Box-Pierce Q检验的改进方法

Box-Pierce Q检验采用近似卡方分布分析时间序列的平稳性特征,其检验统计量的参数选取将影响到检验结果.文章多个Q值提取平稳性特征,在此基础上建立新的平稳性判定准则,该准则是自相关函数序列收敛的充分条件;采用欧氏函数作为平稳性特征的相似性度量,借助k-means聚类建立平稳性分类方法;该方法在平稳性分析过程中充分考虑了样本之间的关联性,避免了传统Box-PierceQ检验对统计分布和临界表的过度依赖.实验结果表明,新方法能有效地处理海量时间序列数据,且准确率高于Q检验和ADF检验.     

时间序列的单位根检验与伪检验

文章证明了平稳性的三个结论,即平稳序列的子序列仍是平稳的;非平稳序列子序列单整阶数不会超过原序列;一个序列乘以一个大于0的常数,平稳性不会改变。并利用得到的结论分析GDP序列,指出一些文献中的检验属于伪检验。对GDP数据序列（1952～2008）的平稳性检验得出结论：实际GDP取自然对数后是I（1）序列;实际人均GDPI（2）序列;实际人均GDP对数序列是I（1）序列;实际GDP增长率是I（0）序列。     

运用空间统计方法分析我国社会福利的有关问题

在研究经济问题时,处理的数据大多是时间序列数据,对这类数据的分析采用的是时间序列分析方法,较少进行空间分析,建立的模型也是以时间序列为主。虽然这种以时间序列数据为对象进行分析、研究问题的方法能够反映一定的经济问题,但是往往会掩盖空间的差异。比如一个问题从时间序     

基于DWT的相似性搜索算法

时间序列数据聚类在统计分析中具有重要意义。然而高维时间序列数据挖掘高度依赖的相似性搜索方法仍面临计算量大、准确率低等问题。为了提升高维时间序列数据挖掘任务的准确率和效率，提出一种基于波动特征的时间序列相似性搜索算法。该算法首先提出局部高频离散小波变换(LHFDWT)方法，通过合理的分解与重构来实现序列的降维；然后提出基于欧氏距离(ED)、波动幅度和秩相关系数从时间序列形态波动的相对偏差和趋势一致性角度计算相似度；最后提出一种相似性搜索算法和新的基于波动特征的时间序列聚类方法，并利用k-medoids聚类技术进行聚类分析。基于UCR标准时间序列数据集的实验结果表明，相对于动态时间规整(DTW)和最长公共子序列(LCSS)方法，所提新方法下的聚类准确率表现更优，置信度达到99%;在正确预测聚类数目和搜索效率方面具有更好的效果，且聚类结果具有更高的稳定性；1-NN分类准确率更高，说明其在确定更好的聚类中心方面效果更优，置信度至少为85%,证明了所提新方法的相似性搜索算法的优越性。     

能源消费与经济增长动态关系比较研究

文章以1990～2006年我国能源消费各组成部分煤炭,石油,天然气,水电、风电、核电消费量和GDP的时间序列数据为样本,采用ADF检验检验序列的平稳性,采用协整检验方法检验序列变量是否存在长期均衡关系,并在协整的基础上建立误差修正模型,采用格兰杰因果关系检验序列变量之间是否存在因果关系,比较研究我国煤炭,石油,天然气,水电、风电、核电消费与经济增长之间的短期波动和长期均衡关系,并对未来我国能源和经济的协调发展提出了几点建议.     

中国国防费时间序列预测模型的建立

时间序列模型(ARMA)是一种精度较高的短期预测模型.本文综合运用B-J时间序列建模方法,对中国国防费时间序列平稳性进行了判别;利用单位根方法检验了时间序列的单整阶数;利用自相关函数和偏自相关函数判别了时间序列模型的自回归阶数(AR(p))和移动平均阶数(MA(q));最后利用Eviews统计软件建立了合适的中国国防费时间序列模型,并进行了分析和预测.     

空间统计方法在社会福利分析中的应用

在研究经济问题时,处理的数据大多是时间序列数据,对这类数据的分析采用的是时间序列分析方法,较少进行空间分析,建立的模型也是以时间序列为主。虽然这种以时间序列数据为对象进行分析、研究问题的方法能够反映一定的经济问题,但是往往会掩盖空间的差异。因为我们生活在由时间     

多指标面板数据聚类方法及其应用

文章针对多指标面板数据的样品分类问题,从多元统计学理论角度提出一个多指标面板数据的聚类分析方法。该方法综合考虑面板数据的水平指标、增量指标和增量变化率指标的时间序列特征及其非同步时间序列问题,在重新构造了离差平方和函数基础上,提出了一种聚类方法。通过实证分析,表明新方法能够解决多指标面板数据聚类的问题,分类效果较好。     

中国城镇化进程与经济增长关系的实证研究

 以我国1978-2009年城镇化率和人均GDP年度时间序列数据为基础,建立反映城镇化水平和经济增长动态关系的向量自回归(VAR)模型;在VAR模型的基础上,运用脉冲响应函数和方差分解分析了城镇化进程与经济增长相互之间的动态影响。为了弥补时间序列数据只包含时间和指标两维信息的缺陷,进一步采用2000-2009年我国31个省市的城镇化率和人均GDP的面板数据,利用横截面、时间和指标三维信息对两者之间的关系进行分析。通过运用面板数据的单位根检验和面板数据协整检验,得出我国城镇化进程与经济发展水平之间存在长期稳定的均衡关系。在此基础上,建立面板数据固定效应变系数模型,从弹性角度分析,认为我国城镇化率每提高一个百分点,可以维持7.1%的经济增长。     

郑州期货市场量价关系的实证分析

一、研究方法和模型选择(一)交易量处理本文采集了2004年6月1日至2006年7月28日棉花期货合约每天的收盘价和交易量(数据来源:郑州商品交易所网站)。由于每个期货合约都将在一定时间到期,因此如何产生一个连续的期货价格序列是个难题。本文选取离交割期最近月份的期货合约作为代表,在进入交割月后选取下一个最靠近交割月份的合约,得到连续期货价格序列和交易量序列。原始的交易量数据存在着非平稳性和时间序列相关性问题,因此需要用下面的自回归模型ARMA(p,q)对交易量数据进行处理,以得到一个平稳的、非相关的交易量序列作为信息指标的代理:     

F-tests for seasonal differencing with a break-point

The classification between stochastic trend stationarity and deterministic broken trend stationarity is important because incorrect inferences can follow if a stationary series with a broken trend is incorrectly classified as integrated. In this paper, we consider joint tests for regular and seasonal unit roots null hypothesis against broken trend stationarity alternatives where the location of the break is known or unknown. Based on the F-test proposed by Hasza and Fuller (1982, Ann. Statist. 10, 1209–1216), we develop testing procedures for distinguishing these two types of process. The asymptotic distributions of test statistics are derived as functions of Wiener processes. A response surface regression analysis directed to relating the finite sample distributions and the breaking position is studied. Simulation experiments suggest that the power of the test is reasonable. The testing procedure is illustrated by the Canadian consumer price index series.     

Measuring serial dependence in categorical time series

The analysis of time-indexed categorical data is important in many fields, e.g., in telecommunication network monitoring, manufacturing process control, ecology, etc. Primary interest is in detecting and measuring serial associations and dependencies in such data. For cardinal time series analysis, autocorrelation is a convenient and informative measure of serial association. Yet, for categorical time series analysis an analogous convenient measure and corresponding concepts of weak stationarity have not been provided. For two categorical variables, several ways of measuring association have been suggested. This paper reviews such measures and investigates their properties in a serial context. We discuss concepts of weak stationarity of a categorical time series, in particular of stationarity in association measures. Serial association and weak stationarity are studied in the class of discrete ARMA processes introduced by Jacobs and Lewis (J. Time Ser. Anal. 4(1):19–36, 1983). An intrinsic feature of a time series is that, typically, adjacent observations are dependent. The nature of this dependence among observations of a time series is of considerable practical interest. Time series analysis is concerned with techniques for the analysis of this dependence. (Box et al. 1994p. 1)     

The effects of additive outliers on the seasonal KPSS test: a Monte Carlo analysis

This article builds on the test proposed by Lyhagen [The seasonal KPSS statistic, Econom. Bull. 3 (2006), pp. 1–9] for seasonal time series and having the null hypothesis of level stationarity against the alternative of unit root behaviour at some or all of the zero and seasonal frequencies. This new test is qualified as seasonal-frequency Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test and it is not originally supported by a regression framework.

The purpose of this paper is twofold. Firstly, we propose a model-based regression method and provide a clear illustration of Lyhagen's test and we establish its asymptotic theory in the time domain. Secondly, we use the Monte Carlo method to study the finite-sample performance of the seasonal KPSS test in the presence of additive outliers. Our simulation analysis shows that this test is robust to the magnitude and the number of outliers and the statistical results obtained cast an overall good performance of the test finite-sample properties.     

Johansen和Juselius协整检验应注意的几个问题

Johansen和Juselius的似然比检验多变量协整关系的方法在实证分析中得到了广泛应用。在总结该方法的基础上,针对国内使用该方法存在比较混乱的状况指出了一些注意事项,譬如根据经济时间序列的数据生成过程选择确定性成分,检验临界值的使用以及协整关系个数的非唯一性等问题,还简要论述了阶数的确定、外生性与因果关系检验等问题,最后指出了该检验的一些不足。通过对上述问题的讨论,试图为实证研究人员在使用该方法时提供简单有效的指导性建议。     

On Local Power Properties of Frequency Domain‐based Tests for Stationarity

A framework for the asymptotic analysis of local power properties of tests of stationarity in time series analysis is developed. Appropriate sequences of locally stationary processes are defined that converge at a controlled rate to a limiting stationary process as the length of the time series increases. Different interesting classes of local alternatives to the null hypothesis of stationarity are then considered, and the local power properties of some recently proposed, frequency domain‐based tests for stationarity are investigated. Some simulations illustrate our theoretical findings.     

Testing stationarity and trend stationarity against the unit root hypothesis

In this paper we propose a family of relativel simple nonparametrics tests for a unit root in a univariate time series. Almost all the tests proposed in the literature test the unit root hypothesis against the alternative that the time series involved is stationarity or trend stationary. In this paper we take the (trend) stationarity hypothesis as the null and the unit root hypothesis as the alternative. The order differnce with most of the tests proposed in the literature is that in all four cases the asymptotic null distribution is of a well-known type, namely standard Cauchy. In the first instance we propose four Cauchy tests of the stationarity hypothesis against the unit root hypothesis. Under H1 these four test statistics involved, divided by the sample size n, converge weakly to a non-central Cauchy distribution, to one, and to the product of two normal variates, respectively. Hence, the absolute values of these test statistics converge in probability to infinity 9at order n). The tests involved are therefore consistent against the unit root hypothesis. Moreover, the small sample performance of these test are compared by Monte Carlo simulations. Furthermore, we propose two additional Cauchy tests of the trend stationarity hypothesis against the alternative of a unit root with drift.     

Structural changes and unit roots in non-stationary time series

The problem of testing hypotheses of a unit root and a structural change in one-dimensional time series is considered. A non-parametric two-step method for solution of the problem is proposed. The method is based upon the modified Kolmogorov-Smirnov statistic. At the first step of this method the hypothesis of stationarity of an obtained sample is tested against a unified alternative of a statistical non-stationarity of a time series (a unit root or a structural change). At the second step of the proposed method, in case of rejecting the stationarity hypothesis at the first step, the hypothesis of an unknown structural change is tested against the alternative of a unit root. We prove that probabilities of errors (false classification of hypotheses) of the proposed method converge to zero as the sample size tends to infinity.     

Randomized singular spectrum analysis for long time series

ABSTRACT

Singular spectrum analysis (SSA) is a relatively new method for time series analysis and comes as a non-parametric alternative to the classical methods. This methodology has proven to be effective in analysing non-stationary and complex time series since it is a non-parametric method and do not require the classical assumptions over the stationarity or over the normality of the residuals. Although SSA have proved to provide advantages over traditional methods, the challenges that arise when long time series are considered, make the standard SSA very demanding computationally and often not suitable. In this paper we propose the randomized SSA which is an alternative to SSA for long time series without losing the quality of the analysis. The SSA and the randomized SSA are compared in terms of quality of the model fit and forecasting, and computational time. This is done by using Monte Carlo simulations and real data about the daily prices of five of the major world commodities.     

Variance Shifts,Structural Breaks,and Stationarity Tests

This article considers the problem of testing the null hypothesis of stochastic stationarity in time series characterized by variance shifts at some (known or unknown) point in the sample. It is shown that existing stationarity tests can be severely biased in the presence of such shifts, either oversized or undersized, with associated spurious power gains or losses, depending on the values of the breakpoint parameter and on the ratio of the prebreak to postbreak variance. Under the assumption of a serially independent Gaussian error term with known break date and known variance ratio, a locally best invariant (LBI) test of the null hypothesis of stationarity in the presence of variance shifts is then derived. Both the test statistic and its asymptotic null distribution depend on the breakpoint parameter and also, in general, on the variance ratio. Modifications of the LBI test statistic are proposed for which the limiting distribution is independent of such nuisance parameters and belongs to the family of Cramér–von Mises distributions. One such modification is particularly appealing in that it is simultaneously exact invariant to variance shifts and to structural breaks in the slope and/or level of the series. Monte Carlo simulations demonstrate that the power loss from using our modified statistics in place of the LBI statistic is not large, even in the neighborhood of the null hypothesis, and particularly for series with shifts in the slope and/or level. The tests are extended to cover the cases of weakly dependent error processes and unknown breakpoints. The implementation of the tests are illustrated using output, inflation, and exchange rate data series.     

我国统计数据质量的评估方法研究————————趋势模拟评估法及其应用

 本文采用组合模型的形式对时间序列数据的变化特点建模，在模型通过各种检验、具有良好统计预测功能的基础上，从检验异常值的角度来分析预测值与实际值之间差异的程度，找出离群数据，利用数理统计中检验实验观测数据异常值的方法，对离群数据的误差进行统计上的显著检验，从而评估统计数据的质量。文章以我国国内生产总值（GDP）为研究对象，选取我国1978-2003年间的GDP作为样本，运用趋势模拟评估法来评估我国2004年国内生产总值的准确性。对我国经济指标的时间序列数据进行了实证分析。