State Space Modelling of Cross-Classified Time Series of Counts

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

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GQL Versus Conditional GQL Inferences for Non-Stationary Time Series of Counts with Overdispersion

Journal of Time Series Analysis ◽

10.1111/j.1467-9892.2007.00570.x ◽

2008 ◽

Vol 29 (2) ◽

pp. 402-420 ◽

Cited By ~ 10

Author(s):

Taslim S. Mallick ◽

Brajendra C. Sutradhar

Keyword(s):

Time Series ◽

Stationary Time Series ◽

Time Series Of Counts ◽

Stationary Time

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Estimating long-term tree mortality rate time series by combining data from periodic inventories and harvest reports in a Bayesian state-space model

Forest Ecology and Management ◽

10.1016/j.foreco.2012.12.022 ◽

2013 ◽

Vol 292 ◽

pp. 64-74 ◽

Cited By ~ 7

Author(s):

Katalin Csilléry ◽

Maëlle Seignobosc ◽

Valentine Lafond ◽

Georges Kunstler ◽

Benoît Courbaud

Keyword(s):

Time Series ◽

Mortality Rate ◽

State Space ◽

Tree Mortality ◽

State Space Model ◽

Space Model ◽

Combining Data

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LSTM-Guided Coaching Assistant for Table Tennis Practice

Sensors ◽

10.3390/s18124112 ◽

2018 ◽

Vol 18 (12) ◽

pp. 4112 ◽

Cited By ~ 6

Author(s):

Se-Min Lim ◽

Hyeong-Cheol Oh ◽

Jaein Kim ◽

Juwon Lee ◽

Jooyoung Park

Keyword(s):

Time Series ◽

State Space ◽

Time Series Data ◽

State Space Model ◽

Skill Assessment ◽

Series Data ◽

High Dimensional ◽

Table Tennis ◽

Space Model ◽

Low Dimensional

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.

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Chaotic Patterns in Aeroelastic Signals

Mathematical Problems in Engineering ◽

10.1155/2009/802970 ◽

2009 ◽

Vol 2009 ◽

pp. 1-19 ◽

Cited By ~ 2

Author(s):

F. D. Marques ◽

R. M. G. Vasconcellos

Keyword(s):

Time Series ◽

State Space ◽

Complex Dynamics ◽

Chaotic Behavior ◽

Separated Flow ◽

Direct Analysis ◽

Surrogate Data ◽

The State ◽

Aeroelastic System ◽

Value Decomposition

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

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