Abstract
In order to estimate the conditional variance of some specific day, the sum of squared intraday returns, as known as "realized volatility" (RV) or "realized variance," is often used. Although this estimator does not converge to the true volatility when the observed price involves market microstructure noise, some subsample-based estimator is known to resolve this problem. In this paper, we will study the asymptotics of this estimator, assuming that market microstructure noise follows a non-Gaussian autoregressive conditional heteroskedastic model of order ∞ (ARCH(∞)). There we elucidate the asymptotics of RV and subsample estimator, which are influenced by the non-Gaussianity and dependent structure of the noise. Some numerical studies are given, and they illuminate interesting features of the asymptotics.
| Original language | English |
|---|---|
| Article number | nbs005 |
| Pages (from-to) | 617-636 |
| Number of pages | 20 |
| Journal | Journal of Financial Econometrics |
| Volume | 10 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2012 Sep |
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Keywords
- ARCH (∞) model
- Fourth-order cumulant spectra
- Market microstructure
- Realized volatility
- Statistical asymptotic theory
- Subsampling
ASJC Scopus subject areas
- Economics and Econometrics
- Finance
Cite this
Asymptotics of realized volatility with non-Gaussian ARCH(∞) microstructure noise. / Taniai, Hiroyuki; Usami, Takashi; Suto, Nobuyuki; Taniguchi, Masanobu.
In: Journal of Financial Econometrics, Vol. 10, No. 4, nbs005, 09.2012, p. 617-636.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotics of realized volatility with non-Gaussian ARCH(∞) microstructure noise
AU - Taniai, Hiroyuki
AU - Usami, Takashi
AU - Suto, Nobuyuki
AU - Taniguchi, Masanobu
PY - 2012/9
Y1 - 2012/9
N2 - In order to estimate the conditional variance of some specific day, the sum of squared intraday returns, as known as "realized volatility" (RV) or "realized variance," is often used. Although this estimator does not converge to the true volatility when the observed price involves market microstructure noise, some subsample-based estimator is known to resolve this problem. In this paper, we will study the asymptotics of this estimator, assuming that market microstructure noise follows a non-Gaussian autoregressive conditional heteroskedastic model of order ∞ (ARCH(∞)). There we elucidate the asymptotics of RV and subsample estimator, which are influenced by the non-Gaussianity and dependent structure of the noise. Some numerical studies are given, and they illuminate interesting features of the asymptotics.
AB - In order to estimate the conditional variance of some specific day, the sum of squared intraday returns, as known as "realized volatility" (RV) or "realized variance," is often used. Although this estimator does not converge to the true volatility when the observed price involves market microstructure noise, some subsample-based estimator is known to resolve this problem. In this paper, we will study the asymptotics of this estimator, assuming that market microstructure noise follows a non-Gaussian autoregressive conditional heteroskedastic model of order ∞ (ARCH(∞)). There we elucidate the asymptotics of RV and subsample estimator, which are influenced by the non-Gaussianity and dependent structure of the noise. Some numerical studies are given, and they illuminate interesting features of the asymptotics.
KW - ARCH (∞) model
KW - Fourth-order cumulant spectra
KW - Market microstructure
KW - Realized volatility
KW - Statistical asymptotic theory
KW - Subsampling
UR - http://www.scopus.com/inward/record.url?scp=84866370372&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84866370372&partnerID=8YFLogxK
U2 - 10.1093/jjfinec/nbs005
DO - 10.1093/jjfinec/nbs005
M3 - Article
VL - 10
SP - 617
EP - 636
JO - Journal of Financial Econometrics
JF - Journal of Financial Econometrics
SN - 1479-8409
IS - 4
M1 - nbs005
ER -