由一般平均数计算序时平均数的方法释疑

序时平均数是进行动态水平分析的重要指标,本文就根据一般平均数时间数列计算序时平均数的计算方法中存在的一些问题进行了探讨。     

平均发展水平就是序时平均数码

长期以来人们认为平均发展水平就是序时平均数，又称动态平均数。其计算方法有三种：由绝对数动态数列计算平均发展水平；由相对数动态数列计算平均发展水平；由平均数动态数列计算平均发展水平。笔者认为，由相对数动态数列计算的平均发展水平不能称为序时平均数。     

平均发展水平就是序时平均数吗

长期以来人们认为平均发展水平就是序时平均数,又称动态平均数。其计算方法有三种:由绝对数动态数列计算平均发展水平;由相对数动态数列计算平均发展水平;由平均数动态数列计算平均发展水平。笔者认为,由相对数动态数列计算的平均发展水平不能称为序时平均数。     

动态数列序时平均数的计算方法

序时平均数是非常重要的动态分析方法,其计算过程较为复杂.根据构成指标的三种表现形式,动态数列也相应分为三大类:绝对数动态数列、相对数和平均数动态数列,其序时平均数的计算也因指标的多样化表现变得比较复杂,不仅公三种类型数列分别采用不同的计算法,而且同一类型数列也有多种情况采用不同的计算方法,往往让初学者一头雾水,苦不堪言.     

介绍两种计算序时平均数的方法

介绍两种计算序时平均数的方法统计制度改革后，填报新的定期报表要计算几个序时平均数，每月填报一次报表均要从头至尾计算一次，比较繁琐。现介绍二种计算序时平均数的简捷方法．一、还原计算法：即将上月的序时平均数乘上上月的日序号，加上本月的平均数后再除以本月的...     

关于组中值和序时平均数计算方法的思考

本文通过对组中值、序时平均数计算方法进行讨论,比较这两个指标计算过程中的差异,并结合自己的教学实践,提出了一些看法。     

论统计指标的时间性质及其序时平均

文章指出了国内最流行的１０本大学教科书中共同存在的关于统计指标时间性质上的４点错误认识，给出了统计指标时间性质的科学表述。最后，重新定义了时间数列的构成要素，重新划分了时间数列的类型，重新构造了序时平均数的计算公式体系     

对三大数值平均数之关系成立的条件补充

大多数《统计学原理》教科书把平均数分成两大类 :一类是数值平均数 ,包括算术平均数、调和平均数和几何平均数 ;另一类是位置平均数 ,包括众数、中位数等。而且都认为 ,对同一数列计算的三大数值平均数之间存在这样的数量关系 ,即几何平均数大于调和平均数而小于算术平均数 ,只有当所有的变量值相同时 ,三大平均数才相等。用数学公式表示 ,它们之间的关系式为 : Ｘ≥Ｇ≥Ｈ笔者以为 ,上述三大数值平均数之关系成立的条件是 :数列中的各个变量值都为正数 ,不能为负数和零。现举例说明 ,在数列中 ,若有负数和零 ,上述关系不能成立。例一 ,甲…     

算术平均数与调和平均数的应用

一、算术平均数算术平均数是统计中最常用的一种平均指标。算术平均数之所以得到广泛的应用，是因为它的计算方法是与许多社会经济现象中的个别现象与总体现象之间存在的客观数量关系相符合的。例如：企业职工的工资总额就是各个职工工资总额的总和。因此，职工的平均工资应等于职工的工资总额与职工总人数之比。所以算术平均数的基本公式应该是：”“、、。＿：sr－－AI－－－－－－一算术平均数一省召普兰芝幕＿，、—瓜总体单位总数利用上式基本公式计算平均数时，要注意公式的子项（标志总量）与母项（单位总数）在总体范围上的可比性…     

调和平均数的两种计算功能

平均数有算术平均数、调和平均数、几何平均数、中位数和众数五种，其中除了中位数和众数是位置平均数外，根据数值计算的平均数有算术平均数、调和平均数、几何平均数，也称为数值平均数。在三种数值平均数中，算术平均数和几何平均数是独立的平均数，它们有各自的适用范围。而对于调和平均数，有些人认为调和平均数不过是算术平均数的一种变形，不是独立的平均数。这种看法实际是不全面的。我在几年的统计学教学过程中，总结出调和平均数有两方面的计算功能，即在不同的资料条件下，一、调和平均数是算术平均数的一种变形；二、调和平均数…     

Detecting Directionality in Time Series

Abstract

Directionality can be seen in many stationary time series from various disciplines, but it is overlooked when fitting linear models with Gaussian errors. Moreover, we cannot rely on distinguishing directionality by comparing a plot of a time series in time order with a plot in reverse time order. In general, a statistical measure is required to detect and quantify directionality. There are several quite different qualitative forms of directionality, and we distinguish: rapid rises followed by slow recessions; rapid increases and rapid decreases from the mean followed by slow recovery toward the mean; directionality above or below some threshold; and intermittent directionality. The first objective is to develop a suite of statistical measures that will detect directionality and help classify its nature. The second objective is to demonstrate the potential benefits of detecting directionality. We consider applications from business, environmental science, finance, and medicine. Time series data are collected from many processes, both natural and anthropogenic, by a wide range of organizations, and directionality can easily be monitored as part of routine analysis. We suggest that doing so may provide new insights to the processes.     

Time Series Properties of the Class of Generalized First-Order Autoregressive Processes with Moving Average Errors

A new class of time series models known as Generalized Autoregressive of order one with first-order moving average errors has been introduced in order to reveal some hidden features of certain time series data. The variance and autocovariance of the process is derived in order to study the behaviour of the process. It is shown that in special cases these new results reduce to the standard ARMA results. Estimation of parameters based on the Whittle procedure is discussed. We illustrate the use of this class of model by using two examples.     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.     

Why Aggregate Long Memory Time Series?

This article shows that, for large samples, temporally aggregating a true long memory time series (in order to get an improved estimator) may make little or no sense, as the practitioner can get virtually the same estimates as those from the aggregated series by choosing the appropriate bandwidths on the original one, provided some fairly general conditions apply. Besides, the practitioner has a wider choice of bandwidths than she has of aggregating levels. However, these results apply only to two specific and commonly used estimators, and do not apply to the aggregation procedure undertaken to compute the realized volatility. Also, aggregating a time series in order to test true versus spurious long memory (as in Ohanissian et al., 2008) is a relevant issue, particularly regarding stochastic and/or realized volatility, as many nonlinear processes display spurious long memory where the above result does not apply.     

Time Series and Model Selection

In this article, we investigate the behavior of Bozdogan's Information criterion (ICOMP) and other information criteria in a time series context. The study entails simulating stationary autoregressive moving average models 1,000 times and then fitting different time series models to the simulated series. Different series will be considered by changing the size of the residual variance as well as the sample size of the time series. It was found that under certain conditions ICOMP selects the correct time series model most often, although it is suggested that no single information criteria should be used independently of other information criteria.     

Simulation of Multivariate Gaussian Time Series

The paper discusses a simulation method for multivariate Gaussian time series by means of the discrete Fourier transform (Borgman, 1982). The procedure is quite general with respect to the correlation and spectral properties of the series and allows In addition simulations conditional on a subset of the time series. Simulations of the output from a set of ocean wave recorders are shown as an illustration of the method.     

Generalized EGARCH Random Effect Models Application to Financial Time Series

In this article, we propose a simple alternative model to analyze the volatility of the financial time series. In the applications, the performance of this model is compared with the performance of the GARCH type models. Using GARCH, EGARCH, and the proposed models, we analyze the time series of the Bovespa and Dow Jones Industrial Average indexes. In the applications we can see that the proposed models have good performance compared with the usual GARCH type model.     

A Note on the Estimation of Missing Values in Time Series

This paper derives an expression for the likelihood function of the parameters in an autoregressive-moving average model when some values are missing from the observed time series. The estimation of the missing values and their mean squared errors is discussed. Stationary as well as nonstationary models are considered.     

Forward Moving Average Representation in Multivariate MA(1) Processes

Forward-moving average coefficients are in general different from their corresponding backward-moving average coefficients in multivariate stationary time series. There is lack of practical methods to derive forward-moving average coefficients from the backward ones. In this article, we establish a new practical approach for obtaining the forward-moving average coefficients for multivariate moving average processes of order one.     

Time Series Models for Count or Qualitative Observations

Time series sometimes consist of count data in which the number of events occurring in a given time interval is recorded. Such data are necessarily nonnegative integers, and an assumption of a Poisson or negative binomial distribution is often appropriate. This article sets ups a model in which the level of the process generating the observations changes over time. A recursion analogous to the Kalman filter is used to construct the likelihood function and to make predictions of future observations. Qualitative variables, based on a binomial or multinomial distribution, may be handled in a similar way. The model for count data may be extended to include explanatory variables. This enables nonstochastic slope and seasonal components to be included in the model, as well as permitting intervention analysis. The techniques are illustrated with a number of applications, and an attempt is made to develop a model-selection strategy along the lines of that used for Gaussian structural time series models. The applications include an analysis of the results of international football matches played between England and Scotland and an assessment of the effect of the British seat-belt law on the drivers of light-goods vehicles.