On a time deformation reducing nonstationary stochastic processes to local stationarity

Genton, Marc G.; Perrin, Olivier

doi:10.1239/jap/1077134681

Cited by 20 publications

(8 citation statements)

References 14 publications

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“…In a similar spirit, during the last decades a number of new time-varying dependence models have been proposed. One of these methodologies, the socalled locally stationary processes developed by Dahlhaus (1996Dahlhaus ( , 1997, has been widely discussed in the recent time series literature, see, for example, Dahlhaus (2000), von Sachs and MacGibbon (2000), Jensen and Whitcher (2000), Guo et al (2003), Genton and Perrin (2004), Orbe, Ferreira and Rodriguez-Poo (2005), Polonik (2006, 2009), Chandler and Polonik (2006), Fryzlewicz, Sapatinas and Subba Rao (2006) and Beran This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in The Annals of Statistics, 2010, Vol. 38, No.…”

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confidence: 99%

An efficient estimator for locally stationary Gaussian long-memory processes

Palma¹,

Olea²

2010

Ann. Statist.

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This paper addresses the estimation of locally stationary longrange dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying parametric formulation of these models is introduced and a Whittle likelihood technique is proposed for estimating the parameters involved. Large sample properties of these Whittle estimates such as consistency, normality and efficiency are established in this work. Furthermore, the finite sample behavior of the estimators is investigated through Monte Carlo experiments. As a result from these simulations, we show that the estimates behave well even for relatively small sample sizes.

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confidence: 99%

An efficient estimator for locally stationary Gaussian long-memory processes

Palma¹,

Olea²

2010

Ann. Statist.

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“…From the structure of the covariance function and recalling that X is strictly stationary, we immediately get that the process Y belongs to the class of so-called locally stationary reducible random fields, cf. Genton et al (2007, p. 403) and also Genton & Perrin (2004).…”

Section: Definitions and Generalised Lamperti Transformmentioning

confidence: 94%

Stationary and multi-self-similar random fields with stochastic volatility

Veraart

2015

Stochastics

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This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields and their probabilistic properties are discussed. Also, two methods for parameterising the weight functions in the moving average representation are presented: One method is based on Fourier techniques and aims at reproducing a given correlation structure, the other method is based on ideas from stochastic partial differential equations. Moreover, using a generalised Lamperti transform we construct volatility modulated multi-self-similar random fields which have type G distribution.

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“…Maximum likelihood and Bayesian variants of this approach have been developed by Mardia and Goodall [9], Smith [10], Damian et al [11], Schmidt and O'Hagan [12]. Perrin and Meiring [13], Perrin and Senoussi [14], Perrin and Meiring [15], Genton and Perrin [16], Porcu et al [17] established some theoretical properties about uniqueness and richness of this class of non-stationary models. Some adaptations have been proposed recently by Castro Morales et al [18], Bornn et al [19], Schmidt et al [20], Vera et al [21,22].…”

Section: Introductionmentioning

confidence: 99%

Estimation of space deformation model for non-stationary random functions

2015

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Stationary Random Functions have been successfully applied in geostatistical applications for decades. In some instances, the assumption of a homogeneous spatial dependence structure across the entire domain of interest is unrealistic. A practical approach for modelling and estimating non-stationary spatial dependence structure is considered. This consists in transforming a non-stationary Random Function into a stationary and isotropic one via a bijective continuous deformation of the index space. So far, this approach has been successfully applied in the context of data from several independent realizations of a Random Function. In this work, we propose an approach for non-stationary geostatistical modelling using space deformation in the context of a single realization with possibly irregularly spaced data. The estimation method is based on a non-stationary variogram kernel estimator which serves as a dissimilarity measure between two locations in the geographical space. The proposed procedure combines aspects of kernel smoothing, weighted non-metric multi-dimensional scaling and thin-plate spline radial basis functions. On a simulated data, the method is able to retrieve the true deformation. Performances are assessed on both synthetic and real datasets. It is shown in particular that our approach outperforms the stationary approach. Beyond the prediction, the proposed method can also serve as a tool for exploratory analysis of the non-stationarity.

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On a time deformation reducing nonstationary stochastic processes to local stationarity

Cited by 20 publications

References 14 publications

An efficient estimator for locally stationary Gaussian long-memory processes

An efficient estimator for locally stationary Gaussian long-memory processes

Stationary and multi-self-similar random fields with stochastic volatility

Estimation of space deformation model for non-stationary random functions

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