Time series analysis dynamic models

Fouskitakis G, Fassois S (2002) Functional series TARMA modeling and simulation of earthquake ground motion. Earthq Eng Struct Dyn 31 399 20 Gersch W, Akaike H (1988) Smoothness priors in time series. In Spall J (ed) Bayesian analysis of time series and dynamic models. Marcel Dekker, New York, pp 431 76... 

Although the detailed features of the interactions involved in cortisol secretion are still unknown, some observations indicate that the irregular behavior of cortisol levels originates from the underlying dynamics of the hypothalamic-pituitary-adrenal process. Indeed, Ilias et al. [514], using time series analysis, have shown that the reconstructed phase space of cortisol concentrations of healthy individuals has an attractor of fractal dimension dj = 2.65 0.03. This value indicates that at least three state variables control cortisol secretion [515]. A nonlinear model of cortisol secretion with three state variables that takes into account the simultaneous changes of adrenocorticotropic hormone and corticotropin-releasing hormone has been proposed [516]. 

Type of endpoint. The type of endpoint recording is essential for the application of different types of mixture toxicity models. Endpoints measured at only 1 point in time may only be used to derive concentration-response-related parameters, such as ECx or LCx or NOECs. Continuous recording or at least repeated recording of responses may allow for time series analysis. Time-related responses may, for example, be used for the derivation of kinetic parameters by applying pharmacokinetic/dynamic models (like the PBPK models in human toxicology see, e.g., Krishnan et al. 1994) or... 

The application of embedding time-series analysis to multivariate observables [75,84,86] is desired in order to extract a good projection, revealing the dynamical structure from a limited set of observables. It is known [89,90] that an application of the embedding analysis to time series involving intermittency, like those of the Go-like model, is not straightforward and involves many problems that need to be overcome. 

The time series analysis is a statistical method to reveal the dynamic law of a system through dynamic data (Box 2005). Its core idea is that, with the finite number of data in the series, a model could be created to precisely reflect the dynamic relationship hided in the time series, and then to forecast the future. 

Stochastic identification techniques, in principle, provide a more reliable method of determining the process transfer function. Most workers have used the Box and Jenkins [59] time-series analysis techniques to develop dynamic models. An introduction to these methods is given by Davies [60]. In stochastic identification, a low amplitude sequence (usually a pseudorandom binary sequence, PRBS) is used to perturb the setting of the manipulated variable. The sequence generally has an implementation period smaller than the process response time. By evaiuating the auto- and cross-correlations of the input series and the corresponding output data, a quantitative model can be constructed. The parameters of the model can be determined by using a least squares analysis on the input and output sequences. Because this identification technique can handle many more parameters than simple first-order plus dead-time models, the process and its related noise can be modeled more accurately. 

In the case of climate modeling such series are abundant, and since atmospheric phenomena present very complex and sophisticated structure, it is not possible easily to model them through analytical and physical approaches. The remaining open door for their behavior assessment is the use of time series analysis. The classical time series analysis does not provide any insight into the dynamism of the phenomenon but only about its mechanical decomposition into various trends. 

Viola, R, Paiva, S., and Savi, M. (2010) Analysis of global warming dynamics from temperature time series. Ecological Modelling, 221 1964-1978. 

HANUSSE - In fact the morphology analysis is performed on the complete trajectory given by the simulation of the full model. One interesting result is that the results do not seem to depend on the space in which you work (concentrations, reaction rates, combinations of them). You obtain the same essential dynamical features. This stability of the solution is to be compared to that of the reconstruction procedure of three dimensional attractors from a unique time series, in studies of chaotic behaviour. 

Both deterministic and stochastic simulations can be used for response-history dynamic analysis, but only stochastic simulations can be utilized for stochastic dynamic (i.e., random vibration) analysis, because the latter analysis method requires a random process model of the earthquake ground motion. Synthetic ground motions are particularly useful for nonlinear dynamic analysis due to the scarcity of recorded motions for large-magnitude earthquakes that are capable of causing nonlinear responses. Two approaches are available for nonlinear dynamic analysis of structures subjected to earthquakes (1) nonlinear response-history analysis by the use of a selected set of ground motion time series and (2) nonlinear stochastic dynamic analysis by the use of a stochastic representation of the ground motion. 

The use of thermogravimetric analysis (TGA) apparatus to obtain kinetic data involves a series of trade-offs. Since we chose to employ a unit which is significantly larger than commercially available instruments (in order to obtain accurate chromatographic data), it was difficult to achieve time invariant O2 concentrations for runs with relatively rapid combustion rates. The reactor closely approximated ideal back-mixing conditions and consequently a dynamic mathematical model was used to describe the time-varying O2 concentration, temperature excursions on the shale surface and the simultaneous reaction rate. Kinetic information was extracted from the model by matching the computational predictions to the measured experimental data. 

---