A wavelet Whittle estimator of generalized long-memory stochastic volatility

Gonzaga, Alex; Hauser, Michael A.

doi:10.1007/s10260-010-0153-9

Cited by 8 publications

(7 citation statements)

References 31 publications

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“…It is shown that the wavelet coefficients are decorrelated when the wavelet basis is orthonormal and d 0 D 0, but it is not valid in general settings. Many propositions of estimators of long memory can be found in Wornell and Oppenheim (1992), Abry and Veitch (1998), Jensen (1999) and Gonzaga and Hauser (2011), among others. These works assume that the wavelet coefficients are decorrelated.…”

Section: Spectral Approximation Of Wavelet Coefficientsmentioning

confidence: 99%

Multivariate Wavelet Whittle Estimation in Long‐range Dependence

Achard

Gannaz

2015

Journal Time Series Analysis

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Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual estimations of correlation can be highly biased due to phase-shifts caused by the differences in the properties of autocorrelation in the processes. To address this issue, we introduce a semiparametric estimation of multivariate long-range dependent processes. The parameters of interest in the model are the vector of the long-range dependence parameters and the long-run covariance matrix, also called functional connectivity in neuroscience. This matrix characterizes coupling between time series. The proposed multivariate wavelet-based Whittle estimation is shown to be consistent for the estimation of both the long-range dependence and the covariance matrix and to encompass both stationary and nonstationary processes. A simulation study and a real data example are presented to illustrate the finite sample behaviour.

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Section: Spectral Approximation Of Wavelet Coefficientsmentioning

confidence: 99%

Multivariate Wavelet Whittle Estimation in Long‐range Dependence

Achard

Gannaz

2015

Journal Time Series Analysis

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“…The generalized long-memory stochastic volatility (GLMSV) model [2] provides a general framework in modeling volatility dynamics incorporating persistence or long-memory and multiple periodicities or seasonalities. We consider the stochastic volatility model given by is a k-GARMA process, which is independent of   t e .…”

Section: Generalized Long-memory Stochastic Volatilitymentioning

confidence: 99%

“…Time-varying volatility is a well-documented feature of signals with applications to high-frequency financial time series (see e.g. [1], [2] and [3]). It has also been observed in the dynamics of some biosignals such as the noise of brain electrical responses [4].…”

Section: Introductionmentioning

confidence: 99%

“…However, it does not account for periodic or seasonal components, which are often seen as prominent peaks in the periodogram of the signal. In this case, [2] considered an extension of the LMSV model called the generalized long-memory stochastic volatility (GLMSV) by representing the log-volatility by a k-factor Gegenbauer autoregressive moving average (k-GARMA) process, which is known to account for k persistent periodicities in the volatility series. It is a relatively general model of stochastic volatility that accounts for persistence (or long-memory) and seasonality (or periodicity) at several frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Generalized Long-Memory Stochastic Volatility for High-Frequency Data

Gonzaga¹

2017

International Journal of Applied Engineering Research

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We consider the generalized long-memory stochastic volatility (GLMSV) model, a relatively general model of stochastic volatility that accounts for persistent (or longmemory) and seasonal (or cyclic) behavior at several frequencies. We employ the decorrelating properties of discrete wavelet packet transform (DWPT) to provide a wavelet-based approximate maximum likelihood estimator that allows for analysis of high-frequency data by simplifying the variance-covariance matrix into a diagonalized matrix, whose diagonal elements have the least distinct variances to compute using a computationally efficient quadrature. We apply the proposed method to the estimation of highfrequency simulated data.

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“…Whitcher (2004) applies WWE based on a discrete wavelet packet transform (DWPT) to a seasonal persistent process and again finds good performance of this estima-tion strategy. Heni & Mohamed (2011) apply this strategy on a FIGARCH-GARMA model, further application can be seen in Gonzaga & Hauser (2011).…”

Section: Introductionmentioning

confidence: 99%

Estimation of long memory in volatility using wavelets

Kraicová

Baruník

2017

Studies in Nonlinear Dynamics &Amp; Econometrics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This work studies wavelet-based Whittle estimator of the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroscedasticity (FIEGARCH) model, often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behaviour of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation. Terms of use: Documents in AbstractThis work studies wavelet-based Whittle estimator of the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroscedasticity (FIEGARCH) model often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behavior of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation.

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A wavelet Whittle estimator of generalized long-memory stochastic volatility

Abstract: Long-memory, k-GARMA, Stochastic volatility, Whittle estimator, Wavelets,

Cited by 8 publications

References 31 publications

Multivariate Wavelet Whittle Estimation in Long‐range Dependence

Multivariate Wavelet Whittle Estimation in Long‐range Dependence

Estimation of Generalized Long-Memory Stochastic Volatility for High-Frequency Data

Estimation of long memory in volatility using wavelets

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