Some tests for the power series distibutions in one parameter using the kullback-leibler information measure

The purpose of the article is, in case of one sample, to obtain tests concerning the parameter in the power series distribution in one parameter using Ku11back-Leibier information measure. The class of power series distibutions contains a host of discrete distributions. Ve illustrate the general results obtained in case of the geometric distibution.     

A SADDLEPOINT APPROXIMATION TO THE DISTRIBUTION FUNCTION OF THE ANDERSON-DARLING TEST STATISTIC

The Anderson-Darling goodness-of-fit test has a highly skewed and non-standard limit distribution. Various attempts have been made to tabulate the associated critical points, using both theoretical approximations and simulation methods. We show that a standard saddlepoint approximation performs well in both tails of the distribution. It is markedly superior to other theoretical approximations in the lower tail of the distribution.     

GENERALIZED SIGNED-RANK ESTIMATORS FOR AUTOREGRESSION PARAMETERS

ABSTRACT

A new class of weighted signed-rank-based estimates for estimating the parameter vector of an autoregressive time series is considered. The Wilcoxon signed-rank estimate and the GR-estimates of Terpstra et al. (GR-Estimates for an Autoregressive Time Series. Statistics and Probability Letters 2001, 51, 165–172; Generalized Rank Estimates for an Autoregressive Time Series: A U-Statistic Approach. Statistical Inference for Stochastic Processes 2001, 4, 155–179) can be viewed as special cases of the so-called GSR-estimates. Asymptotic linearity properties are derived for the GSR-estimates. Based on these properties, and a symmetry assumption, the GSR-estimates are shown to be asymptotically normal at rate n ^1/2. The theory of U-Statistics along with a characterization of weak dependence that is inherent in stationary AR(p) models are the primary tools used to obtain the results. Tests of hypotheses as well as standard errors for confidence interval procedures can be based on such results. An efficiency study indicates that, for an appropriately chosen set of weights, the GSR-estimate is more efficient than the GR-estimate. Furthermore, the GSR-estimate has an added advantage in that an intercept term can be estimated simultaneously; unlike the GR-estimate. Two examples and a small simulation study are used to illustrate the computational and robust aspects of the GSR-estimates.     

浪漫派诗歌关乎图征,还是象征——华兹华斯与柯尔律治的诗学思想比较

试图剖析华兹华斯与柯尔律治诗学理念格格不入的原因,提出浪漫派诗歌内部在图征和象征上的巨大差别,以及考察这两种古老的艺术手段对浪漫派诗歌在内容和形式上的创新和贡献。     

A diagnostic statistic for functional-coefficient autoregressive models

In this paper, functional coefficient autoregressive (FAR) models proposed by Chen and Tsay (1993) are considered. We propose a diagnostic statistic for FAR models constructed by comparing between parametric and nonparametric estimators of the functional form of the FAR models. We show asymptotic properties of our statistic mathematically and it can be applied to the estimation of the delay parameter and the specification of the functional form of FAR models.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

平稳性检验方法的有效性研究

平稳性检验是时间序列分析的重要研究内容,现有检验方法的性能缺乏系统的比较分析。文章从样本长度的视角研究平稳性检验方法的性能,采用ADF检验、PP检验、KPSS检验和LMC检验四种方法展开实证研究。仿真实验结果表明:时间序列数据长度会对检验方法的准确率产生明显的影响,数据长度较小时检验准确率偏低;数据长度增大时可以提升检验方法的准确率,但仍未能达到100%的上限值。当样本长度较小时,这些方法的检验统计量的渐进分布难以满足,因此其实际检验效果值得探究。样本长度是有限的,因此渐进分布检验方式的改进空间有限,新的检验方式值得探究。     

Empirical Likelihood for the Additive Hazards Model with Current Status Data

We investigate empirical likelihood for the additive hazards model with current status data. An empirical log-likelihood ratio for a vector or subvector of regression parameters is defined and its limiting distribution is shown to be a standard chi-squared distribution. The proposed inference procedure enables us to make empirical likelihood-based inference for the regression parameters. Finite sample performance of the proposed method is assessed in simulation studies to compare with that of a normal approximation method, it shows that the empirical likelihood method provides more accurate inference than the normal approximation method. A real data example is used for illustration.     

The Comparison of Performances of Widely Used Cointegration Tests

The aim of this study is to compare performances of commonly cointegration tests used in literature in terms of their empirical power and type I error probabilty for various sample sizes. As a result of the study, it has been found that some tests are not appropriate in testing cointegration in terms of empirical power and type I error probability. As a result of simulation study, λ_max test for any values of ρ and sample sizes have been found most appropriate test in conclusion.     

Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.