The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

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The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing. / Christensen, Kim; Thyrsgaard, Martin; Veliyev, Bezirgen.

In: Journal of Econometrics, Vol. 212, No. 2, 10.2019, p. 556-583.

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@article{dbeb28d78b154a53becd88884c33481e,
title = "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing",
abstract = "We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) – inferred from noisy high-frequency data – is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it exists. We exploit these results to construct some new goodness-of-fit tests for stochastic volatility models. In a Monte Carlo study, the REDF is found to be accurate over the entire support of volatility. This leads to goodness-of-fit tests that are both correctly sized and relatively powerful against common alternatives. In an empirical application, we recover the REDF from stock market high-frequency data. We inspect the goodness-of-fit of several two-parameter marginal distributions that are inherent in standard stochastic volatility models. The inverse Gaussian offers the best overall description of random equity variation, but the fit is less than perfect. This suggests an extra parameter (as available in, e.g., the generalized inverse Gaussian) is required to model stochastic variance.",
keywords = "Empirical processes, Goodness-of-fit, High-frequency data, Microstructure noise, Pre-averaging, Realized variance, Stochastic volatility",
author = "Kim Christensen and Martin Thyrsgaard and Bezirgen Veliyev",
year = "2019",
month = "10",
doi = "10.1016/j.jeconom.2019.06.002",
language = "English",
volume = "212",
pages = "556--583",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "2",

}

RIS

TY - JOUR

T1 - The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

AU - Christensen, Kim

AU - Thyrsgaard, Martin

AU - Veliyev, Bezirgen

PY - 2019/10

Y1 - 2019/10

N2 - We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) – inferred from noisy high-frequency data – is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it exists. We exploit these results to construct some new goodness-of-fit tests for stochastic volatility models. In a Monte Carlo study, the REDF is found to be accurate over the entire support of volatility. This leads to goodness-of-fit tests that are both correctly sized and relatively powerful against common alternatives. In an empirical application, we recover the REDF from stock market high-frequency data. We inspect the goodness-of-fit of several two-parameter marginal distributions that are inherent in standard stochastic volatility models. The inverse Gaussian offers the best overall description of random equity variation, but the fit is less than perfect. This suggests an extra parameter (as available in, e.g., the generalized inverse Gaussian) is required to model stochastic variance.

AB - We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) – inferred from noisy high-frequency data – is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it exists. We exploit these results to construct some new goodness-of-fit tests for stochastic volatility models. In a Monte Carlo study, the REDF is found to be accurate over the entire support of volatility. This leads to goodness-of-fit tests that are both correctly sized and relatively powerful against common alternatives. In an empirical application, we recover the REDF from stock market high-frequency data. We inspect the goodness-of-fit of several two-parameter marginal distributions that are inherent in standard stochastic volatility models. The inverse Gaussian offers the best overall description of random equity variation, but the fit is less than perfect. This suggests an extra parameter (as available in, e.g., the generalized inverse Gaussian) is required to model stochastic variance.

KW - Empirical processes

KW - Goodness-of-fit

KW - High-frequency data

KW - Microstructure noise

KW - Pre-averaging

KW - Realized variance

KW - Stochastic volatility

UR - http://www.scopus.com/inward/record.url?scp=85067879168&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2019.06.002

DO - 10.1016/j.jeconom.2019.06.002

M3 - Journal article

AN - SCOPUS:85067879168

VL - 212

SP - 556

EP - 583

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2

ER -