Multiple Comparisons with More than One Control for Exponential Location Parameters Under Heteroscedasticity

In this article we present a simple bootstrap method for time series. The proposed method is model-free, and hence it enables us to avoid certain situations where the bootstrap samples may contain impossible values due to resampling from the residuals. The method is easy to implement and can be applied to stationary and nonstationary time series. The simulation results and the application to real time series data show that the method works very well.     

A simulation method for finite non-stationary time series

In this paper, we propose a novel simulation method which enables us to obtain a large number of simulated time series cheaply. The developed method can be applied to any non-stationary time series of finite length and it guarantees that not only the marginal distributions but also the autocorrelation structures of observed and simulated time series are the same. Extensive simulation studies have been conducted to check the performance of our method and to assess if the overall dynamics of the observed time series is preserved by the simulated realizations. The developed simulation method has also been applied to the real size data of cocoon filament, which can be reeled from a cocoon produced by a silkworm. Very good results have been achieved in all the cases considered in the paper.     

Forecasting functional time series using weighted likelihood methodology

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus, the underlying model may produce high forecast errors. We introduce a robust forecasting technique based on weighted likelihood methodology to obtain point and interval forecasts in functional time series in the presence of outliers. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and four real-data examples. Numerical results reveal that the proposed method exhibits superior performance compared with the existing method(s).     

Comparison of Times Series with Unequal Length in the Frequency Domain

In statistical data analysis it is often important to compare, classify, and cluster different time series. For these purposes various methods have been proposed in the literature, but they usually assume time series with the same sample size. In this article, we propose a spectral domain method for handling time series of unequal length. The method make the spectral estimates comparable by producing statistics at the same frequency. The procedure is compared with other methods proposed in the literature by a Monte Carlo simulation study. As an illustrative example, the proposed spectral method is applied to cluster industrial production series of some developed countries.     

On Detecting the Dependence of Time Series

The author suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak, such that the traditional methods are not effective. The method requires comparison of some special functionals on the sample characteristic functions with the same functionals computed for the benchmark time series with a known degree of correlation. Some experiments for financial time series are presented.     

A simple diagnostic method of outlier detection for stationary Gaussian time series

In this paper we present a "model free' method of outlier detection for Gaussian time series by using the autocorrelation structure of the time series. We also present a graphic diagnostic method in order to distinguish an additive outlier (AO) from an innovation outlier (IO). The test statistic for detecting the outlier has a χ ² distribution with one degree of freedom. We show that this method works well when the time series contain either one type of the outliers or both additive and innovation type outliers, and this method has the advantage that no time series model needs to be estimated from the data. Simulation evidence shows that different types of outliers can be graphically distinguished by using the techniques proposed.     

A Simple Method Using CuScore to Monitor Changes in ARMA Coefficients

This paper suggests a simple nonmetric method for smoothing time series data. The smoothed series is the closest polytone curve to the presmoothed series in terms of least sum of absolute deviations. The method is exemplified on several seasonally adjusted series in order to estimate their trend component.     

Multiple-index approach to multiple autoregressive time series model

Time series which have more than one time dependent variable require building an appropriate model in which the variables not only have relationships with each other, but also depend on previous values in time. Based on developments for a sufficient dimension reduction, we investigate a new class of multiple time series models without parametric assumptions. First, for the dependent and independent time series, we simply use a univariate time series central subspace to estimate the autoregressive lags of the series. Secondly, we extract the successive directions to estimate the time series central subspace for regressors which include past lags of dependent and independent series in a mutual information multiple-index time series. Lastly, we estimate a multiple time series model for the reduced directions. In this article, we propose a unified estimation method of minimal dimension using an Akaike information criterion, for situations in which the dimension for multiple regressors is unknown. We present an analysis using real data from the housing price index showing that our approach is an alternative for multiple time series modeling. In addition, we check the accuracy for the multiple time series central subspace method using three simulated data sets.     

A robust functional time series forecasting method

Univariate time series often take the form of a collection of curves observed sequentially over time. Examples of these include hourly ground-level ozone concentration curves. These curves can be viewed as a time series of functions observed at equally spaced intervals over a dense grid. Since functional time series may contain various types of outliers, we introduce a robust functional time series forecasting method to down-weigh the influence of outliers in forecasting. Through a robust principal component analysis based on projection pursuit, a time series of functions can be decomposed into a set of robust dynamic functional principal components and their associated scores. Conditioning on the estimated functional principal components, the crux of the curve-forecasting problem lies in modelling and forecasting principal component scores, through a robust vector autoregressive forecasting method. Via a simulation study and an empirical study on forecasting ground-level ozone concentration, the robust method demonstrates the superior forecast accuracy that dynamic functional principal component regression entails. The robust method also shows the superior estimation accuracy of the parameters in the vector autoregressive models for modelling and forecasting principal component scores, and thus improves curve forecast accuracy.     

The multidimensional markov chain with prespecified asymptotic means,and (auto-)covariances

In this paper a method is presented to construct random time series which, starting from their present values, converge to stationary time series with a priori specified mean values, standard deviations, correlations and autocorrelations. The method is applied to simulate time series of price-inflation, wage-inflation, and interest rates, whose mean values, standard deviations, correlations and autocorrelations converge to the values which are estimated from historical data This application is a circular part of a Decision Support System which assists management of pension funds in analysing new methods of calculating pension premiums.     

Importance sampling for signal extraction model in time series analysis

In time series analysis, signal extraction model (SEM) is used to estimate unobserved signal component from observed time series data. Since parameters of the components in SEM are often unknown in practice, a commonly used method is to estimate unobserved signal component using the maximum likelihood estimates (MLEs) of parameters of the components. This paper explores an alternative way to estimate unobserved signal component when parameters of the components are unknown. The suggested method makes use of importance sampling (IS) with Bayesian inference. The basic idea is to treat parameters of the components in SEM as a random vector and compute a posterior probability density function of the parameters using Bayesian inference. Then IS method is applied to integrate out the parameters and thus estimates of unobserved signal component, unconditional to the parameters, can be obtained. This method is illustrated with a real time series data. Then a Monte Carlo study with four different types of time series models is carried out to compare a performance of this method with that of a commonly used method. The study shows that IS method with Bayesian inference is computationally feasible and robust, and more efficient in terms of mean square errors (MSEs) than a commonly used method.     

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。     

Bayesian Time Series Analysis of Structural Changes in Level and Trend

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.     

Bayesian analysis of bilinear time series models : a gibbs sampling approach

Nonlinear time series analysis plays an important role in recent econometric literature, especially the bilinear model. In this paper, we cast the bilinear time series model in a Bayesian framework and make inference by using the Gibbs sampler, a Monte Carlo method. The methodology proposed is illustrated by using generated examples, two real data sets, as well as a simulation study. The results show that the Gibbs sampler provides a very encouraging option in analyzing bilinear time series.     

非平稳时间序列外生性结构突变检验设计的一个实例

一、引言由于世界经济结构的剧烈动荡,如金融危机、政策变更等,致使经济时间序列中的结构突变时有发生,经济过程的结构突变会影响协整分析的结果,使协整方法论中许多有代表性的检验失去原有的功效,如单位根检验[单位根可能会发生漂移(特征根的取值不稳定),单位根检验统计量也可     

An efficient algorithm for Harrison-Stevens forecasting using the multi-process multivariate dynamic linear model

This paper develops a computationally efficient algorithm for Harrison-Stevens forecasting in a multivariate time series which has correlated errors. The algorithm uses the observation vector one component at a time on the multiprocess multivariate dynamic linear model. This gives a computationally efficient, robust, quick adapting forecasting method for non stationary multivariate time series.     

Seasonal Adjustment Using Structural Time Series Models: An Application and a Comparison With the Census X-11 Method

This article makes the method of seasonal adjustment operational using suitable structural time series models (STM). This so-called STM method is applied to several relevant Dutch macro- economic quarterly and monthly time series. The results are compared with those of the Census X-11 method using several formal criteria as yardsticks. The STM method proves to compete well with the Census X-11 method in this respect.     

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.     

The “Caterpillar”-SSA method for analysis of time series with missing values

The paper concerns the problem of applying singular spectrum analysis to time series with missing data. A method of filling in the missing data is proposed and is applied to time series of finite rank. Conditions of exact reconstruction of missing data are developed and versions of the algorithm applicable to real-life time series are presented. The proposed algorithms result in the extraction of additive components of time series such as trends and periodic components, with simultaneous filling in of the missing data. An example is presented.