Long memory continuous time models

Comte, Fabienne; Renault, Éric

doi:10.1016/0304-4076(95)01735-6

Cited by 197 publications

(127 citation statements)

References 18 publications

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“…Existence of some other models corresponding to (3) has been established by Comte and Renault (1996), Anh, Heyde and Leonenko (2002), Anh and Inoue (2005), and Anh, Inoue and Kasahara (2005). As discussed in the these papers, models with solutions given by (3) and having a spectral density of the form (4) include a mean-reverting model with a fractional noise of the form…”

Section: Introductionmentioning

confidence: 90%

Econometric estimation in long-range dependent volatility models: Theory and practice

Casas¹,

Gao²

2008

Journal of Econometrics

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It is commonly accepted that some financial data may exhibit long-range dependence, while other financial data exhibit intermediate-range dependence or short-range dependence. These behaviours may be fitted to a continuous-time fractional stochastic model.The estimation procedure proposed in this paper is based on a continuous-time version of the Gauss-Whittle objective function to find the parameter estimates that minimize the discrepancy between the spectral density and the data periodogram. As a special case, the proposed estimation procedure is applied to a class of fractional stochastic volatility models to estimate the drift, standard deviation and memory parameters of the volatility process under consideration. As an aplication, the volatility of the Dow Jones, S&P 500, CAC 40, DAX 30, FTSE 100 and NIKKEI 225 is estimated.

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Section: Introductionmentioning

confidence: 90%

Econometric estimation in long-range dependent volatility models: Theory and practice

Casas¹,

Gao²

2008

Journal of Econometrics

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“…This assumption holds in the well-known case in which V t is also an Itô semimartingale with locally bounded characteristics. It also holds for long-memory specifications that are driven by fractional Brownian motion; see Comte and Renault (1996). Assumption A2 coincides, albeit with a different norm, to the one maintained by Renault et al (2014).…”

Section: The Underlying Processmentioning

confidence: 99%

Estimating the Volatility Occupation Time via Regularized Laplace Inversion

Jia

Todorov²,

Tauchen

2015

Econom. Theory

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We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in the second step, we conduct a regularized Laplace inversion. Monte Carlo evidence suggests that the proposed estimator has good small-sample performance and in particular it is far better at estimating lower volatility quantiles and the volatility median than a direct estimator formed from the empirical cumulative distribution function of local spot volatility estimates. An empirical application shows the use of the developed techniques for nonparametric analysis of variation of volatility.

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“…This local estimate was used in Jacod and Todorov (2014) to get an efficient estimator of the integrated volatility, and Kong et al (2015) For long-memory volatility models that are driven by fractional Brownian motion, we refer to Comte and Renault (1996) and Comte and Renault (1998). The major advantage of this Laplace-transform-based local estimator is that it can easily separate the effect of the Brownian force and the stable-like driving force.…”

Section: Methods Of Devolatizing the Incrementsmentioning

confidence: 99%

Lack of Fit Test for Infinite Variation Jumps at High Frequencies

Kong¹

2018

STAT SINICA

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This paper is concerned with testing for infinite variation jumps in addition to a continuous local martingale component driven by Brownian motion using high-frequency data. We developed a lack of fit type test based on the empirical distribution of the "devolatized" increments. Under the null hypothesis that the jump component is of finite variation, the empirical process associated with the "devolatized" increments converges to a Gaussian process in the Skorohod topology. Under the alternative hypothesis that the jumps are of infinite variation, the empirical process explodes instead. Theoretical results and simulation show good performance on the size and power of the test. A real financial data set is analyzed.

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Long memory continuous time models

Cited by 197 publications

References 18 publications

Econometric estimation in long-range dependent volatility models: Theory and practice

Econometric estimation in long-range dependent volatility models: Theory and practice

Estimating the Volatility Occupation Time via Regularized Laplace Inversion

Lack of Fit Test for Infinite Variation Jumps at High Frequencies

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