Regression quantiles for time series

This is the publisher's version, also available electronically from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=92739&fulltextType=RA&fileId=S0266466602181096.In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for [alpha]-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology

Trending Time-Varying Coefficient Models With Serially Correlated Errors

In this paper we study time-varying coefficient models with time trend function and serially correlated errors to characterize nonlinear, nonstationary and trending phenomenon in time series. Compared with the Nadaraya-Watson method, the local linear approach is developed to estimate the time trend and coefficient functions. The consistency of the proposed estimators is obtained without any specification of the error distribution and the asymptotic normality of the proposed estimators is established under the alpha-mixing conditions. The explicit expressions of the asymptotic bias and variance are given for both estimators. The asymptotic bias is just in a regular nonparametric form but the asymptotic variance is shared by parametric estimators. Also, the asymptotic behaviors at both interior and boundary points are studied for both estimators and it shows that two estimators share the exact same asymptotic properties at the interior points but not at the boundaries. Moreover, proposed are a new bandwidth selector based on the nonparametric version of the Akaike information criterion, a consistent estimator of the asymptotic variance, and a simple nonparametric version of bootstrap (i.e. wild bootstrap) test for testing the misspecification and stationarity. Finally, we conduct some Monte Carlo experiments to examine the finite sample performances of the proposed modeling procedures and test

Nonparametric estimation of varying coefficient dynamic panel models

This is the publisher's version, also available electronically from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2059888&fileId=S0266466608080523.We suggest using a class of semiparametric dynamic panel data models to capture individual variations in panel data. The model assumes linearity in some continuous/discrete variables that can be exogenous/endogenous and allows for nonlinearity in other weakly exogenous variables. We propose a nonparametric generalized method of moments (NPGMM) procedure to estimate the functional coefficients, and we establish the consistency and asymptotic normality of the resulting estimators

Nonparametric estimation of additive nonlinear ARX time series: Local Linear Fitting and Projections

This is the publisher's version, also available electronically from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=55027&fulltextType=RA&fileId=S0266466600164011.We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ a local polynomial fitting scheme coupled with projections. We establish the weak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given

Kaplan–Meier Estimator under Association

AbstractConsider a long term study, where a series of possibly censored failure times is observed. Suppose the failure times have a common marginal distribution functionF, but they exhibit a mode of dependence characterized by positive or negative association. Under suitable regularity conditions, it is shown that the Kaplan–Meier estimatorFnofFis uniformly strongly consistent; rates for the convergence are also provided. Similar results are established for the empirical cumulative hazard rate function involved. Furthermore, a stochastic process generated byFnis shown to be weakly convergent to an appropriate Gaussian process. Finally, an estimator of the limiting variance of the Kaplan–Meier estimator is proposed and it is shown to be weakly convergent

Functional Coefficient Models for Economic and Financial Data

This paper gives a selective overview on the functional coefficient models with their particular applications in economics and finance. Functional coefficient models are very useful analytic tools to explore complex dynamic structures and evolutions for functional data in various areas, particularly in economics and finance. They are natural generalizations of classical parametric models with good interpretability by allowing coefficients to be governed by some variables or to change over time, and also they have abilities to capture nonlinearity and heteroscedasticity. Furthermore, they can be regarded as one of dimensionality reduction methods for functional data exploration and have nice interpretability. Due to their great properties, functional coefficient models have had many methodological and theoretical developments and they have become very popular in various applications

The examination of residual plots

This is the publisher's version, also available electronically from http://www3.stat.sinica.edu.tw/statistica/j8n2/j8n29/j8n29.htm.Linear and squared residual plots are proposed to assess nonlinearity and heteroscedasticity in regression diagnostics. It is shown that linear residual plots are useful for diagnosing nonlinearity and squared residual plots are powerful for detecting nonconstant variance. A paradigm for the graphical interpretation of residual plots is presented

Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models

We suggest using a class of semiparametric dynamic panel data models to capture individual variations in panel data. The model assumes linearity in some continuous/discrete variables that can be exogenous/endogenous and allows for nonlinearity in other weakly exogenous variables. We propose a nonparametric generalized method of moments (NPGMM) procedure to estimate the functional coefficients, and we establish the consistency and asymptotic normality of the resulting estimators. Econometric Theory, 24, 2008, 1321–1342+ Printed in the United States of America+ doi:10+10170S0266466608080523