Specification tests for time-varying coefficient models

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.

This paper proposes a Bayesian regression model with time-varying coefficients (TVC) that makes it possible to estimate jointly the degree of instability and the time-path of regression coefficients. Thanks to its computational tractability, the model proves suitable to perform the first (to our knowledge) Monte Carlo study of the finite-sample properties of a TVC model. Under several specifications of the data generating process, the proposed model’s estimation precision and forecasting accuracy compare favourably with those of other methods commonly used to deal with parameter instability. Furthermore, the TVC model leads to small losses of efficiency under the null of stability and it is robust to mis-specification, providing a satisfactory performance also when regression coefficients experience discrete structural breaks. As a demonstrative application, we use our TVC model to estimate the exposures of S&P 500 stocks to market-wide risk factors: we find that a vast majority of stocks have time-varying risk exposures and that the TVC model helps to forecast these exposures more accurately.

Bayesian Bandwidth Selection in Nonparametric Time-Varying Coefficient Models

In this paper, we discuss wavelet estimation of time-varying coefficient models based on censored data where the survival and the censoring times are from a stationary α-mixing sequence. Under the appropriate conditions, the Berry-Esseen bouds of wavelet estimators are established. For the purpose of statistical inference, a random weighted wavelet estimator of the time-varying coefficient is also constructed, and some approximation rates are given.

Econometric analysis of time series data is frequently preceded by regression on time to remove a trent component in the date. The resulting residuals are then treated as a stationary series to which procedures requiring stationarity, such as spectral analysis, can be applied. The objective is often to investigate the dynamics of transitory movements in the systems, for example, in econometric models of the business cycle. When the data does consist of a deterministic function of time plus a stationary error then regression residuals will clearly be unbiased estimates of the stationary component. However, if the data is generated by (possibly repeated) summation of a satisfactory and inevitable process then the series cannot be expressed as a deterministic function of time plus a stationary deviation, even though a least squares trend line and the associated residuals can always be calculated for any given finite sample. In a recent paper, Chan, Hayya, and Ord (1977) hereafter CHO) were able to show that a residuals from linear regression of a realization of a random walk (the summation of a purely random series) on time have autocovariances which for given lag are a function of time and thereafter that the residuals are not stationary. Further, CHO established that the expected sample autocovariance function (the expected autocovariances for given lag averaged over the time interval of the sample) is a function of sample size as well as lag and therefore an artifact of the detrending procedure. This function is characterized by CHO in their figure 1 as being effectively linear in lag (although the exact function is a fifth degree polynomial) with the rate of decay from unity at the origin depending inversely on sample size.

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.

In this paper, we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions involving a bandwidth, centered around a given set of time points. In addition, we study different alternatives of estimation and inference including a Frequentist approach using weighted least squares along with bootstrap methods, and a Bayesian approach through both Markov chain Monte Carlo and variational methods. We compare the estimation strategies mention above with each other, and our radial kernel functions proposal with an expansion based on regression spline, by means of an extensive simulation study considering multiples scenarios in terms of sample size, number of repeated measurements, and subject-specific correlation. Our experiments show that the capabilities of our proposal based on radial kernel functions are indeed comparable with or even better than those obtained from regression splines. We illustrate our methodology by analyzing data from two AIDS clinical studies.

Financial time series data tend to exhibit stochastic trends. To uncover relationship among financial variables it is important to model changes in stochastic trends over time. Cointegration can be used to identify common stochastic trend among different financial variables. If financial variables are cointegrated, it can also be shown that the variables exhibit long-run relationship. Keywords: deterministic trends; stationarity; unit root process; autoregression; cointegration; vector autoregressive model; error correction; Granger causality

We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two rather than of order one. It turns out that standard augmented Dickey–Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips–Perron class of semi‐parametric tests is shown to diverge to plus infinity asymptotically and thus favouring the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples.

This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey and Fuller. Some simulations are reported which provide evidence on the performance of the new tests in finite samples.

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).

This article proposes a Bayesian time-varying coefficient model to evaluate the temporal profile of intensity for multitype recurrent events. The model obtains smooth estimates for both time-varying coefficients and the baseline intensity using Bayesian penalized splines. One major challenge in Bayesian penalized splines is that the smoothness of a spline fit is sensitive to the subjective choice of hyperparameters. We establish a procedure to objectively determine the hyperparameters through robust prior specification. To effectively update the high-dimensional spline parameters, we develop a Markov chain Monte Carlo procedure based on the Metropolis-adjusted Langevin algorithms. A joint sampling scheme is used to achieve better convergence and mixing properties. A simulation study confirms satisfactory model performance in estimating time-varying coefficients under different curvature and event rate scenarios. Application to a commercial truck driver naturalistic driving data reveals that drivers with 7-hours-or-less sleep time have a significantly higher safety-critical event intensity after 8 hr of driving and the intensity remains high after taking a break. The findings provide crucial information for the truck driver hours-of-service regulation and fatigue management. The proposed model provides a flexible and robust tool to evaluate the temporal profile of intensity for multitype recurrent events. Supplemental materials for this article are available online.

We propose a (trend) stationarity test with a good finite sample size even when a process is (trend) stationary with strong persistence; this is useful for distinguishing between a (trend) stationary process with strong persistence and a unit root process. It could be considered as a modified version of Leybourne and McCabe's test (1994, LMC), but with adi fferent correction method for serial correlation. A Monte Carlo simulation reveals that in terms of empirical size, our test is closer to the nominal one than the original LMC test and is more powerful than the LMC test with size-adjusted critical values.

This paper provides a general procedure to estimate structural vector autoregressions. The algorithm can be used in constant or time-varying coefficient models, and in the latter case, the law of motion of the coefficients can be linear or nonlinear. It can deal in a unified way with just-identified (recursive or nonrecursive) or overidentified systems where identification restrictions are of linear or of nonlinear form. We study the transmission of monetary policy shocks in models with time-varying and time-invariant parameters.

Leverage and Alpha: The Case of Funds of Hedge Funds