MULTIVARIATE TIME-VARYING AUTOREGRESSIVE MODELING OF FETAL SYMPATHO-VAGAL BALANCE THROUGH GESTATION

2013 ◽  
Vol 25 (01) ◽  
pp. 1350014 ◽  
Author(s):  
D. Gutiérrez
Keyword(s):  
High Specificity ◽  
Time Varying ◽  
Autoregressive Modeling ◽  
Short Term ◽  
Data Set ◽  
Varying Coefficients ◽  
Non Invasive ◽  
Time Varying Coefficients ◽  
The Time Domain ◽  
Short Term Variability

A processing framework is proposed to model relative changes in fetal sympatho-vagal balance at equally spaced gestational periods. The proposed method is based on a multivariable time-varying autoregression (TVAR) of the beat-to-beat time differences obtained from non-invasive fetal electrocardiographic (ECG) or magnetocardiographic (MCG) measurements. In order to quantify the sympatho-vagal balance at each measured gestational period, the ratio between the standard deviation of normal-to-normal (SDNN) beat intervals and the sum of absolute differences (SAD) is computed. While the SDNN quantifies the overall variability of the sympathetic and vagal systems, the SAD enhances short-term variability components related to vagal control, then the ratio of these two compares with high specificity the overall variability against the short-term vagal component in the time domain. The SDNN/SAD ratio is used to form a new data set by removing short-term variability events, then leaving only those corresponding to longer-term sympatho-vagal balance. The new data set is then analyzed as a dynamical system by fitting it to a suitable multivariate TVAR, and relative changes in the sympatho-vagal balance through the analyzed gestational periods are assumed to be related to the dynamics of the time-varying coefficients of the TVAR. In order to demonstrate the applicability of the proposed method, simulated and real fetal E/MCG data are analyzed. The results show that the modeling approach is able to infer the expected trend seen through sympatho-vagal development.

Generalized Frequency Response Functions for Systems with Time-Varying Coefficients

1994 ◽  
Vol 208 (3) ◽  
pp. 145-153 ◽  
Author(s):  
M R Belmont
Keyword(s):  
Frequency Response ◽  
Time Domain ◽  
Illustrative Case ◽  
Time Varying ◽  
Response Functions ◽  
Governing Equations ◽  
Varying Coefficients ◽  
Wide Range ◽  
Time Varying Coefficients ◽  
The Time Domain

An extension of the concept of frequency response is introduced which can be applied to systems described by differential equations whose coefficients vary periodically or almost periodically with time. Such systems are not accessible to traditional frequency response function methods because while the governing equations may be linear in the time domain they are non-linear in frequency. The basic theory of the technique is introduced and results are obtained for a wide range of systems. Time domain solutions are also deduced to complement the spectral development. Numerical results are calculated for an illustrative case that deals with a photochemical problem driven by a solar daylight cycle.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

scholarly journals Gray’s Time-Varying Coefficients Model for Posttransplant Survival of Pediatric Liver Transplant Recipients with a Diagnosis of Cancer

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yi Ren ◽  
Chung-Chou H. Chang ◽  
Gabriel L. Zenarosa ◽  
Heather E. Tomko ◽  
Drew Michael S. Donnell ◽  
...  
Keyword(s):  
Liver Transplant ◽  
Failure Time ◽  
Penalized Splines ◽  
Time Varying ◽  
Piecewise Constant ◽  
Varying Coefficients ◽  
Covariate Effects ◽  
Pediatric Liver ◽  
Time Varying Coefficients ◽  
Pediatric Liver Transplant

Transplantation is often the only viable treatment for pediatric patients with end-stage liver disease. Making well-informed decisions on when to proceed with transplantation requires accurate predictors of transplant survival. The standard Cox proportional hazards (PH) model assumes that covariate effects are time-invariant on right-censored failure time; however, this assumption may not always hold. Gray’s piecewise constant time-varying coefficients (PC-TVC) model offers greater flexibility to capture the temporal changes of covariate effects without losing the mathematical simplicity of Cox PH model. In the present work, we examined the Cox PH and Gray PC-TVC models on the posttransplant survival analysis of 288 pediatric liver transplant patients diagnosed with cancer. We obtained potential predictors through univariable(P<0.15)and multivariable models with forward selection(P<0.05)for the Cox PH and Gray PC-TVC models, which coincide. While the Cox PH model provided reasonable average results in estimating covariate effects on posttransplant survival, the Gray model using piecewise constant penalized splines showed more details of how those effects change over time.

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