Time series methodology

The remainder of this section introduces the relevant notation with an additional focus on the extension to heteroscedastic models (so-called (G)ARCH and ARMA-GARCH models) as these can be seen as the discrete-time counterpart of continuous stochastic processes formulated in terms of SDEs. 

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The analysis of available and relevant data typically requires a set of statistical methods. They are applied to extract deeper knowledge about the processes to be modelled. The set of methods is vast and the choice of methods depends on the needs of the speciflc project. Time series methodology is one prominent branch of methods. 

Forecast demand in a supply chain given historical demand data using time-series methodologies. 

Yearly water balance time series since 1901 based on measured data have been established and analyzed by [23-25]. Recently, special importance has been attached to the fact that quantification of areal precipitation in mountainous environment remains a very difficult task. With the aim of achieving high spatial resolution, a specific methodology has been developed based on a comprehensive view of the water balance in different spatial and time scales [26]. 

In order to assess the O3 trend, a well-known statistical methodology, based on the Mann-Kendall-Sneyers and Pettitt tests (described in [4] and [5]), is applied to the long time series, not filtered by means of the Rao and Zurbenko technique. A significance level of 95% is chosen to interpret the results. The analysis shows the existence of a negative trend of 2.7% every ten years, from 1979 to 1998, for Arosa and a negative... 

Transport and dispersion was evaluated without any form of tuning by comparing a simulation of the ETEX-1 release to the official measurements of surface concentration. To facilitate comparisons with models evaluated during ATMES 11 (Atmospheric Transport Model Evaluation Study) an identical statistical methodology was employed (Mosca et al. 1998). Background values were subtracted so that only the pure tracer concentration was used. Measurements of zero concentration (concentrations below the background level) were included in time series to the extent that they lay between two non-zero measurements or within two before or two after a non-zero measurement. Hereby, spurious correlations between predicted and measured zero-values far away from the plume track are reduced. 

What can a scalar time series tell us about the multivariate state (or phase) space buried in the observations The so-called embedology attributed to Whitney [75] and Takens [76] provides us with an essential clue to the answer of such a question. A detailed description of the mathematical proof is beyond the scope of this review, and here we focus on describing the brief concept and methodology. 

The analysis of process signals may be facilitated if the time series data can be cast into a symbolic form. The relevant trends and generic data features can then be extracted and monitored using this qualitative representation. Such a transformation is often carried out by defining a set of primitives (alphabet) that define a visual characteristic of the signal [78, 142, 247]. Here, the methodology proposed by Stephanopoulos and coworkers is discussed [9, 34, 35]. They treated the problem of trend representation graphically... 

The methodology for multivariate time series models is similar to the univariate cases except for the fact that all notation is changed into vectors and matrices such that most... 

Dielman, T. E. (1983). Pooled cross-sectional and time series data Asurvey of current statistical methodology. The American Statistician, 37, 111-122. 

If the right hand side of Equation (4.13) is replaced by Yl =i r(tWA)gr(t)> the Bayesian time-domain methodology is applicable for excitations having different modulating functions, e.g., ambient vibrations with a series of wind gusts. 

Tang, Z., Dealmeida, C. and Fishwick, R, 1991. Time-series forecasting using neural networks vs Box-Jenkins methodology. Simulation, 57,303-310. 

Both the power demand and the feed-in from RES and CHP are given in the form of characteristic normalized time series of the hourly mean value of power for each year. These are scaled to the varying annual amounts of electricity consumption and demand. The characteristic time series are taken from [15]. They are based on a coherent data set, which comprises values of air temperature, solar radiation and wind speed for the test reference years provided by the German weather service (DWD). The methodology in IMAKUS only allows the use of deterministic time series of demand and feed-in from RES and CHP. It should be noted that the quality of the results, especially the expansion and dispatch of storages, largely depends on the quality of the given time series, i.e. to what extent they can be considered typically. 

Other quantitative techniques proposed by Kahn (2006) include those techniques that employ unique methodologies or represent a hybrid of time series and regression techniques. Examples of these forecasting techniques are ... 

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