Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates

We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square based ratio test and Wald test to identify significant parametric and nonparametric components. To improve accuracy of the proposed tests for small or moderate sample sizes, a wild bootstrap version is also proposed to calculate the critical values. Intensive simulation experiments are conducted to illustrate the proposed approaches.Comment: Published in at http://dx.doi.org/10.1214/07-AOS561 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modelling and Forecasting Noisy Realized Volatility

Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent (modified) realized volatility (RV) estimates of the integrated volatility can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility error”. Since such measurement errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators due to model misspecification; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of , which can be applied to linear and nonlinear, short and long memory models. An empirical example for S&P 500 data is used to demonstrate that neglecting RV errors can lead to serious bias in estimating the model of integrated volatility, and that the new method proposed here can eliminate the effects of the RV noise. The empirical results also show that the full correction for is necessary for an accurate description of goodness-of-fit.Realized volatility; diffusion; financial econometrics; measurement errors; forecasting; model evaluation; goodness-of-fit

"Modelling and Forecasting Noisy Realized Volatility"

Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent (modified) realized volatility (RV) estimates of the integrated volatility can contain residual microstructure noise and other measurement errors. Such noise is called "realized volatility error". As such measurement errors ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators due to model misspecification; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected R2 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R2 , which can be applied to linear and nonlinear, short and long memory models. An empirical example for &P 500 data is used to demonstrate that neglecting RV errors can lead to serious bias in estimating the model of integrated volatility, and that the new method proposed here can eliminate the effects of the RV noise. The empirical results also show that the full correction for R2 is necessary for an accurate description of goodness-of-fit.

Variable selection in measurement error models

Measurement error data or errors-in-variable data have been collected in many studies. Natural criterion functions are often unavailable for general functional measurement error models due to the lack of information on the distribution of the unobservable covariates. Typically, the parameter estimation is via solving estimating equations. In addition, the construction of such estimating equations routinely requires solving integral equations, hence the computation is often much more intensive compared with ordinary regression models. Because of these difficulties, traditional best subset variable selection procedures are not applicable, and in the measurement error model context, variable selection remains an unsolved issue. In this paper, we develop a framework for variable selection in measurement error models via penalized estimating equations. We first propose a class of selection procedures for general parametric measurement error models and for general semi-parametric measurement error models, and study the asymptotic properties of the proposed procedures. Then, under certain regularity conditions and with a properly chosen regularization parameter, we demonstrate that the proposed procedure performs as well as an oracle procedure. We assess the finite sample performance via Monte Carlo simulation studies and illustrate the proposed methodology through the empirical analysis of a familiar data set.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ205 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm