Time-varying Coefficient Models Research Articles

Bootstrap inference for linear time-varying coefficient models in locally stationary time series

Time-varying coefficient models can capture evolving relationships. However, constructing asymptotic confidence bands for coefficient curves in these models is challenging due to slow convergence rates and the presence of various nuisance parameters. A residual-based sieve bootstrap method has recently been proposed to address these issues. While it successfully produces confidence bands with accurate empirical coverage, its applicability is restricted to strictly stationary processes. We introduce a new bootstrap scheme, the local blockwise wild bootstrap (LBWB), that allows for locally stationary processes. The LBWB can replicate the distribution of the parameter estimates while automatically accounting for nuisance parameters. An extensive simulation study reveals the superior performance of the LBWB compared to various benchmark approaches. It also shows the potential applicability of the LBWB in broader scenarios, including time-varying cointegrating models. We then examine herding effects in the Chinese renewable energy market using the proposed methods. Our findings strongly support the presence of herding behaviors before 2016, aligning with earlier studies. However, contrary to previous research, we find no significant evidence of herding between around 2018 and 2021. Online supplementary materials are available for this article.

Productive electricity and non-electricity consumption effects on economic growth: A Latin America analysis

Electrification is a key pillar in energy transformation to reduce emissions. However, it may also have consequences on production. This study analyzes the effect of using electricity and non-electricity energy sources on production growth. An extended neoclassical production function, with the two uses of energy (electricity and non-electricity), is estimated for 17 Latin American countries from 1990 to 2019 and, for subsamples, based on the level of production per persons employed. The study is performed applying the cross-sectionally augmented, autoregressive distributed lag modeling approach and a non-parametric time-varying coefficients model. The parametric results indicate that the effect of both sources of energy on production are positive and significant. However, the production elasticity with respect to non-electricity consumption is higher than that with respect to electricity consumption. Only in countries with the lowest production levels could electrification be neutral. The non-parametric results show that the effect of non-electricity consumption is decreasing slightly over the period, while the effect of electricity use is increasing slightly, with a tendency towards stabilization at the end of the period. Nevertheless, these changes have been small.

A Bayesian Time-Varying Coefficient Model for Cobb–Douglas Production Function

A Bayesian Time-Varying Coefficient Model for Cobb–Douglas Production Function

Online monitoring of profiles via RVC model with an application to industrial busbar

ABSTRACT Profile monitoring is used to check the stability of the functional relationship of the process response on several predictors. In most of the existing literature, the monitored functional relationship usually involves only one covariate and the coefficient of the covariate is assumed to be constant. In some applications, the process response depends on multiple covariates, and the functional relationship is not constant but dynamic over time, which is different from those studied in the literature. To implement profile monitoring in these applications, a semiparametric random time-varying coefficient model is employed to characterize this dynamic relationship over time. Based on this model, a profile monitoring scheme integrated with dynamic probability control limits is proposed, which can adapt to the case of the within-profile autocorrelation and arbitrary design points. In Phase I, this paper uses a backfitting iterative procedure with the REML-Based EM-Algorithm to estimate the model. In Phase II, an exponentially weighted moving average scheme on residuals with dynamic probability control limits is developed. The simulation results show that the proposed scheme performs better in many scenarios. Finally, an application to industrial busbar running process monitoring is given to illustrate the scheme’s implementation.

A Symmetric Kernel Smoothing Estimation of the Time-Varying Coefficient for Medical Costs

In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT).

Empirical stream thermal sensitivity cluster on the landscape according to geology and climate

Abstract. Climate change is modifying river temperature regimes across the world. To apply management interventions in an effective and efficient fashion, it is critical to both understand the underlying processes causing stream warming and identify the streams most and least sensitive to environmental change. Empirical stream thermal sensitivity, defined as the change in water temperature with a single degree change in air temperature, is a useful tool to characterize historical stream temperature conditions and to predict how streams might respond to future climate warming. We measured air and stream temperature across the Snoqualmie and Wenatchee basins, Washington, during the hydrologic years 2015–2021. We used ordinary least squares regression to calculate seasonal summary metrics of thermal sensitivity and time-varying coefficient models to derive continuous estimates of thermal sensitivity for each site. We then applied classification approaches to determine unique thermal sensitivity regimes and, further, to establish a link between environmental covariates and thermal sensitivity regimes. We found a diversity of thermal sensitivity responses across our basins that differed in both timing and magnitude of sensitivity. We also found that covariates describing underlying geology and snowmelt were the most important in differentiating clusters. Our findings and our approach can be used to inform strategies for river basin restoration and conservation in the context of climate change, such as identifying climate-insensitive areas of the basin that should be preserved and protected.

Water in Epoxy Coatings: Basic Principles of Interaction with Polymer Matrix and the Influence on Coating Life Cycle

This review describes the interaction of epoxy coatings with water, the kinetics of water uptake in epoxy resins, and the methods of studying the latter (gravimetric, IR (Infrared) and NMR (Nuclear magnetic resonance) spectroscopies). The analysis of experimental data requires using mathematical models which simulate the processes that occur during water uptake in a polymer matrix. This review classifies the numerous models applied for the study of water absorption into two large groups: Fickian and non-Fickian models. Fickian models involve the Fickian diffusion model and its development for the case of anomalous diffusion, as well as the models of Jacobs–Jones, Berens–Hopfenberg, and the time-varying diffusion coefficient model. The Carter–Kibler approach is provided as an example of a non-Fickian or Langmuir-type model. A critical analysis of the experimental methods is provided, including advantages and possible experimental errors. The methods used for processing experimental data are discussed as well as the effect of water on the exploitation properties and life cycle of epoxy coatings.

A new time-varying coefficient regression approach for analyzing infectious disease data

Since the beginning of the global pandemic of Coronavirus (SARS-COV-2), there has been many studies devoted to predicting the COVID-19 related deaths/hospitalizations. The aim of our work is to (1) explore the lagged dependence between the time series of case counts and the time series of death counts; and (2) utilize such a relationship for prediction. The proposed approach can also be applied to other infectious diseases or wherever dynamics in lagged dependence are of primary interest. Different from the previous studies, we focus on time-varying coefficient models to account for the evolution of the coronavirus. Using two different types of time-varying coefficient models, local polynomial regression models and piecewise linear regression models, we analyze the province-level data in Canada as well as country-level data using cumulative counts. We use out-of-sample prediction to evaluate the model performance. Based on our data analyses, both time-varying coefficient modeling strategies work well. Local polynomial regression models generally work better than piecewise linear regression models, especially when the pattern of the relationship between the two time series of counts gets more complicated (e.g., more segments are needed to portray the pattern). Our proposed methods can be easily and quickly implemented via existing R packages.

Asynchronous and error-prone longitudinal data analysis via functional calibration.

In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing kernel-based methods suffer from slow convergence rates and large variations. To address these challenges, we propose a new functional calibration approach to efficiently learn longitudinal covariate processes based on sparse functional data with measurement error. Our approach, stemming from functional principal component analysis, calibrates the unobserved synchronized covariate values from the observed asynchronous and error-prone covariate values, and is broadly applicable to asynchronous longitudinal regression with time-invariant or time-varying coefficients. For regression with time-invariant coefficients, our estimator is asymptotically unbiased, root-n consistent, and asymptotically normal; for time-varying coefficient models, our estimator has the optimal varying coefficient model convergence rate with inflated asymptotic variance from the calibration. In both cases, our estimators present asymptotic properties superior to the existing methods. The feasibility and usability of the proposed methods are verified by simulations and an application to the Study of Women's Health Across the Nation, a large-scale multisite longitudinal study on women's health duringmidlife.

Kernel Estimation of Bivariate Time-Varying Coefficient Model for Longitudinal Data with Terminal Event

We propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal trajectories of covariate effects along with both the followup time and the residual lifetime. The proposed model extends the parametric conditional approach given terminal event time in recent literature, and thus avoids potential model misspecification. We consider a kernel smoothing method for estimating regression coefficients in our model and use cross-validation for bandwidth selection, applying undersmoothing in the final analysis to eliminate the asymptotic bias of the kernel estimator. We show that the kernel estimates follow a finite-dimensional normal distribution asymptotically under mild regularity conditions, and provide an easily computed sandwich covariance matrix estimator. We conduct extensive simulations that show desirable performance of the proposed approach, and apply the method to analyzing the medical cost data for patients with end-stage renal disease. Supplementary materials for this article are available online.

Herding in the Chinese renewable energy market: Evidence from a bootstrapping time-varying coefficient autoregressive model

In this paper, we examine the herd behaviour of the Chinese renewable energy sector using both static and time-varying coefficient models. Examining daily data from January 05, 2015 to April 29, 2022, we find strong evidence of herding behaviour changing over time in this market. We find that herding asymmetry is more pronounced during up markets and among smaller firms. When within-industry herding weakens, large price movements in the overall stock market provide additional trading signals for herding formation in this sector.

A Stratified Penalized Kernel Method for Semiparametric Variable Labeling and Estimation of Multi-Output Time-Varying Coefficient Models for Nonstationary Time Series

A Stratified Penalized Kernel Method for Semiparametric Variable Labeling and Estimation of Multi-Output Time-Varying Coefficient Models for Nonstationary Time Series

Comparison between the Local Polynomial Kernel Method and cubic spline to Estimating Time-Varying Coefficients Model

The research deals with the study of the varying coefficient model as well as the Time-Varying Coefficient Model because of their remarkable interest in recent years. Methods Two methods were used, local polynomial kernal method and the cubic spline method. The simulation method was used for comparison. Compared to three mathematical functions that represented the variable coefficients, different sample sizes, and different levels of the model's standard deviation, the cubic spline method was best.

Sieve bootstrap inference for linear time-varying coefficient models

We propose a sieve bootstrap framework to conduct pointwise and simultaneous inference for time-varying coefficient regression models based on a local linear estimator. The asymptotic validity of the sieve bootstrap in the presence of autocorrelation is established. The bootstrap automatically produces a consistent estimate of nuisance parameters, both at the interior and boundary points. In addition, we develop a bootstrap-based test for parameter constancy and examine its asymptotic properties. An extensive simulation study demonstrates a good finite sample performance of our methods. The proposed methods are applied to assess the price development of CO2 certificates in the European Emissions Trading System. We find evidence of time variation in the relationship between allowance prices and their fundamental price drivers. The time variation might offer an explanation for previous contradicting findings using linear regression models with constant coefficients.

Specification tests for time-varying coefficient models

Time-varying coefficient models have been widely used to characterize changing relationships among economic and financial variables. The existing literature usually specifies the time-varying coefficient vector as a stationary stochastic process, a deterministic function of time, and a unit root process, respectively. In this paper, we propose two tests to distinguish these three specifications. Both test statistics follow asymptotic normal distributions under the respective null hypotheses and diverge to infinity in probability under the corresponding alternatives. To improve the finite sample performance of the tests, we propose a dependent wild bootstrap to obtain the bootstrap critical value (or P-value) and establish its asymptotic validity. Simulation studies show that our bootstrap-based tests perform reasonably well in finite samples. We apply the proposed tests to the time-varying specifications of the equity return’s predictive model, the U.S. Taylor rule, and inflation persistence, respectively. The results suggest that a unit root process is favored for the first application, whereas a deterministic function of time should be adopted for the latter two applications.

Social Mobility and Sense of Purpose From Midlife to Old Age: Examining the Role of Major Life Events.

Purpose in life (PIL) has been linked with numerous health benefits and adaptive aging, yet it diminishes with age, possibly due to loss of social or familial roles through life transitions. Drawing from the longitudinal surveys of the Midlife in the US study (n = 3418), we use time-varying coefficient models to investigate how the trajectory of PIL differs across cumulatively (dis)advantaged, upwardly mobile, and downwardly mobile groups and the role of major life events in shaping these trajectories. We found the upwardly mobile group exhibits higher PIL than the cumulatively disadvantaged and downwardly mobile groups. The consistently disadvantaged group experiences more adverse events at non-normative times. Socioeconomic status disparities in PIL during old age decrease after controlling for life events. We discuss how and why well-being changes and the role of structural and social factors in facilitating or impeding the development or maintenance of PIL over the life course.

Kidney Graft Failure and Patient Survival Modelling Based on Competing Risks Under Nonproportional Hazards

We analyze data on Silesian patients after kidney transplantation under competing events scenarios where time to death and time to graft failure are considered as absorbing competing events. Our objectives are to use model diagnostics in identifying violations of proportionality assumption under the framework of subdistribution and cause-specific hazards. We use the Fine-Gray proportional hazards model for the subdistribution. Under the cause-specific hazards (CSH) scenario we use the Cox proportional hazards model and Gray's time-varying coefficients model and available model diagnostics. We show that violation of proportional subdistribution hazards assumption may be conveniently identified using residual diagnostics and properly accounted for by involving time interactions with appropriate model predictors. We also show that although the nonproportional effects on cumulative incidence do not necessarily translate in those on cause-specific hazards, they often take place simultaneously, and a violation of the proportionality assumption needs to be checked rigorously. Time-varying effects have a profound impact on clinical inference under competing risks. They do not translate directly between the frameworks of subdistribution and cause-specific hazards because the cumulative incidence is obtained via integrating the cause-specific hazard weighted by the overall survival function. Also, a different definition of the risk set is in place under the cumulative incidence and CSH framework, respectively. However, a simultaneous violation of the proportionality assumption under both frameworks is still possible. Clinical inference may change considerably when such a violation occurs. Nonproportional effects may be properly identified under each framework using available model diagnostics.

Survival Analysis via Ordinary Differential Equations

This article introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable, and easy-to-implement procedure for estimation and inference. Specifically, the ODE modeling framework unifies many existing survival models, such as the proportional hazards model, the linear transformation model, the accelerated failure time model, and the time-varying coefficient model as special cases. The generality of the proposed framework serves as the foundation of a widely applicable estimation procedure. As an illustrative example, we develop a sieve maximum likelihood estimator for a general semiparametric class of ODE models. In comparison to existing estimation methods, the proposed procedure has advantages in terms of computational scalability and numerical stability. Moreover, to address unique theoretical challenges induced by the ODE notion, we establish a new general sieve M-theorem for bundled parameters and show that the proposed sieve estimator is consistent and asymptotically normal, and achieves the semiparametric efficiency bound. The finite sample performance of the proposed estimator is examined in simulation studies and a real-world data example. Supplementary materials for this article are available online.

Network-adaptive robust penalized estimation of time-varying coefficient models with longitudinal data

Longitudinal data are commonly encountered in many fields. Many statistical models have been developed, among which the time-varying coefficient model has been shown to be effective for many practical problems. Long-tailed/contaminated distributions are not uncommon and cannot be accommodated using non-robust likelihood-based estimation. Another common limitation shared by many of the existing methods is the insufficient account for the interconnections among covariates. In this study, we adopt a least absolute deviation loss function to achieve robustness. For the selection of relevant covariates, a penalization approach is adopted. Significantly advancing from the existing literature, we describe the interconnections among covariates using a network structure and develop novel penalties to accommodate the network connectivity and connection measures. Consistency properties are rigorously established. Numerical studies, including both simulations and data analysis, demonstrate the competitive practical performance of the proposed method.

Comparison of Cox proportional hazards model, Cox proportional hazards with time-varying coefficients model, and lognormal accelerated failure time model: Application in time to event analysis of melioidosis patients

Objective: To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time (AFT), Cox proportional hazards (PH), and Cox PH with time-varying coefficient (TVC) models.Methods: A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah, Kedah and Hospital Tuanku Fauziah, Perlis in Northern Malaysia due to confirmed-cultured melioidosis. The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis, and Cox’s models and the findings were compared by using the goodness of fit methods. The analyses were done by using Stata SE version 14.0.Results: A total of 242 patients (53.4%) survived. In this study, the median survival time of melioidosis patients was 30.0 days (95% CI 0.0-60.9). Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model. In AFT survival analysis, a total of seven significant prognostic factors were identified. The results were found to be only a slight difference between the identified prognostic factors among the models. AFT survival showed better results compared to Cox’s models, with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions: AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.