State-Space Modelling of Time Series

M Aoki. State Space Modeling of Time Series. Springer-Verlag, New York, NY, 2nd edition, 1990. 

Various multivariate regression techniques are outlined in Section 4.1. Section 4.2 introduces PCA-based regression and its extension to capture d3mamic variations in data. PLS regression is discussed in Section 4.3. Input-output modeling of d3mamic processes with time series models is introduced in Section 4.4 and state-space modeling techniques are presented in Section 4.5. 

The data used in subspace state-space model development consists of the time series data of output and input variables. For illustration, assume a case with only output data and the objective is to build a model of the form Eq. 4.62. Since the whole data set is already known, it can be partitioned as past and future with respect to any sampling time. Defining a past data window of length K and a future data window of length J that are shifted from the beginning to the end of the data set, stacked vectors of data are formed. The Hankel matrix (Eq. 4.64) is used to develop subspace... 

Metaxoglou, K. and Smith, A. Maximum likelihood estimation of vanna models using a state-space em algorithm. Journal of Time Series Analysis, 28(5) 666- 5, 2007. 

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]. 

Now, let us look deeply into the question of what the dimensionality of the state space is, buried in the complexity of the time series of the protein dynamics. Here we apply Cao s embedding technique to every principal component time series for the original BLN model at a wide range of... 

This work required a large amount of subsidiary R D in (1) hydrodynamic sediment-plant mesocosm design, replication, and monitoring, (2) synthetic and analytical chemistry, including the synthesis of commercially unavailable standards and development analytical approaches to detect minor differences in organic chemicals between time points and treatments and (3) sensor design, time series data acquisition and wavelet analysis of non-stationary series [6], and covariance structure modeling of mesocosm and ecosystem data [1]. Basic questions (e.g., what constitutes a true spatiotemporal replicate in a multivariate, multiply colinear system What is the minimum number of indicator variables needed to characterize the states of such a system and how often do they need to be sampled in space and time ) arose and had to... 

Given the pre-eminence of the transfer function and frequency-domain-based approaches in process and chemical engineering, these two approaches will be discussed in greatest detail in this chapter. Nevertheless, information about the state-space-based approach will also be considered. This chapter will present the basic, univariate approach to time series analysis, which will be extended in Chap. 6 to consider the multivariate case containing both stochastic and deterministic components in order to model complex processes for process control, economic analysis, and simulation development. 

The structural time series analysis methods also referred to as state-space methods [HAR 86, COM 07] have been used more and more for modeling the aggregate number of fatalities at national level [DUP 07], The approach that the authors adopt is innovative, as usually such analyses are led on an annual basis - in order to explain and forecast long-term changes in the aggregate number of fatalities at national level [LAS 01]). On the contrary, short-term changes can only be modeled on an infra-annual basis similar but uncompleted approaches were taken on a quarterly basis - without the inclusion of exogenous variables [COM 2007] and on a monthly basis - without the inclusion of economic variables [BER 13]. 

As mentioned earlier, heavy polar diatomic molecules, such as BaF, YbF, T1F, and PbO, are the prime experimental probes for the search of the violation of space inversion symmetry (P) and time reversal invariance (T). The experimental detection of these effects has important consequences [37, 38] for the theory of fundamental interactions or for physics beyond the standard model [39, 40]. For instance, a series of experiments on T1F [41] have already been reported, which provide the tightest limit available on the tensor coupling constant Cj, proton electric dipole moment (EDM) dp, and so on. Experiments on the YbF and BaF molecules are also of fundamental significance for the study of symmetry violation in nature, as these experiments have the potential to detect effects due to the electron EDM de. Accurate theoretical calculations are also absolutely necessary to interpret these ongoing (and perhaps forthcoming) experimental outcomes. For example, knowledge of the effective electric field E (characterized by Wd) on the unpaired electron is required to link the experimentally determined P,T-odd frequency shift with the electron s EDM de in the ground (X2X /2) state of YbF and BaF. 

---