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Let $𝐗$ and $𝐘$ be stationarily cross-correlated multivariate stationary sequences. Assume that all values of $𝐘$ and all but one values of $𝐗$ are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Analyse des effets d'intervention sur les prévisions issues de modèles ARIMA

J. P. Indjehagopian (1981)

Revue de Statistique Appliquée

Analyse spectrale et théorème de prédiction statistique de Wiener

Pierre Cartier (1960/1961)

Séminaire Bourbaki

Analysing time series for forecasting (a personal view)

Oliver D. Anderson (1989)

RAIRO - Operations Research - Recherche Opérationnelle

Aplicación de redes neuronales artificiales a la previsión de series temporales no estacionarias o no invertibles.

Raúl Pino, David de la Fuente, José Parreño, Paolo Priore (2002)

Qüestiió

En los últimos tiempos se ha comprobado un aumento del interés en la aplicación de las Redes Neuronales Artificiales a la previsión de series temporales, intentando explotar las indudables ventajas de estas herramientas. En este artículo se calculan previsiones de series no estacionarias o no invertibles, que presentan dificultades cuando se intentan pronosticar utilizando la metodología ARIMA de Box-Jenkins. Las ventajas de la aplicación de redes neuronales se aprecian con más claridad, cuando...

Artificial neural networks in time series forecasting: a comparative analysis

Héctor Allende, Claudio Moraga, Rodrigo Salas (2002)

Kybernetika

Artificial neural networks (ANN) have received a great deal of attention in many fields of engineering and science. Inspired by the study of brain architecture, ANN represent a class of non-linear models capable of learning from data. ANN have been applied in many areas where statistical methods are traditionally employed. They have been used in pattern recognition, classification, prediction and process control. The purpose of this paper is to discuss ANN and compare them to non-linear time series...

Asymmetric recursive methods for time series

Tomáš Cipra (1994)

Applications of Mathematics

The problem of asymmetry appears in various aspects of time series modelling. Typical examples are asymmetric time series, asymmetric error distributions and asymmetric loss functions in estimating and predicting. The paper deals with asymmetric modifications of some recursive time series methods including Kalman filtering, exponential smoothing and recursive treatment of Box-Jenkins models.

Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

A. Budhiraja (2003)

Annales de l'I.H.P. Probabilités et statistiques

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