scholarly journals Climatic responses to systematic time variations of parameters: A dynamical approach

2018 ◽  
Author(s):  
Catherine Nicolis
Keyword(s):  
Evolution Equations ◽  
Time Dependent ◽  
Time Varying ◽  
Climatic Response ◽  
Varying Coefficients ◽  
Classical Stability ◽  
Theoretical Predictions ◽  
Time Variations ◽  
Time Varying Coefficients ◽  
Climatic Responses

Abstract. The climatic response to time-dependent parameters is revisited from a nonlinear dynamics perspective. Some general trends are identified, based on a generalised stability criterion extending classical stability analysis to account for the presence of time-varying coefficients in the evolution equations of the system's variables. Theoretical predictions are validated by the results of numerical integration of the evolution equations of prototypical systems of relevance in atmospheric and climatic dynamics.

scholarly journals Climatic responses to systematic time variations of parameters: a dynamical approach

2018 ◽  
Vol 25 (3) ◽  
pp. 649-658 ◽  
Author(s):  
Catherine Nicolis
Keyword(s):  
Evolution Equations ◽  
Time Dependent ◽  
Time Varying ◽  
Climatic Response ◽  
Varying Coefficients ◽  
Classical Stability ◽  
Theoretical Predictions ◽  
Time Variations ◽  
Time Varying Coefficients ◽  
Climatic Responses

Abstract. The climatic response to time-dependent parameters is revisited from a nonlinear dynamics perspective. Some general trends are identified, based on a generalized stability criterion extending classical stability analysis to account for the presence of time-varying coefficients in the evolution equations of the system's variables. Theoretical predictions are validated by the results of numerical integration of the evolution equations of prototypical systems of relevance in atmospheric and climatic dynamics.

scholarly journals Estimating Survival Functions after Stcox with Time-varying Coefficients

2016 ◽  
Vol 16 (4) ◽  
pp. 867-879 ◽  
Author(s):  
Constantin Ruhe
Keyword(s):  
Proportional Hazards ◽  
Cox Model ◽  
Survival Function ◽  
Time Dependent ◽  
Time Varying ◽  
Survival Functions ◽  
Nonproportional Hazards ◽  
Varying Coefficients ◽  
Proportional Hazards Assumption ◽  
Time Varying Coefficients

In many applications of the Cox model, the proportional-hazards assumption is implausible. In these cases, the solution to nonproportional hazards usually consists of modeling the effect of the variable of interest and its interaction effect with some function of time. Although Stata provides a command to implement this interaction in stcox, it does not allow the typical visualizations using stcurve if stcox was estimated with the tvc() option. In this article, I provide a short workaround that estimates the survival function after stcox with time-dependent coefficients. I introduce and describe the scurve_tvc command, which automates this procedure and allows users to easily visualize survival functions for models with time-varying effects.

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.

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