Application of time series analysis and modern control theory to the cement plant

Cement plant process is full of internal noise sources and feedback loops. Therefore, statistical approach is required to understand its dynamic characteristics. Time series analysis has been applied to some important subprocesses of a cement plant process. These are the vertical mill process, calcining process and clinker cooling process. Based on the AR models of these, a set of optimum controllers have been designed by modern control theory. Successful results of application are reported in this paper. A method of determining optimal production level is also discussed.     

An angular–linear time series model for waveheight prediction

The modeling of the dynamic relationship between the changes of the wind and the waveheight has been an important topic from various standpoints such as oceanography, technology and navigation safety. Generally, when we apply the standard statistical models for the waveheight prediction, the observation of wind direction has been treated as the ordinary time series data, not reflecting unique properties as directional data. In this article, we develop a time series model with linear and angular–linear variables, by extending the angular–linear regression model considered by Johnson and Wehrly. Our prediction test based on extrapolation suggested the possibility that the angular–linear time series structure gave positive effect on improving the prediction accuracy of the time series model, in which the original wind direction is included as a linear variable.     

Time-varying parameter auto-regressive models for autocovariance nonstationary time series

In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TVPAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out. This work was supported by the Doctoral Research Fund of the Ministry of Education, China (Grant No. 20040285008), and Grant-in-Aid for Scientific Research (B), the Ministry of Education, Science, Sports and Culture, Japan, 2005 (Grant No. 17300228)     

MODWT-ARMA model for time series prediction

Many time series in the applied sciences display a time-varying second order structure and long-range dependence (LRD). In this paper, we present a hybrid MODWT-ARMA model by combining the maximal overlap discrete wavelet transform (MODWT) and the ARMA model to deal with the non-stationary and LRD time series. We prove theoretically that the details series obtained by MODWT are stationary and short-range dependent (SRD). Then we derive the general form of MODWT-ARMA model. In the experimental study, the daily rainfall and Mackey–Glass time series are used to assess the performance of the hybrid model. Finally, the normalized error comparison with DWT-ARMA, EMD-ARMA and ARIMA model indicates that this combined model is an effective way to improve forecasting accuracy.     

Estimation of second-order properties from jittered time series

This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.     

An improved fuzzy time series forecasting method using trapezoidal fuzzy numbers

One of the major drawbacks of the existing fuzzy time series forecasting models is the fact that they only provide a single-point forecasted value just like the output of the traditional time series methods. Hence, they cannot provide a decision analyst more useful information. The aim of this present research is to design an improved fuzzy time series forecasting method in which the forecasted value will be a trapezoidal fuzzy number instead of a single-point value. Furthermore, the proposed method may also increase the forecasting accuracy. Two numerical data sets were used to illustrate the proposed method and compare the forecasting accuracy with three fuzzy time series methods. The results of the comparison indicate that the proposed method can generate forecasting values that are more accurate.     

On the invertibility of time series models

A generalized definition of invertibility is proposed and applied to linear, non-linear and bilinear models. It is shown that some recently studied non-linear models are not invertible, but conditions for invertibility can be achieved for the other models.     

基于时间序列分析方法的伊犁州GDP的预测研究

基于时间序列理论,以伊犁州1978年至2014年来生产总值为基础数据,利用Eviewes8.0软件对数据进行处理分析,并对模型进行显著性检验,综合各种条件确定最终时间序列回归模型,对伊犁州未来三年的生产总值做出预测,为伊犁州党委、政府制定相关经济政策和发展战略提供科学依据.     

Lower bounds on entropy via the Conley index with application to time series

A proof of a localized version of the proven entropy conjecture for C^∞ smooth maps is given. This allows for computational methods for bounding topological entropy through properties of the Conley index. Chaos can then be determined by a non-global index calculation robust under possibly large (and noisy) perturbations. In addition, a proof of a Wazewski's Principle for time series analysis is given which allows for lifting of entropy to the observed dynamical system under certain conditions.     

青岛港货运吞吐量的时间序列模型

运用时间序列分析方法对时间序列建立ARMA,ARIMA模型.搜集了青岛港1999年1月～2003年5月的货运吞吐量数据,对进行分析,建立了青岛港货运吞吐量的模型.通过预留的部分数据对模型进行检验,并对模型的残差进行检验,得出模型比较合理.     

A hybrid algorithm to optimize RBF network architecture and parameters for nonlinear time series prediction

This paper proposes a novel hybrid algorithm for automatic selection of the proper input variables, the number of hidden nodes of the radial basis function (RBF) network, and optimizing network parameters (weights, centers and widths) simultaneously. In the proposed algorithm, the inputs and the number of hidden nodes of the RBF network are represented by binary-coded strings and evolved by a genetic algorithm (GA). Simultaneously, for each chromosome with fixed inputs and number of hidden nodes, the corresponding parameters of the network are real-coded and optimized by a gradient-based fast-converging parameter estimation method. Performance of the presented hybrid approach is evaluated by several benchmark time series modeling and prediction problems. Experimental results show that the proposed approach produces parsimonious RBF networks, and obtains better modeling accuracy than some other algorithms.     

Frequency domain characteristics of linear operator to decompose a time series into the multi-components

Frequency domain properties of the operators to decompose a time series into the multi-components along the Akaike's Bayesian model (Akaike (1980, Bayesian Statistics, 143–165, University Press, Valencia, Spain)) are shown. In that analysis a normal disturbance-linear-stochastic regression prior model is applied to the time series. A prior distribution, characterized by a small number of hyperparameters, is specified for model parameters. The posterior distribution is a linear function (filter) of observations. Here we use frequency domain analysis or filter characteristics of several prior models parametrically as a function of the hyperparameters.     

A note on quadratic forms of stationary functional time series under mild conditions

We study distributional properties of a quadratic form of a stationary functional time series under mild moment conditions. As an important application, we obtain consistency rates of estimators of spectral density operators and prove joint weak convergence to a vector of complex Gaussian random operators. Weak convergence is established based on an approximation of the form via transforms of Hilbert-valued martingale difference sequences. As a side-result, the distributional properties of the long-run covariance operator are established.     

我国外汇储备变动的时间序列建模预测

本文通过对我国最近十三年来的外汇储备月度数据进行分析,利用不同的建模思想建立了三次趋势模型、Holter-Winter非季节模型和AR IMA模型来分析短期内我国外汇储备的变动趋势。这三种模型对原始数据都能够较好的拟合,而且用于预测时的结果也相差不大,可以为短期内预测管理我国外汇储备提供有效参考。     

An approach to the nonstationary process analysis

Summary A Bayesian approach to nonstationary process analysis is proposed. Given a set of data, it is divided into several blocks with the same length, and in each block an autoregressive model is fitted to the data. A constraint on the autoregressive coefficients of the successive blocks is considered. This constraint controls the smoothness of the temporal change of spectrum as shown in Section 2. A smoothness parameter, which is called a hyper parameter in this article, is determined with the aid of the minimum ABIC (Akaike Bayesian Information Criterion) procedure. Numerical examples of our procedure are also given. The Institute of Statistical Mathematics     

A note on the time series which is the product of two stationary time series

The time series […,x_-1y_-1,x₀y₀,x₁y₁,…]> which is the product of two stationary time series x_t and y_t is studied. Such sequences arise in the study of nonlinear time series, censored time series, amplitude modulated time series, time series with random parameters, and time series with missing observations. The mean and autocovariance function of the product sequence are derived.     

Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator

This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The consistency of the maximum likelihood estimators is then derived for well-specified and misspecified models.     

A multivariate time series approach to projected life tables

The method of mortality forecasting proposed by Lee and Carter describes a time series of age‐specific log‐death rates as a sum of an independent of time age‐specific component and a bilinear term in which one of the component is a time‐varying factor reflecting general change in mortality and the second one is an age‐specific parameter. Such a rigid model structure implies that on average the mortality improvements for different age groups should be proportional, regardless of the calendar period: a single time factor drives the future death rates. This paper investigates the use of multivariate time series techniques for forecasting age‐specific death rates. This approach allows for relative speed of decline in the log death rates specific to the different ages. The dynamic factor analysis and the Johansen cointegration methodology are successfully applied to project mortality. The inclusion of several time factors allows the model to capture the imperfect correlations in death rates from 1 year to the next. The benchmark Lee–Carter model appears as a special case of these approaches. An empirical study is conducted with the help of the Johansen cointegration methodology. A vector‐error correction model is fitted to Belgian general population death rates. A comparison is performed with the forecast of life expectancies obtained from the classical Lee–Carter model. Copyright © 2009 John Wiley & Sons, Ltd.     

Spectral modeling of time series with missing data

Singular spectrum analysis is a natural generalization of principal component methods for time series data. In this paper we propose an imputation method to be used with singular spectrum-based techniques which is based on a weighted combination of the forecasts and hindcasts yield by the recurrent forecast method. Despite its ease of implementation, the obtained results suggest an overall good fit of our method, being able to yield a similar adjustment ability in comparison with the alternative method, according to some measures of predictive performance.     

A test of conditional heteroscedasticity in time series

A new test of conditional heteroscedasticity for time series is proposed. The new testing method is based on a goodness of fit type test statistics and a Cramer-von Mises type test statistic. The asymptotic properties of the new test statistic is establised. The results demonstrate that such a test is consistent. Project supported by the National Natural Science Foundation of China (Grant No. 19231050) and Postdoctoral Fund of China.