Basic Methods of Time Series Analysis

Until recently mathematical methods of time series analysis in the environmental sciences have only been used quite rarely the methods have mostly been applied in economic science. Consequently, the mathematical fundamentals of time series analysis are mainly described in textbooks and papers dealing with statistics and econometrics [FORSTER and RONZ, 1979 COX, 1981 SCHLITTGEN and STREITBERG, 1989 CHATFIELD, 1989 BROCKWELL and DAVIS, 1987 BOX and JENKINS, 1976 FOMBYet al., 1984 METZLER and NICKEL, 1986 PANDIT and WU, 1990], This section explains the basic methods of time series analysis and their applicability in environmental analysis. 

In general, time series analysis has the following main purposes  

In practical environmental analysis and valuation complex questions concerning environmental relationships in time often have to be answered. 

Most of the above purposes can be fulfilled with modern time series models but the environmental scientist also needs a guide to clear interpretation of the results of the applied mathematical methods. The practician should be given time series analytical methods, i.e. mathematical techniques or computer programs which are relatively simple to use, as a tool for his daily work. The interpretation of the computations must be easy. More complicated time series models are, therefore, not included. 

The various time series analytical methods were applied to the same environmental example - a series of nitrate concentrations in a storage reservoir. A comparison of the power of time series methods is, therefore, possible. 

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By executing the steps of the analytical process, we can take advantage of most of the basic methods of chemometrics, e.g., statistics including analysis of variance, experimental design and optimization, regression modeling, and methods of time series analysis. 

Basically, four main areas of methods for gear fault detection have been published. Signal processing techniques. Statistical analysis (ANDRADE, ESAT, BADI, 2001 BAYDAR eta/., 2001 TUMER HUFF, 2003 HE, KONG, YAN, 2007), Time-series analysis (ZHAN JARDINE, 2005 ZHAN, MAKIS, JAR-DINE, 2006) and Artificial neural networks AYA ESAT, 1997 SAMANTA, 2004 SANZ, PERERA, HUERTA, 2007 RAFIEE et cd., 2007). 

Semi-automatic software These are moderately priced but they require the user to have some basic knowledge of forecasting principles and fechniques. Here, fhe user has to select an appropriate forecasting technique based on the analysis of time series data. The software will then compute the optimal parameters for the chosen method using some measure of forecasf error. It also gives the forecasts and all the statistics, such as MAD, MAPE, MSE, Bias, etc. The software makes no recommendation as to which forecasting technique is appropriate for the given data. 

A major objective of carrying out the ab initio simulations was to find the correlations of hydrogen bonds and spectral observables like vibrational stretch frequencies. For this purpose, a time series analysis was performed by using the wavelet method. The details of this method can be found elsewhere. - Here, we only discuss the basic idea. A time-dependent function/(t) is expressed in terms of base functions, which are constructed as translations and dilations of a mother wavelet, i.e.. 

Any advanced absorbance/fluorescence spectrophotometer designed for routine acquistion of absorption or emission on the subsecond time scale. The basic goal is to obtain a series of complete UV/visible or fluorescence spectra as a function of time, usually after samples are mixed in a stopped-flow device. Such data help the investigator to infer the most likely structures of transient intermediates whose electronic spectra or fluorescence spectra can be determined by deconvoluting the spectra with appropriate reaction kinetic simulation software or by some other global analysis method (Fig. 1). 

One of the basic methods for investigation of chemical reactions is the analysis of reaction intermediates by various physico-chemical methods. The best method for such studies is analysis in situ, in real time, and in the real reaction environment. However, in many cases, analysis in situ is complicated by the limitations of analysis methods, e.g., the time of sample study may exceed the reaction time. In order to overcome these limitations, a series of reaction intermediates should be... 

The preparation of HNCC in the form of well-shaped crystals suitable for diffractometric analysis is extremely important because of the basic need for this type of characterization. In the last few years, we have used extensively crystallization methods involving slow diffusion of solvents in which the complex is insoluble. Generally, it is sufficient to stratify slowly a lower-density solvent over the solution of the compound (e.g., i-PrOH on acetone, t-Pr20 on MeOH, toluene on THF) crystallization occurs by simple diffusion for a couple of days. Unfortunately, with salts of carbonyl-metalates the ease of formation of crystals is generally unpredictable and dependent on the particular cation. Often it is necessary to try a whole series of cations, which may be very time-consuming, in order to obtain proper crystals. 

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