Cointegrated systems II

The three invited papers in this special issue of Econometric Reviews on "Cointegrated Systems II" complement the previous special issue of the journal. The paper by Eric Zivot and Peter Phillips provides a comprehensive Bayesian analysis of trend determination in economic time series. Two interesting comments on some aspects of current research involving cointegration and the modelling of dynamic economic relationships are provided by Clive Granger and Denzil Fiebig.     

Exact Likelihood Equations for Autoregression Models with Multivariate Elliptically Contoured Distributions

Abstract

The multivariate elliptically contoured distributions provide a viable framework for modeling time-series data. It includes the multivariate normal, power exponential, t, and Cauchy distributions as special cases. For multivariate elliptically contoured autoregressive models, we derive the exact likelihood equations for the model parameters. They are closely related to the Yule-Walker equations and involve simple function of the data. The maximum likelihood estimators are obtained by alternately solving two linear systems and illustrated using the simulation data.     

Consistency of the normal equations

This note provides an alternative proof of consistency of the normal equations by appealing to well-known results in linear programming.     

Analyzing Cohort Mortality Data

Several methods for analyzing data from mortality studies of occupationally or environmentally exposed cohorts are shown to be special cases of a single procedure. The procedure assumes a proportional hazards model for exposure effects and represents the log-likelihood kernel for the data as that of N independent Poisson variates, where N is the total number of person-units of mortality observation time in the study. It formalizes and justifies the epidemiological techniques of classifying deaths and person-months of study time into categories defined by exposure and other covariates, and of computing standardized mortality ratios and indirectly standardized death rates. Parameters representing exposure effects can be estimated by using standard software packages. Special cases and applications are described in the context of lung cancer mortality among U.S. uranium miners.     

Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects

Abstract. We consider N independent stochastic processes (X _i (t), t ∈ [0,T _i ]), i=1,…, N, defined by a stochastic differential equation with drift term depending on a random variable φ _i . The distribution of the random effect φ _i depends on unknown parameters which are to be estimated from the continuous observation of the processes X_i. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect φ _i and φ _i has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when T _i =T for all i and N tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large.     

Robust Correlation Structure for Multivariate Failure Time Data

When incomplete repeated failure times are collected from a large number of independent individuals, interest is focused primarily on the consistent and efficient estimation of the effects of the associated covariates on the failure times. Since repeated failure times are likely to be correlated, it is important to exploit the correlation structure of the failure data in order to obtain such consistent and efficient estimates. However, it may be difficult to specify an appropriate correlation structure for a real life data set. We propose a robust correlation structure that can be used irrespective of the true correlation structure. This structure is used in constructing an estimating equation for the hazard ratio parameter, under the assumption that the number of repeated failure times for an individual is random. The consistency and efficiency of the estimates is examined through a simulation study, where we consider failure times that marginally follow an exponential distribution and a Poisson distribution is assumed for the random number of repeated failure times. We conclude by using the proposed method to analyze a bladder cancer dataset.     

非线性时滞差分方程解的振动性

讨论了时滞差分系统yn＋1－yn＋Pnf（yn－k）＝0n＝0,1,2,...（y≠0）的振动性,得到了上式方程解振动的一组充分条件．     

耦合KdV方程组的孤波精确解

本文利用一种简明的方法得出一类耦合KdV方程组的孤波精确解。     

一类变系数边值问题的样条解法

本文讨论了一类三阶变系数微分方程的边值问题的样条解法．构造了一个四次样条的近似解,并证明了它的唯一性和收敛性．在文末举例说明本方法是可行的．