Simple detection of outlying short time series

Sets of relatively short time series arise in many situations. One aspect of their analysis may be the detection of outlying series. We examine the performance of standard normal outlier tests applied to the means, or to simple functions of the means, of AR(1) series, not necessarily of equal lengths. Although unequal lengths of series implies that the means have unequal variances, that are only known approximately, it is shown that nominal significance levels hold good under most circumstances. Thus a standard outlier test can usefully be applied, avoiding the complication of estimating the time series' parameters. The test's power is affected by unequal lengths, being higher when the slippage occurs in one of the longer series     

基于最大熵谱估计的机载雷达杂波抑制技术

在讨论机载雷达地面杂波的基础上，利用最大熵估计法对机载雷达杂波进行抑制，并引入了ｃｈｏｌｃｓｋｙ分解快速算法求解最大熵谱的ＡＲ模型参数。计算机模拟表明，基于最大熵谱估计的机载雷达杂波抑制技术有很高的谱分辨率，不仅能跟踪主杂波的频率位置而且能跟踪其谱宽度，因而具有较为满意的杂波对消化与改善因子。     

中国电力消费周期的路径演化识别——基于Markov区制转移模型

基于1980-2016年中国第一产业、第二产业（工业、建筑业）和第三产业的年度电力消费数据,采用H-P滤波技术对中国电力消费的趋势成分和波动成分轨迹进行刻画,运用马尔科夫区制转移[MS（n）-AR（p）]模型分析中国电力消费周期在各区制间的动态转移过程,识别改革开放以来中国电力消费周期的路径演化特征,在此基础上预测未来5年中国电力消费周期的区制分布情况。研究发现:（1）中国电力消费增长率的波动程度自2003年明显缩窄,且从2007年开始进入下行周期。（2）中国电力消费周期具有较强的稳定性,不易向着其收缩期和扩张期跨越。且中国电力消费处于"低速增长区制"的年份往往对应着中国经济发展相对趋缓的大环境。（3）2014-2015年中国电力消费向其收缩期转移的迹象明显,但预测结果表明,未来5年中国电力消费整体上将继续保持稳定增长的趋势。     

Uniform Test for Predictive Regression With AR Errors

Testing predictability is of importance in economics and finance. Based on a predictive regression model with independent and identically distributed errors, some uniform tests have been proposed in the literature without distinguishing whether the predicting variable is stationary or nearly integrated. In this article, we extend the empirical likelihood methods of Zhu, Cai, and Peng with independent errors to the case of an AR error process. Again, the proposed new tests do not need to know whether the predicting variable is stationary or nearly integrated, and whether it has a finite variance or an infinite variance. A simulation study shows the new methodologies perform well in finite sample.     

Bayesian bridge-randomized penalized quantile regression estimation for linear regression model with AP(q) perturbation

Bridge penalized regression has many desirable statistical properties such as unbiasedness, sparseness as well as ‘oracle’. In Bayesian framework, bridge regularized penalty can be implemented based on generalized Gaussian distribution (GGD) prior. In this paper, we incorporate Bayesian bridge-randomized penalty and its adaptive version into the quantile regression (QR) models with autoregressive perturbations to conduct Bayesian penalization estimation. Employing the working likelihood of the asymmetric Laplace distribution (ALD) perturbations, the Bayesian joint hierarchical models are established. Based on the mixture representations of the ALD and generalized Gaussian distribution (GGD) priors of coefficients, the hybrid algorithms based on Gibbs sampler and Metropolis-Hasting sampler are provided to conduct fully Bayesian posterior estimation. Finally, the proposed Bayesian procedures are illustrated by some simulation examples and applied to a real data application of the electricity consumption.     

The robustness of the systemwise breusch-godfrey autocorrelation test for non-normal distributed error terms

Using Monte Carlo methods, the properties of systemwise generalisations of the Breusch-Godfrey test for autocorrelated errors are studied in situations when the error terms follow either normal or non-normal distributions, and when these errors follow either AR(1) or MA(1) processes. Edgerton and Shukur (1999) studied the properties of the test using normally distributed error terms and when these errors follow an AR(1) process. When the errors follow a non-normal distribution, the performances of the tests deteriorate especially when the tails are very heavy. The performances of the tests become better (as in the case when the errors are generated by the normal distribution) when the errors are less heavy tailed.     

Diagnostics for elliptical linear mixed models with first-order autoregressive errors

For longitudinal time series data, linear mixed models that contain both random effects across individuals and first-order autoregressive errors within individuals may be appropriate. Some statistical diagnostics based on the models under a proposed elliptical error structure are developed in this work. It is well known that the class of elliptical distributions offers a more flexible framework for modelling since it contains both light- and heavy-tailed distributions. Iterative procedures for the maximum-likelihood estimates of the model parameters are presented. Score tests for the presence of autocorrelation and the homogeneity of autocorrelation coefficients among individuals are constructed. The properties of test statistics are investigated through Monte Carlo simulations. The local influence method for the models is also given. The analysed results of a real data set illustrate the values of the models and diagnostic statistics.     

A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation

The responses obtained from response surface designs that are run sequentially often exhibit serial correlation or time trends. The order in which the runs of the design are performed then has an impact on the precision of the parameter estimators. This article proposes the use of a variable-neighbourhood search algorithm to compute run orders that guarantee a precise estimation of the effects of the experimental factors. The importance of using good run orders is demonstrated by seeking D-optimal run orders for a central composite design in the presence of an AR(1) autocorrelation pattern.     

Geometric ergodicity of nonlinear autoregressive models with changing conditional variances

The authors give easy‐to‐check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process x_t = ?(x_t‐1,…, x_t‐p) + ?_tσ(x_t‐1,…, x_t‐q) in which ?: R^p → R, σ R^q → R and (?_t) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)‐ARCH(p), and the double‐threshold autoregressive models.