareto as special cases is introduced. The distribution possesses many interesting properties like decreasing hazard rate, zero vertex uni-modality, over-dispersion, infinite divisibility and compound Poisson representation, which makes the proposed distribution well suited for count data modeling. Other issues including closure property under minima, comparison of its distribution tail with other distributions via actuarial indices are discussed. The method of proportion and maximum likelihood method are presented for parameter estimation. Finally the performance of the proposed distribution over other classical and newly proposed infinitely divisible distributions are discussed.     

A new aging concept derived from the increasing convex ordering

In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented.     

On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.     

MARKET PENETRATION AND LOCATIONAL CONFLICT IN FRANCHISE SYSTEMS*

This paper addresses the questions of market penetration and locational conflict in a franchise system of distribution. The models developed provide a means to evaluate alternative scenarios and the effects of various franchise policies. It is shown that the market penetration and location goals of the members of a franchise system coincide only under a very limited set of circumstances.     

Finite normal mixture copulas for multivariate discrete data modeling

A new family of copulas is introduced that provides flexible dependence structure while being tractable and simple to use for multivariate discrete data modeling. The construction exploits finite mixtures of uncorrelated normal distributions. Accordingly, the cumulative distribution function is simply the product of univariate normal distributions. At the same time, however, the mixing operation introduces association. The properties of the new family of copulas are examined and a concrete application is used to show its applicability.     

Characterization of Lindley distribution by truncated moments

In the past few years, the Lindley distribution has gained popularity for modeling lifetime data as an alternative to the exponential distribution. This paper provides two new characterizations of the Lindley distribution. The first characterization is based on a relation between left truncated moments and failure rate function. The second characterization is based on a relation between right truncated moments and reversed failure rate function.     

Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes

In this article, we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted integrated conditional moment (ICM) test of Bierens (1984 Bierens, H. J. (1984). Model specification testing of time series regressions. Journal of Econometrics 26:323–353.[Crossref], [Web of Science ®] , [Google Scholar]) for time series regression models with the simulated ICM test of Bierens and Wang (2012 Bierens, H. J., Wang, L. (2012). Integrated conditional moment tests for parametric conditional distributions. Econometric Theory 28:328–362.[Crossref], [Web of Science ®] , [Google Scholar]) of conditional distribution models for cross-section data. To the best of our knowledge, no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors.     

Identification-robust moment-based tests for Markov switching in autoregressive models

ABSTRACT

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based inference methods. The approach exploits the moments of normal mixtures implied by the regime-switching process and uses Monte Carlo test techniques to deal with the presence of an autoregressive component in the model specification. The proposed tests have very respectable power in comparison with the optimal tests for Markov-switching parameters of Carrasco et al. (2014 Carrasco, M., Hu, L., Ploberger, W. (2014). Optimal test for Markov switching parameters. Econometrica 82(2):765–784.[Crossref], [Web of Science ®] , [Google Scholar]), and they are also quite attractive owing to their computational simplicity. The new tests are illustrated with an empirical application to an autoregressive model of USA output growth.