3 Limit theorems for markets with non-random time-varying coefficients

2021 ◽  
pp. 243-278
Keyword(s):  
Limit Theorems ◽  
Random Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Varying Coefficients

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.

scholarly journals Survey Expectations and Learning

2021 ◽  
pp. 3-27
Author(s):  
Sergey Slobodyan ◽  
◽  
Raf Wouters ◽  
◽  
Keyword(s):  
Real Time ◽  
Time Variation ◽  
Autoregressive Model ◽  
Dsge Models ◽  
Inflation Expectations ◽  
Time Varying ◽  
Time Data ◽  
Varying Coefficients ◽  
Real Time Data ◽  
Time Varying Coefficients

In this paper, we evaluate a model that describes real-time inflation data together with the inflation expectations measured by the Survey of Professional Forecasters (SPF). We work with a second-order autoregressive model in which the agents learn over time the intercept and persistence coefficients based on real-time data. To model the process of revisions in real time data, we allow for news and noise disturbances. In contrast to the usual time-varying parameter vector autoregression, we use non-linear Kalman filter techniques to estimate the time-varying coefficients of the underlying inflation process. We identify systematic changes in the persistence of the inflation process and in the long-run expected inflation rate that are implied by the model. The inflation forecasts implied by the model are then compared with the SPF forecasts. As we cannot reject the hypothesis that the SPF forecasts are produced based on our model, we re-estimate the model using Survey nowcasts and forecasts as additional observables. This augmented model does not change the nature and magnitude of the time variation in the coefficients of the autoregressive model, but it does help to reduce the uncertainty in the estimates. Overall, the estimated time-variation confirms our results on the perceived inflation process present in estimated DSGE models with learning (Slobodyan and Wouters, 2012a, 2012b).

Uniform global asymptotic stability for half-linear differential systems with time-varying coefficients

2011 ◽  
Vol 141 (5) ◽  
pp. 1083-1101 ◽  
Author(s):  
Masakazu Onitsuka ◽  
Jitsuro Sugie
Keyword(s):  
Linear System ◽  
Zero Solution ◽  
Integrable Case ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Linear Differential Systems ◽  
Time Varying Coefficients ◽  
Linear Differential ◽  
Image Position

The present paper deals with the following system:where p and p* are positive numbers satisfying 1/p + 1/p* = 1, and ϕq(z) = |z|q−2z for q = p or q = p*. This system is referred to as a half-linear system. We herein establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) for the zero solution to be uniformly globally asymptotically stable. If (e(t), f(t)) ≡ (h(t), g(t)), then the half-linear system is integrable. We consider two cases: the integrable case (e(t), f(t)) ≡ (h(t), g(t)) and the non-integrable case (e(t), f(t)) ≢ (h(t), g(t)). Finally, some simple examples are presented to illustrate our results.

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