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.

Estimation of Dynamic Term Structure Models

2012 ◽  
Vol 02 (02) ◽  
pp. 1250008 ◽  
Author(s):  
Gregory R. Duffee ◽  
Richard H. Stanton
Keyword(s):  
Maximum Likelihood ◽  
Term Structure ◽  
Empirical Work ◽  
Interest Rate Risk ◽  
Small Sample ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Finite Sample ◽  
Term Structure Models ◽  
Finite Sample Properties

We study the finite-sample properties of some of the standard techniques used to estimate modern term structure models. For sample sizes and models similar to those used in most empirical work, we reach three surprising conclusions. First, while maximum likelihood works well for simple models, it produces strongly biased parameter estimates when the model includes a flexible specification of the dynamics of interest rate risk. Second, despite having the same asymptotic efficiency as maximum likelihood, the small-sample performance of Efficient Method of Moments (a commonly used method for estimating complicated models) is unacceptable even in the simplest term structure settings. Third, the linearized Kalman filter is a tractable and reasonably accurate estimation technique, which we recommend in settings where maximum likelihood is impractical.

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.

FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA

2013 ◽  
Vol 29 (4) ◽  
pp. 838-856 ◽  
Author(s):  
Minjing Tao ◽  
Yazhen Wang ◽  
Xiaohong Chen
Keyword(s):  
Sample Size ◽  
High Frequency ◽  
Convergence Rates ◽  
Fast Convergence ◽  
High Frequency Data ◽  
Frequency Data ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Integrated Volatility ◽  
The Matrix

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the number of assets and the sample size go to infinity, we show that our new estimator is consistent and achieves a fast convergence rate, where the rate is optimal with respect to the sample size. A simulation study is conducted to check the finite sample performance of the proposed estimator.

scholarly journals Asymptotic Theory for Regressions with Smoothly Changing Parameters

2013 ◽  
Vol 5 (2) ◽  
pp. 133-162 ◽  
Author(s):  
Eric Hillebrand ◽  
Marcelo C. Medeiros ◽  
Junyue Xu
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Smooth Transition ◽  
Finite Sample ◽  
Likelihood Estimator ◽  
Output Data ◽  
Asymptotically Normal ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood

Abstract: We derive asymptotic properties of the quasi-maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual -rate and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data.

The Case-time-control Method for Nonbinary Exposures

2017 ◽  
Vol 47 (1) ◽  
pp. 182-211 ◽  
Author(s):  
Arvid Sjölander
Keyword(s):  
Control Method ◽  
Asymptotic Properties ◽  
Study Participant ◽  
Time Varying ◽  
Finite Sample ◽  
Time Points ◽  
Time Control ◽  
Finite Sample Properties ◽  
Study Participants ◽  
Time Varying Covariates

A popular way to reduce confounding in observational studies is to use each study participant as his or her own control. This is possible when both the exposure and the outcome are time varying and have been measured at several time points for each individual. The case-time-control method is a special case, which, under certain assumptions, allows the analyst to control for confounding by time-varying covariates, while controlling for all time-stationary characteristics of the study participants. There are two formulations of the case-time-control method. One formulation requires that the exposure be binary, and the other requires that there be no more than two time points per individual. In this article the author proposes a generalization of the case-time-control method for nonbinary exposures and an arbitrary number of time points. The author derives the asymptotic properties of the resulting estimator and assesses its finite sample properties in a simulation study.

scholarly journals Bayesian Analysis of Coefficient Instability in Dynamic Regressions

Econometrics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 29
Author(s):  
Emanuela Ciapanna ◽  
Marco Taboga
Keyword(s):  
Structural Breaks ◽  
Bayesian Regression ◽  
Regression Coefficients ◽  
Time Varying ◽  
Finite Sample ◽  
Parameter Instability ◽  
Varying Coefficients ◽  
Monte Carlo Experiments ◽  
Finite Sample Properties ◽  
Time Varying Coefficients

This paper deals with instability in regression coefficients. We propose a Bayesian regression model with time-varying coefficients (TVC) that allows to jointly estimate the degree of instability and the time-path of the coefficients. Thanks to the computational tractability of the model and to the fact that it is fully automatic, we are able to run Monte Carlo experiments and analyze its finite-sample properties. We find that the estimation precision and the forecasting accuracy of the TVC model compare favorably to those of other methods commonly employed to deal with parameter instability. A distinguishing feature of the TVC model is its robustness to mis-specification: Its performance is also satisfactory when regression coefficients are stable or when they experience discrete structural breaks. As a demonstrative application, we used our TVC model to estimate the exposures of S&P 500 stocks to market-wide risk factors: We found that a vast majority of stocks had time-varying exposures and the TVC model helped to better forecast these exposures.

scholarly journals Distributional consistency of the lasso by perturbation bootstrap

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 957-964
Author(s):  
Debraj Das ◽  
S N Lahiri
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Bootstrap Method ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Lasso Estimator

Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the proposed bootstrap method in a moderately large simulation study.

Fixed-Effects Vector Decomposition: Properties, Reliability, and Instruments

2011 ◽  
Vol 19 (2) ◽  
pp. 147-164 ◽  
Author(s):  
Thomas Plümper ◽  
Vera E. Troeger
Keyword(s):  
Fixed Effects ◽  
Shrinkage Estimator ◽  
Time Varying ◽  
Finite Sample ◽  
Simultaneous Presence ◽  
Political Analysis ◽  
Vector Decomposition ◽  
Finite Sample Properties ◽  
Time Invariant ◽  
Decomposition Properties

This article reinforces our 2007 Political Analysis publication in demonstrating that the fixed-effects vector decomposition (FEVD) procedure outperforms any other estimator in estimating models that suffer from the simultaneous presence of time-varying variables correlated with unobserved unit effects and time-invariant variables. We compare the finite-sample properties of FEVD not only to the Hausman-Taylor estimator but also to the pretest estimator and the shrinkage estimator suggested by Breusch, Ward, Nguyen and Kompas (BWNK), and Greene in this symposium. Moreover, we correct the discussion of Greene and BWNK of FEVD's asymptotic and finite-sample properties.

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.

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