NONPARAMETRIC FILTERING OF THE REALIZED SPOT VOLATILITY: A KERNEL-BASED APPROACH

2009 ◽  
Vol 26 (1) ◽  
pp. 60-93 ◽  
Author(s):  
Dennis Kristensen
Keyword(s):  
Realized Volatility ◽  
Data Driven ◽  
Selection Methods ◽  
Finite Sample ◽  
Weighted Version ◽  
Integrated Volatility ◽  
Finite Sample Properties ◽  
Boundary Issues ◽  
Consistency And Asymptotic Normality ◽  
Spot Volatility

A kernel weighted version of the standard realized integrated volatility estimator is proposed. By different choices of the kernel and bandwidth, the measure allows us to focus on specific characteristics of the volatility process. In particular, as the bandwidth vanishes, an estimator of the realized spot volatility is obtained. We denote this the filtered spot volatility. We show consistency and asymptotic normality of the kernel smoothed realized volatility and the filtered spot volatility. We consider boundary issues and propose two methods to handle these. The choice of bandwidth is discussed and data-driven selection methods are proposed. A simulation study examines the finite sample properties of the estimators.

scholarly journals Additive Nonparametric Instrumental Regressions: A Guide to Implementation

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Samuele Centorrino ◽  
Frederique Feve ◽  
Jean-Pierre Florens
Keyword(s):  
Instrumental Variables ◽  
Regularization Method ◽  
Regression Models ◽  
Regression Function ◽  
Data Driven ◽  
Finite Sample ◽  
Partially Linear ◽  
Regularization Parameters ◽  
Finite Sample Properties ◽  
Additive Nonparametric Regression

AbstractWe present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

scholarly journals BOOTSTRAPPING PRE-AVERAGED REALIZED VOLATILITY UNDER MARKET MICROSTRUCTURE NOISE

2016 ◽  
Vol 33 (4) ◽  
pp. 791-838 ◽  
Author(s):  
Ulrich Hounyo ◽  
Sílvia Gonçalves ◽  
Nour Meddahi
Keyword(s):  
Asymptotic Theory ◽  
Bootstrap Method ◽  
Empirical Work ◽  
Time Varying ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Integrated Volatility ◽  
First Order ◽  
Finite Sample Properties ◽  
Asymptotic Validity

The main contribution of this paper is to propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach, where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that the leading martingale part in the pre-averaged returns arekn-dependent withkngrowing slowly with the sample sizen. This motivates the application of a blockwise bootstrap method. We show that the “blocks of blocks” bootstrap method is not valid when volatility is time-varying. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. We provide a proof of the first order asymptotic validity of this method for percentile and percentile-tintervals. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. We use empirical work to illustrate its use in practice.

scholarly journals A LOCAL GAUSSIAN BOOTSTRAP METHOD FOR REALIZED VOLATILITY AND REALIZED BETA

2018 ◽  
Vol 35 (2) ◽  
pp. 360-416 ◽  
Author(s):  
Ulrich Hounyo
Keyword(s):  
Bootstrap Method ◽  
Original Data ◽  
Realized Volatility ◽  
Second Order ◽  
Finite Sample ◽  
Integrated Volatility ◽  
New Class ◽  
Class Of Estimators ◽  
Log Price ◽  
Multivariate Volatility

This article introduces a local Gaussian bootstrap method useful for the estimation of the asymptotic distribution of high-frequency data-based statistics such as functions of realized multivariate volatility measures as well as their asymptotic variances. The new approach consists of dividing the original data into nonoverlapping blocks ofMconsecutive returns sampled at frequencyh(whereh−1denotes the sample size) and then generating the bootstrap observations at each frequency within a block by drawing them randomly from a mean zero Gaussian distribution with a variance given by the realized variance computed over the corresponding block.Our main contributions are as follows. First, we show that the local Gaussian bootstrap is first-order consistent when used to estimate the distributions of realized volatility and realized betas under assumptions on the log-price process which follows a continuous Brownian semimartingale process. Second, we show that the local Gaussian bootstrap matches accurately the first four cumulants of realized volatility up too(h), implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009,Econometrica77(1), 283–306), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able to provide second-order refinements for the realized beta, which is also an improvement of the existing bootstrap results in Dovonon, Gonçalves, and Meddahi (2013,Journal of Econometrics172, 49–65) (where the pairs bootstrap was shown not to be second-order correct under general stochastic volatility). In addition, we highlight the connection between the local Gaussian bootstrap and the local Gaussianity approximation of continuous semimartingales established by Mykland and Zhang (2009,Econometrica77, 1403–1455) and show the suitability of this bootstrap method to deal with the new class of estimators introduced in that article. Lastly, we provide Monte Carlo simulations and use empirical data to compare the finite sample accuracy of our new bootstrap confidence intervals for integrated volatility with the existing results.

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

Kernel Based Estimation for a Non-Homogeneous Poisson Processes

2013 ◽  
Vol 805-806 ◽  
pp. 1948-1951
Author(s):  
Tian Jin
Keyword(s):  
Air Pollution ◽  
Nonparametric Estimation ◽  
Simulation Study ◽  
Poisson Model ◽  
Poisson Processes ◽  
Finite Sample ◽  
Process Data ◽  
Homogeneous Poisson Process ◽  
Finite Sample Properties ◽  
Non Homogeneous Poisson Process

The non-homogeneous Poisson model has been applied to various situations, including air pollution data. In this paper, we propose a kernel based nonparametric estimation for fitting the non-homogeneous Poisson process data. We show that our proposed estimator is-consistent and asymptotically normally distributed. We also study the finite-sample properties with a simulation study.

Cause-specific quantile residual life regression

2015 ◽  
Vol 26 (4) ◽  
pp. 1912-1924 ◽  
Author(s):  
Jeong Youn Lim ◽  
Jong-Hyeon Jeong
Keyword(s):  
Residual Life ◽  
Fixed Time ◽  
Estimating Equation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Test Statistic ◽  
Life Distribution ◽  
Finite Sample Properties ◽  
Quantile Residual Life ◽  
Log Linear

We propose a cause-specific quantile residual life regression where the cause-specific quantile residual life, defined as the inverse of the cumulative incidence function of the residual life distribution of a specific type of events of interest conditional on a fixed time point, is log-linear in observable covariates. The proposed test statistic for the effects of prognostic factors does not involve estimation of the improper probability density function of the cause-specific residual life distribution under competing risks. The asymptotic distribution of the test statistic is derived. Simulation studies are performed to assess the finite sample properties of the proposed estimating equation and the test statistic. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.

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