Estimation of the Continuous and Discontinuous Leverage Effects

Aı̈t-Sahalia, Yacine; Fan, Jianqing; Laeven, Roger J. A.; Wang, Christina Dan; Yang, Xiye

doi:10.1080/01621459.2016.1240082

Cited by 54 publications

(42 citation statements)

References 33 publications

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“…Both Fourier leverage estimators reach a smaller asymptotic variance compared to the leverage estimator in [28], while only the Fourier leverage estimator with convolution product obtained using the Fejer kernel has a smaller asymptotic variance than the leverage estimator in [1]. The leverage estimator in [2] reaches an even smaller asymptotic error variance.…”

Section: Introductionmentioning

confidence: 92%

Rate-efficient asymptotic normality for the Fourier estimator of the leverage process

Mancino

Toscano

2022

Statistics and Its Interface

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We prove a Central Limit Theorem for two estimators of the leverage process based on the Fourier method of Malliavin and Mancino [26], showing that they reach the optimal rate 1/4 and a smaller variance compared to different estimators based on a pre-estimation of the instantaneous volatility. The obtained limiting distributions of the estimators are supported by simulation results. Further, we exploit the availability of efficient leverage estimates to show, using S&P500 prices, that adding an extra term which accounts for the leverage effect to the Heterogeneous Auto-Regressive volatility model by Corsi [13] increases the explanatory power of the latter.

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Section: Introductionmentioning

confidence: 92%

Rate-efficient asymptotic normality for the Fourier estimator of the leverage process

Mancino

Toscano

2022

Statistics and Its Interface

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“…Similar tuning involving a variance-variance tradeoff occurs in connection with covariance estimation (Zhang (2011), Bibinger and Mykland (2016), Barndorff-Nielsen, Hansen, Lunde, and Shephard (2011)), spot volatility estimation (see Mykland and Zhang (2008)), estimation of the leverage effect (Wang and Mykland (2014), Aït-Sahalia, Fan, Laeven, Wang, and Yang (2016), Kalnina and Xiu (2016)), and estimation of the volatility of volatility (Vetter (2015), Mykland, Shephard, and Sheppard (2012)). These and other inference situations requiring tuning are described in Section 7.…”

Section: Application: Selection Of Tuning Parametersmentioning

confidence: 78%

“…The estimation of leverage effect was discussed in Mykland and Zhang (2009, Section 4.3, pp. 1426-1428 and Wang and Mykland (2014) for the case where X t is continuous, and in Aït-Sahalia et al (2016) and Kalnina and Xiu (2016) for the case where the process X t can also have jumps. 41 Wang and Mykland (2014) and Aït-Sahalia et al (2016) studied both the case where there is microstructure noise, and the case where there is none.…”

Section: (59)mentioning

confidence: 99%

Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

Mykland¹,

Zhang²

2017

Econometrica

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The availability of high frequency financial data has generated a series of estimators based on intra‐day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θt dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two‐scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.

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“…For example, asset prices are frequently modeled as continuous-time processes, such as (Itô-)semimartingales (see, e.g., Aït-Sahalia (2002a, 2002b; Chernov et al (2003); and Andersen et al (2007b)). At the same time, investors and researchers are also interested in nonparametrically estimable quantities such as spot/integrated volatility (see, e.g., Barndorff-Nielsen (2002); Barndorff-Neilsen and Shephard (2003); Todorov and Tauchen (2011); and Patton and Sheppard (2015)), jump variation (see, e.g., Barndorff-Nielsen and Shephard (2004); Andersen et al (2007a); and Corsi et al (2009)), leverage effect (see, e.g., Kalnina and Xiu (2017) and Aït-Sahalia et al (2017)), and jump activity (see e.g., Aït-Sahalia and Jacod (2011) and Todorov (2015)).…”

Section: Introductionmentioning

confidence: 99%

Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

Cheng

Swanson

2019

Econometrics

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Numerous tests designed to detect realized jumps over a fixed time span have been proposed and extensively studied in the financial econometrics literature. These tests differ from “long time span tests” that detect jumps by examining the magnitude of the jump intensity parameter in the data generating process, and which are consistent. In this paper, long span jump tests are compared and contrasted with a variety of fixed span jump tests in a series of Monte Carlo experiments. It is found that both the long time span tests of Corradi et al. (2018) and the fixed span tests of Aït-Sahalia and Jacod (2009) exhibit reasonably good finite sample properties, for time spans both short and long. Various other tests suffer from finite sample distortions, both under sequential testing and under long time spans. The latter finding is new, and confirms the “pitfall” discussed in Huang and Tauchen (2005), of using asymptotic approximations associated with finite time span tests in order to study long time spans of data. An empirical analysis is carried out to investigate the implications of these findings, and “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected.

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Estimation of the Continuous and Discontinuous Leverage Effects

Cited by 54 publications

References 33 publications

Rate-efficient asymptotic normality for the Fourier estimator of the leverage process

Rate-efficient asymptotic normality for the Fourier estimator of the leverage process

Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

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