Dynamic Modeling and Statistical Analysis of Event Times

This review article provides an overview of recent work in the modeling and analysis of recurrent events arising in engineering, reliability, public health, biomedicine and other areas. Recurrent event modeling possesses unique facets making it different and more difficult to handle than single event settings. For instance, the impact of an increasing number of event occurrences needs to be taken into account, the effects of covariates should be considered, potential association among the interevent times within a unit cannot be ignored, and the effects of performed interventions after each event occurrence need to be factored in. A recent general class of models for recurrent events which simultaneously accommodates these aspects is described. Statistical inference methods for this class of models are presented and illustrated through applications to real data sets. Some existing open research problems are described.Comment: Published at http://dx.doi.org/10.1214/088342306000000349 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Finite sample performance of linear least squares estimators under sub-Gaussian martingale difference noise

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required. Surprisingly, bounding the probability of large errors with finitely many samples has been left open, especially when dealing with correlated noise with unknown covariance. In this paper we analyze the finite sample performance of the linear least squares estimator under sub-Gaussian martingale difference noise. In order to analyze this important question we used concentration of measure bounds. When applying these bounds we obtained tight bounds on the tail of the estimator's distribution. We show the fast exponential convergence of the number of samples required to ensure a given accuracy with high probability. We provide probability tail bounds on the estimation error's norm. Our analysis method is simple and uses simple $L_{\infty}$ type bounds on the estimation error. The tightness of the bounds is tested through simulation. The proposed bounds make it possible to predict the number of samples required for least squares estimation even when least squares is sub-optimal and used for computational simplicity. The finite sample analysis of least squares models with this general noise model is novel

Jump-diffusion model of exchange rate dynamics : estimation via indirect inference

This paper investigates asymmetric effects of monetary policy over the business cycle. A two-state Markov Switching Model is employed to model both recessions and expansions. For the United States and Germany, strong evidence is found that monetary policy is more effective in a recession than during a boom. Also some evidence is found for asymmetry in the United Kingdom and Belgium. In the Netherlands, monetary policy is not very effective in either regime.

A selective overview of nonparametric methods in financial econometrics

This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.Comment: 32 pages include 7 figure

Optimal Instruments in Time Series: A Survey

This article surveys estimation in stationary time series models using the approach of optimal instrumentation. We review tools that allow construction and implementation of optimal instrumental variables estimators in various circumstances { in single- and multiperiod models, in the absence and presence of conditional heteroskedasticity, by considering linear and nonlinear instruments. We also discuss issues adjacent to the theme of optimal instruments. The article is directed primarily towards practitioners, but also may be found useful by econometric theorists and teachers of graduate econometrics.Instrumental variables estimation; Moment restrictions; Optimal instrument; Effciency bounds; Stationary time series.

Dynamic Misspecification in Nonparametric Cointegrating Regression

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification but the variance of the limit distribution is larger. Some applications of the limit theory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed.Dynamic misspecification, Functional regression, Integrable function, Integrated process, Local time, Misspecification, Mixed normality, Nonlinear cointegration, Nonparametric regression