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Linear prediction of long-range dependent time series

Fanny Godet (2009)

ESAIM: Probability and Statistics

We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e.  the projection of the forecast value on the last k observations. It is shown that these two predictors...

Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model

Jean-Michel Loubes, Davy Paindaveine (2011)

ESAIM: Probability and Statistics

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...

Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model*

Jean-Michel Loubes, Davy Paindaveine (2012)

ESAIM: Probability and Statistics

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...

Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method

Pierre Raphaël Bertrand, Mehdi Fhima, Arnaud Guillin (2013)

ESAIM: Probability and Statistics

We investigate here the central limit theorem of the increment ratio statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer–Major theorems and an original freezing of time strategy. A simulation study shows the goodness of fit of this estimator.

Local superefficiency of data-driven projection density estimators in continuous time.

Denis Bosq, Delphine Blanke (2004)

SORT

We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F0 of densities that is dense in the family of all possible densities, and a «reasonable» rate elsewhere. The class F0 may be chosen previously by the analyst. Results apply to Rd-valued processes and to N-valued processes. In the particular case where square-integrable local time does exist, it is shown that our estimator is strictly better than the local...

Locally weighted neural networks for an analysis of the biosensor response

Romas Baronas, Feliksas Ivanauskas, Romualdas Maslovskis, Marijus Radavičius, Pranas Vaitkus (2007)

Kybernetika

This paper presents a semi-global mathematical model for an analysis of a signal of amperometric biosensors. Artificial neural networks were applied to an analysis of the biosensor response to multi-component mixtures. A large amount of the learning and test data was synthesized using computer simulation of the biosensor response. The biosensor signal was analyzed with respect to the concentration of each component of the mixture. The paradigm of locally weighted linear regression was used for retraining...

Log-periodogram regression in asymmetric long memory

Josu Arteche (2000)

Kybernetika

The long memory property of a time series has long been studied and several estimates of the memory or persistence parameter at zero frequency, where the spectral density function is symmetric, are now available. Perhaps the most popular is the log periodogram regression introduced by Geweke and Porter–Hudak [gewe]. In this paper we analyse the asymptotic properties of this estimate in the seasonal or cyclical long memory case allowing for asymmetric spectral poles or zeros. Consistency and asymptotic...

Long memory properties and covariance structure of the EGARCH model

Donatas Surgailis, Marie-Claude Viano (2002)

ESAIM: Probability and Statistics

The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular, a...

Long memory properties and covariance structure of the EGARCH model

Donatas Surgailis, Marie-Claude Viano (2010)

ESAIM: Probability and Statistics

The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular,...

Longitudinal K-sets analysis using lagged variables.

Catrien C. J. H. Bijleveld, Eeke Van der Burg (1993)

Qüestiió

We present an application of nonlinear Generalised Canonical Analysis (GCA) for analysing longitudinal data. The application uses lagged versions of variables to accomodate the time-dependence in the measurements. The usefulness of the proposed method is illustrated in an example from developmental psychology, in which we explore the relationship between mother and child dyadic interaction during the first six months after birth, demonstrating how child behaviour can elicit mother behaviour. We...

M -estimation in nonlinear regression for longitudinal data

Martina Orsáková (2007)

Kybernetika

The longitudinal regression model Z i j = m ( θ 0 , 𝕏 i ( T i j ) ) + ε i j , where Z i j is the j th measurement of the i th subject at random time T i j , m is the regression function, 𝕏 i ( T i j ) is a predictable covariate process observed at time T i j and ε i j is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth M -estimator of unknown parameter θ 0 .

Currently displaying 361 – 380 of 838