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Model selection for (auto-)regression with dependent data

Yannick Baraud, F. Comte, G. Viennet (2001)

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space among...

Model selection for (auto-)regression with dependent data

Yannick Baraud, F. Comte, G. Viennet (2010)

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-Gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space among...

Modelado de series temporales con métodos en bloque y recursivos. Desarrollo de estimadores y predictores adaptativos.

David de la Fuente García, Daniel F. García Martínez (1988)

Qüestiió

En este artículo se presenta un análisis comparativo entre los algoritmos más interesantes para la estimación de parámetros de series temporales, tanto en bloque como recursivos. Se propone que los modelos autorregresivos largos constituyen una parametrización general para modelizar series inestables, cuyos parámetros pueden estimarse adecuadamente con algoritmos recursivos, tales como los filtros celosía.

Modelización de datos longitudinales con estructuras de covarianza no estacionarias: modelos de coeficientes aleatorios frente a modelos alternativos.

Vicente Núñez-Antón, Dale L. Zimmerman (2001)

Qüestiió

Un tema que ha suscitado el interés de los investigadores en datos longitudinales durante las dos últimas décadas, ha sido el desarrollo y uso de modelos paramétricos explícitos para la estructura de covarianza de los datos. Sin embargo, el análisis de estructuras de covarianza no estacionarias en el contexto de datos longitudinales no se ha realizado de forma detallada principalmente debido a que las distintas aplicaciones no hacían necesario su uso. Muchos son los modelos propuestos recientemente,...

Modelling financial time series using reflections of copulas

Jozef Komorník, Magda Komorníková (2013)

Kybernetika

We have intensified studies of reflections of copulas (that we introduced recently in [6]) and found that their convex combinations exhibit potentially useful fitting properties for original copulas of the Normal, Frank, Clayton and Gumbel types. We show that these properties enable us to construct interesting models for the relations between investment in stocks and gold.

Modelling stock returns with AR-GARCH processes.

Elzbieta Ferenstein, Miroslaw Gasowski (2004)

SORT

Financial returns are often modelled as autoregressive time series with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes have been intensely studied in financial and econometric literature as risk models of many financial time series. Analyzing two data sets of stock prices we try to fit AR(1) processes with GARCH or EGARCH errors to the log returns. Moreover, hyperbolic or generalized error distributions occur to be good models...

Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process

S. Valère Bitseki Penda, Hacène Djellout, Frédéric Proïa (2014)

ESAIM: Probability and Statistics

The purpose of this paper is to investigate moderate deviations for the Durbin–Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate deviation...

Moment estimation methods for stationary spatial Cox processes - A comparison

Jiří Dvořák, Michaela Prokešová (2012)

Kybernetika

In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation study in...

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