Estimating parameters of a multiple autoregressive model by the modified maximum likelihood method

We consider a multiple autoregressive model with non-normal error distributions, the latter being more prevalent in practice than the usually assumed normal distribution. Since the maximum likelihood equations have convergence problems (Puthenpura and Sinha, 1986) [11], we work out modified maximum likelihood equations by expressing the maximum likelihood equations in terms of ordered residuals and linearizing intractable nonlinear functions (Tiku and Suresh, 1992) [8]. The solutions, called modified maximum estimators, are explicit functions of sample observations and therefore easy to compute. They are under some very general regularity conditions asymptotically unbiased and efficient (Vaughan and Tiku, 2000) [4]. We show that for small sample sizes, they have negligible bias and are considerably more efficient than the traditional least squares estimators. We show that our estimators are robust to plausible deviations from an assumed distribution and are therefore enormously advantageous as compared to the least squares estimators. We give a real life example.     

Estimation of autoregressive models with epsilon-skew-normal innovations

A non-Gaussian autoregressive model with epsilon-skew-normal innovations is introduced. Moments and maximum likelihood estimators of the parameters are proposed and their limit distributions are derived. Monte Carlo simulation results are analysed and the model is fitted to a real time series.     

On categorical time series models with covariates

We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process and are defined by a GARCH-type recursive equation. We improve considerably upon the existing conditions about stationarity and ergodicity of those models. Proofs are based on theory developed for chains with complete connections. A useful coupling technique is employed for studying ergodicity of infinite order finite-state stochastic processes which generalize finite-state Markov chains. Furthermore, for the case of finite order Markov chains, we discuss ergodicity properties of a model which includes strongly exogenous but not necessarily bounded covariates.     

Statistically Efficient Thinning of a Markov Chain Sampler

It is common to subsample Markov chain output to reduce the storage burden. Geyer shows that discarding k ? 1 out of every k observations will not improve statistical efficiency, as quantified through variance in a given computational budget. That observation is often taken to mean that thinning Markov chain Monte Carlo (MCMC) output cannot improve statistical efficiency. Here, we suppose that it costs one unit of time to advance a Markov chain and then θ > 0 units of time to compute a sampled quantity of interest. For a thinned process, that cost θ is incurred less often, so it can be advanced through more stages. Here, we provide examples to show that thinning will improve statistical efficiency if θ is large and the sample autocorrelations decay slowly enough. If the lag ? ? 1 autocorrelations of a scalar measurement satisfy ρ_? > ρ_{? + 1} > 0, then there is always a θ < ∞ at which thinning becomes more efficient for averages of that scalar. Many sample autocorrelation functions resemble first order AR(1) processes with ρ_? = ρ^|?| for some ? 1 < ρ < 1. For an AR(1) process, it is possible to compute the most efficient subsampling frequency k. The optimal k grows rapidly as ρ increases toward 1. The resulting efficiency gain depends primarily on θ, not ρ. Taking k = 1 (no thinning) is optimal when ρ ? 0. For ρ > 0, it is optimal if and only if θ ? (1 ? ρ)²/(2ρ). This efficiency gain never exceeds 1 + θ. This article also gives efficiency bounds for autocorrelations bounded between those of two AR(1) processes. Supplementary materials for this article are available online.     

平均复本量预测模型研究

在确定采购复本量过程中，重点突出读者借阅行为的影响作用，根据借阅率与平均复本量之间相关关系，运用线性回归分析方法，预测未来2008-2009学年度20个大类图书平均复本量。目的是为了给采购复本量的确定提供参考。选取高校图书馆中具有代表性的H语言类图书为例，介绍平均复本量预测过程。     

On the Asymptotic Expectations of Some Unit Root Tests in a First Order Autoregressive Process in the Presence of Trend

Estimation in a first order autoregressive process with trend isconsidered. Integral expressions for the asymptotic bias of the estimatorunder a unit root and for the expectation of the limit distribution of thelog likelihood ratio test for a unit root are given, and evaluatednumerically.     

线性自回归加权递推模型

本文论述了线性自回归加权递推模型及其预测方法,并将指数窗加权方法用于自回归递推模型。以广西实际资料具体阐述了线性自回归加权递推模型在大林业中的应用。     

NONMRAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIME SERIES MODELS: CONVERGENCE RATES

61.IntroductionConsideranonlinearautoregressive(AR)modelintheformXt~f(Xt~1,'')Xt~.) st,(1.1)wheref'RP-RIisanunknownBorelfunctiononReand{s,}isani.i.d.whitenoisewithEat=0,Ear=aZ相似文献   

NONPARAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIMESERIES MODELS： CONVERGENCE RATES

In this paper the optimal convergence rates of estimators ba~ed on kernel approach fornonlinear AR model are investigated in the sense of Stone[17‘1a]. By combining the mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model axeremoved, and the mild conditions are obtained to guarantee the optimal ratea of the estimatorof autoregTession function. In addition: the strongly coasistent estimator of the ~riance ofwhite noise is also constructed.     

非平稳变量的Granger因果检验

由于非平稳的时间序列不具有有限方差,高斯-马尔科夫定理不再成立,用普通最小二乘法得到得参数估计不再是一致的,出现伪回归的现象,从而导致得出错误的因果关系。针对时间序列的非平稳性,指出目前进行Granger因果分析时所存在的问题,指出对非平稳变量进行因果分析的两种正确方法,并对这些方法的适应范围和优劣性进行比较。