JOURNAL OF THE JAPAN STATISTICAL SOCIETY Vol. 45(2015) No. 2

The Cumulative Residual Entropy (CRE), introduced by Rao et al. (2004), is viewed as a dynamic measure of uncertainty. Recently Asadi and Zohrevand (2007) proposed a dynamic form for the CRE, namely Dynamic Cumulative Residual Entropy (DCRE), and has discussed some of its properties. In this paper, we look into the problem of extending this concept to the conditionally specified models and study various properties of the new measures. We also propose nonparametric estimation for the new measures defined and performance of the estimators are compared using a simulation study.

The Hodrick-Prescott (HP) filter is a popular econometric tool for estimating the trend component of a given time series. Paige and Trindade (2010) present a ridge regression representation of the HP filter, which enhances our understanding of the filter. Schlicht (2005) presents another ridge regression representation of the HP filter. In this paper, we aim to generalize their results. In addition, we present an orthogonal decomposition of the generalized HP trend and newly introduce the pure generalized HP filter.

The BEKK model is a popular multivariate GARCH processes. The paper develops a new general asymmetric BEKK structure, which is based on recent empirical findings by semi-parametric news impact curves. For estimating the new model, a Markov chain Monte Carlo technique is used. Empirical results for triviarte asset returns from firms in the US indicate that the deviance information criterion favors the new model with a multivariate t distribution, and that co-leverage effects exist among the three assets.

We give estimators with bias exponentially small as the sample size increases for a broad class of multivariate power series families for lattice random variables. Examples include the Poisson, multinomial and negative multinomial distributions. Their use is illustrated by simulations and a real data application.