Time-series analyses

Characterization of a set of measurements as a time series in the sense of a stochastic process is of interest in a different way, that is, 

The methods for smoothing, derivation, integration, or transformation as discussed in Section 3.1 can also be applied to time series. In this section, we learn about correlation methods. Correlations within a time series are described in the form of autocorrelation or autocovariance. Two different time series are characterized by means of cross-correlation. 

Relationships between variables can be described by means of correlation and 

Typical information to be derived from such models is about 

We begin with correlations within a measurement series. Autocorrelation and Autocovariance 

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G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Holden-Day, San Francisco, Calif., 1970. 

Nonlinear Dynamics and Topological Time Series Analysis Archive http //t13.lanl.gov/ nxt/intro.html... 

Zinsmeister, A. R. and Redman, T. C. (1980). A time series analysis of aerosol composition measurements, Atmos. Environ. 14,201-215. 

The first level of complexity corresponds to simple, low uncertainty systems, where the issue to be solved has limited scope. Single perspective and simple models would be sufficient to warrant with satisfactory descriptions of the system. Regarding water scarcity, this level corresponds, for example, to the description of precipitation using a time-series analysis or a numerical mathematical model to analyze water consumption evolution. In these cases, the information arising from the analysis may be used for more wide-reaching purposes beyond the scope of the particular researcher. 

Integrated Mnvino Average Model tIMAl. Proper application of time series analysis requires that the variance of the series be constant and that there be no major trend. Any segment of the time series should be very much like any other segment. If this is not the case then the inferences will depend... 

The application of time series techniques to electrochemical data is promising. It is possible to use the ARIMA analysis to study the behavior of a single coating system. It is also possible to use time series analysis to rank coatings with respect to the properties under study. 

The precision of time series predictions far into the future may be limited. Time series analysis requires a relatively large amount of data. Precautions are necessary if the time intervals are not approximately equal (9). However, when enough data can be collected, for example, by an automated process, then time series techniques offer several distinct advantages over more traditional statistical techniques. Time series techniques are flexible, predictive, and able to accommodate historical data. Time series models converge quickly and require few assumptions about the data. 

C.R.Nelson, Annlied Time Series Analysis. Holden-Day, Inc. San Francisco, (1973). 

Time Series Analysis of Irregularly Observed Data. Emanuel Parzen, Ed., Springer-Verlag, Berlin, (1984). 

Application of TimeTemperature Control of Semi-Batch Reactors... 

The positive results obtained at production scale give us confidence in the validity of our approach. Derivation of a simple scaling factor enabled us to conduct a series of experiments in a small pilot plant which would have been expensive and time-consuming on a production scale. Time series analysis not only provided us with estimates of the process gain, dead time and the process time constants, but also yielded an empirical transfer function which is process-specific, not one based on... 

One final note While the techniques used here were applied to control temperature In large, semi-batch polymerization reactors, they are by no means limited to such processes. The Ideas employed here --designing pilot plant control trials to be scalable, calculating transfer functions by time series analysis, and determining the stochastic control algorithm appropriate to the process -- can be applied In a variety of chemical and polymerization process applications. 

Nelson, C. R. Applied Time Series Analysis Holden-Day San Francisco, CA, 1973. 

A homogeneity index or significance coefficienf has been proposed to describe area or spatial homogeneity characteristics of solids based on data evaluation using chemometrical tools, such as analysis of variance, regression models, statistics of stochastic processes (time series analysis) and multivariate data analysis (Singer and... 

Lopman, B., Armstrong, B., Atchison, C., and Gray, J. J. (2009). Host, weather and virological factors drive norovirus epidemiology Time-series analysis of laboratory surveillance data in lingland and Wales. PLoS ONE 4, e6671. 

Box, G.E.P., G.M. Jenkins, G.C. Reinsel and G. Jenkins, Time Series Analysis Forecasting Control, 3ld Ed., Prentice Hall, Eglewood-Cliffs, NJ, 1994. 

Autocorrelation and time series analysis have been successfully applied in testing spatial inhomogeneities (Ehrlich and Kluge [1989], Do-erffel et al. [1990]). This techniques are generalized in the theory of stochastic processes (Bohacek [1977a, b]) which is widely used in chemical process analysis and about them. 

The main goal of time-series analysis (Box and Jenkins [1976], Chat-field [1989], Metzler and Nickel [1986]) apart from process analysis is time-dependent sampling. In both cases fluctuations in time x(t) matter and can be considered as a simple stochastic process or as time series. 

Box CEP, Jenkins CM (1976) Time series analysis. Holden-Day, Oakland, CA... 

Doerffel K, Kuchler L, Meyer N (1990) Treatment of noisy data from distribution analysis using models from time-series analysis. Fresenius J Anal Chem 337 802... 

Montgomery DC, Johnson LA, Gardiner JS (1990) Forecasting and time series analysis. McGraw-Hill, New York... 

Shinnway RH (1988) Applied statistical time series analysis. Prentice Hall, Englewood Cliffs, NJ... 

Percival, D.B., Walden, A.T. (2006). Wavelet Methods for Time Series Analysis, Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, New York. 

Juez and Tamayo51 also apply time-series analysis to the evaluation of the consequences of introducing selective financing in 1993. Using the aggregate monthly data on pharmaceutical expenditure of the National Health System between 1991 and 1995, in constant deseasonalized pesetas, the authors compare the observed evolution with the theoretical evolution according to a linear fit. They conclude that the measure had a notable effect in the short term, but was absorbed in the long term. 

In-Kwon Yeo received the PhD degree in Statistics from University of Wisconsin-Madison in 1997. He joined the Department of Control and Instrumentation Engineering, Kangwon National University as a visiting professor in 2000 and the Division of Mathematics and Statistical Informatics, Chonbuk National University as an assistant professor in Korea. He is currently an associate professor at the Department of Statistics, Sookmyung Women s University. His current research interests include data transformations, multivariate time series analysis and generalized additive models. 

Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astroph. J., 263, 835-53. 

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