Multiple Time Series Modeling and Extended Sample Cross-Correlations

This article provides an expository account of the multivariate autoregressive moving average models and proposes an extended sample cross-correlation approach for practical model identification. An iterative model building procedure for applying these models to real data is discussed and demonstrated by analyzing the 5-series U.S. Hog Data.     

Trends and Cycles in Macroeconomic Time Series

Two structural time series models for annual observations are constructed in terms of trend, cycle, and irregular components. The models are then estimated via the Kalman filter using data on five U.S. macroeconomic time series. The results provide some interesting insights into the dynamic structure of the series, particularly with respect to cyclical behavior. At the same time, they illustrate the development of a model selection strategy for structural time series models.     

基于稳健Cook距离的时间序列异常值诊断

Cook距离公式常用于回归模型的异常值诊断,但由于公式中的样本方差■对异常值敏感,导致公式缺乏稳健性,使得诊断效果不理想。基于以上问题,文章选取绝对离差中位数作为样本标准差的稳健估计量,得到了样本方差■的稳健估计量,进而构造出稳健Cook距离公式;借鉴传统Cook距离的回归模型异常值诊断理论,将稳健Cook距离公式应用于时间序列异常值诊断,拓展了传统Cook距离公式的异常值诊断领域。通过选取模拟样本量分别为50、100、200,污染率分别为0、1%、5%、10%的ARMA(1,1)序列及金融时间序列进行实例分析,结果发现:(1)在无污染时,稳健Cook距离法与常规Cook距离法的诊断正确率均为100%,两者没有出现"误诊"现象;(2)在样本量、污染率同时增大时,常规Cook距离诊断正确率急剧下降,当污染率达到5%及以上时,已基本无诊断力,而稳健Cook距离法依然能保持较高的诊断力。稳健Cook距离法不仅能应用于时间序列异常值诊断,也能应用于回归分析的异常值诊断。     

Some Properties and Generalizations of Non-negative Bayesian Time Series Models

We study the most basic Bayesian forecasting model for exponential family time series, the power steady model (PSM) of Smith, in terms of observable properties of one-step forecast distributions and sample paths. The PSM implies a constraint between location and spread of the forecast distribution. Including a scale parameter in the models does not always give an exact solution free of this problem, but it does suggest how to define related models free of the constraint. We define such a class of models which contains the PSM. We concentrate on the case where observations are non-negative. Probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant, making them unsuitable for modelling in many situations. The results apply more generally to non-negative models defined in terms of exponentially weighted moving averages. We use these and related results to motivate, define and apply very simple models based on directly specifying the forecast distributions.     

An Application of Vector Time Series Techniques to Macroeconomic Forecasting

A wide variety of time series techniques are now used for generating forecasts of economic variables, with each technique attempting to summarize and exploit whatever regularities exist in a given data set. It appears that many researchers arbitrarily choose one of these techniques. The purpose of this article is to provide an example for which the choice of time series technique appears important; merely choosing arbitrarily among available techniques may lead to suboptimal results.     

Joint Modeling of Event Time and Nonignorable Missing Longitudinal Data

Survival studies usually collect on each participant, both duration until some terminal event and repeated measures of a time-dependent covariate. Such a covariate is referred to as an internal time-dependent covariate. Usually, some subjects drop out of the study before occurence of the terminal event of interest. One may then wish to evaluate the relationship between time to dropout and the internal covariate. The Cox model is a standard framework for that purpose. Here, we address this problem in situations where the value of the covariate at dropout is unobserved. We suggest a joint model which combines a first-order Markov model for the longitudinaly measured covariate with a time-dependent Cox model for the dropout process. We consider maximum likelihood estimation in this model and show how estimation can be carried out via the EM-algorithm. We state that the suggested joint model may have applications in the context of longitudinal data with nonignorable dropout. Indeed, it can be viewed as generalizing Diggle and Kenward's model (1994) to situations where dropout may occur at any point in time and may be censored. Hence we apply both models and compare their results on a data set concerning longitudinal measurements among patients in a cancer clinical trial.     

On the Detection of Contemporaneous Relationships Among Multiple Time Series

A study is carried out of a sampling from a half-normal and exponential distributions to develop a test of hypothesis on the mean. Although these distributions are similar, the corresponding uniformly most paerful test statistics are different. The exact distributions of these statistics my be written in terms of the incomplete gamma function. If the experimental data my be fitted by either distributions, it is advisable to carryout the test based on the half-normal distribution as it is generally more powerful than the one based on the exponential one.     

Inferences Concerning Exponential Distributions in the Presence of Randomly Right Censored Data with Missing Censored Values

Inferences concerning exponential distributions are considered from a sampling theory viewpoint when the data are randomly right censored and the censored values are missing. Both one-sample and m-sample (m 2) problems are considered. Likelihood functions are obtained for situations in which the censoring mechanism is informative which leads to natural and intuitively appealing estimators of the unknown proportions of censored observations. For testing hypotheses about the unknown parameters, three well-known test statistics, namely, likelihood ratio test, score test, and Wald-type test are considered.     

基于Copula函数的金融时间序列模型述评

结合当前Copula函数及其应用的热点问题,着重评述了基于Copula函数的金融时间序列模型的应用。鉴于利用Copula可以将边际分布和变量间的相依结构分开来研究这一优良性质,在设定和估计模型时便显得极为方便和灵活。从模型的构造、Copula函数的选择、模型的估计以及拟合优度检验等几方面展开阐述和评价,介绍了Copula模型在金融领域中的几类应用,并对Copula理论和应用的新视角进行了展望。     

基于分层阿基米德Copula的金融时间序列的相关性分析

与阿基米德copula相比,分层阿基米德copula(HAC)的结构更具一般性,而相比于椭圆型copula它的待估参数个数更少。用两阶段极大似然法来估计HAC函数,主要的步骤是先估计出每个分量的边际分布,以此为基础再估计copula函数。实证分析中,采取Clayton和Gumbel型的HAC分析四只股票价格序列之间的相关性。在得出HAC的结构和估计其参数之前,运用ARMA-GARCH过程消除了序列的自相关性和条件异方差。通过比较赤迟信息准则,认为完全嵌套的Gumbel型HAC能更好地刻画这种相关性。     

Least squates estimation of missing values in time series

The minimum mean square error linear interpolator for missing values in time series is extended to handle any pattern of nonconsecutive observations. The paper then develops evidence with simple ARMA models that the usefulness of either the"nonparametric"or the parametric form of the least squares interpolator depends on the time series model, the arrangement of the missing data and the objective for completing the series.     

Nonparametric Trend Estimation for Periodic Autoregressive Time Series

A periodically stationary time series has seasonal variances. A local linear trend estimation is proposed to accommodate unequal variances. A comparison of this proposed estimator with the estimator commonly used for a stationary time series is provided. The optimal bandwidth selection for this new trend estimator is discussed.     

Measuring Measurement Error in Economic Time Series

A spectral decomposition method is described for obtaining an upper bound on the amount of measurement error in a time series. The method is applied to generated data and to M1b, real GNP, and the CPI. The bounds provide insight into both the amount of measurement error in these series and the stochastic specification of the errors.     

A Note on Whittle's Likelihood

The approximate likelihood function introduced by Whittle has been used to estimate the spectral density and certain parameters of a variety of time series models. In this note we attempt to empirically quantify the loss of efficiency of Whittle's method in nonstandard settings. A recently developed representation of some first-order non-Gaussian stationary autoregressive process allows a direct comparison of the true likelihood function with that of Whittle. The conclusion is that Whittle's likelihood can produce unreliable estimates in the non-Gaussian case, even for moderate sample sizes. Moreover, for small samples, and if the autocorrelation of the process is high, Whittle's approximation is not efficient even in the Gaussian case. While these facts are known to some extent, the present study sheds more light on the degree of efficiency loss incurred by using Whittle's likelihood, in both Gaussian and non-Gaussian cases.     

也谈由一般平均数时间数列计算序时平均数——兼与“由一般平均数计算序时平均数的方法释疑”一文商榷

本文指出了由—般平均数时间数列计算序时平均数在教科书上存在错误和“由一般平均数计算序时平均数的方法释疑”一文中的不足之处提出了—般平均数时间数列的序时平均数可以按照相对数时间数列计算序时平均数的方法计算,也可以根据平均指标基本公式计算。     

Effect of systematic sampling on arima models

Given a general homogeneous non-stationary autoregressive integrated moving average process ARIMA(p,d,q), the corresponding model for the subseries obtained by a systematic sampling is derived. The article then shows that the sampled subseries approaches approximately to an integrated moving average process IMA(d,l), l≤(d-l), regardless of the autoregressive and moving average structures in the original series. In particular, the sampled subseries from an ARIMA (p,l,q) process approaches approximately to a simple random walk model.     

Extremes Values of Discrete and Continuous Time Strongly Dependent Gaussian Processes

The joint limit distribution of the maximum of a continuous, strongly dependent stationary Gaussian process and the maximum of this process sampled at discrete time points is studied. It is shown that these two extreme values are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense, and asymptotically dependent if the the grid points are sparse or Pickands grids. Our results are motivated by the deep contributions Piterbarg (2004 Piterbarg , V. I. ( 2004 ). Discrete and continuous time extremes of Gaussian processes . Extremes 7 : 161 – 177 .[Crossref] , [Google Scholar]) and Hüsler (2004 Hüsler , J. ( 2004 ). Dependence between extreme values of discrete and continuous time locally stationary Gaussian processes . Extremes 7 : 179 – 190 .[Crossref] , [Google Scholar]).     

股指时问序列的分形插值模型与R／S分析

运用分形插值模型和R／s分析法研究股指时间序列的变化规律和结构特征,通过建立分形插值模型刻画上证综合指数在一定时间内的变化规律,并预测其在短期内的指数走势。使用R／S分析法和Hurst指数,分析了上证综指的结构特征,指出市场具有状态持续性和分形分布等统计特征。     

A Note on Consistent Estimation of Multivariate Parameters in Ergodic Diffusion Models

Certain aspects of maximum likelihood estimation for ergodic diffusions are studied via recently developed empirical process theory for martingales. This approach enables us to remove some undesirable regularity conditions that usually appear in the statistical literature on ergodic diffusions. In particular, dimension dependent conditions for the existence of a continuous likelihood and for consistency of the maximum likelihood estimator turn out to be unnecessary.