Dynamic models of long-memory processes driven by Lévy noise

Anh, Vo; Heyde, C. C.; Leonenko, Nikolai

doi:10.1239/jap/1037816015

Cited by 63 publications

(87 citation statements)

References 57 publications

(86 reference statements)

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“…In an analogous way to the above, we can construct a procedure for the estimation of the stochastic volatility model proposed in Anh, Heyde and Leonenko (2002), namely, the model for the evolution of an asset price,…”

Section: Remarkmentioning

confidence: 99%

Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence

Anh¹,

Leonenko²,

Sakhno³

2004

Journal of Applied Probability

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Abstract. This paper provides a quasilikelihood/minimum contrast-type method for parameter estimation of random &elds in the frequency domain based on higher-order information. The estimation technique uses the spectral density of the general k-th order and allows for possible long-range dependence in the random &elds. To avoid bias due to edge effects, data tapering is incorporated in the method. The suggested minimum contrast functional is linear with respect to the periodogram of k-th order, hence kernel estimation for the spectral densities is not needed. Furthermore, discretisation is not required in the estimation of continuously observed random &elds. The consistency and asymptotic normality of the resulting estimators are established. Illustrative application of the method to some problems in mathematical &nance and signal detection will be indicated.

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Section: Remarkmentioning

confidence: 99%

Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence

Anh¹,

Leonenko²,

Sakhno³

2004

Journal of Applied Probability

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“…well defined under some conditions (see, for example Anh et al (2002)) which are satisfied in all cases of interest here. For S(t) defined as in (3) it holds…”

Section: General Forms Of the Chfmentioning

confidence: 95%

Characteristic function estimation of Ornstein–Uhlenbeck-based stochastic volatility models

Taufer

Leonenko

Bee

2011

Computational Statistics & Data Analysis

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Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression.In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models. After deriving explicit expressions of the characteristic functions for various cases of interest we analyze the asymptotic properties of the estimators and evaluate their performance by means of a simulation experiment. Finally, a realdata application shows that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.

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“…Anh et al [2] consider f (t) in (3) as Lévy noise, that is, the derivative in the distributional sense of Lévy motion L (t). The integral then exists as an L 2 -stochastic integral if EL 2 (1) < 1 and n > 1=2.…”

Section: Preliminariesmentioning

confidence: 99%

“…Okabe [20] and Inoue [15] considered a class of equations which contain the Stokes-Boussinesq-Langevin equation from hydrodynamics; some of these equations may be formulated in terms of fractional derivatives (Mainardi [18]). Anh et al [2] proposed a class of fractional di¬erential equations driven by Lévy noise and considered possible applications to nance and macroeconomics. Anh and McVinish [3] studied the sample path properties of this latter class of models and proposed a simulation scheme.…”

Section: Introductionmentioning

confidence: 99%