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Linear Smoothing of Noisy Spatial Temporal Series

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Author(s): Valter Di Giacinto | Ian Dryden | Luigi Ippoliti | Luca Romagnoli

Journal: Journal of Mathematics and Statistics
ISSN 1549-3644

Volume: 1;
Issue: 4;
Start page: 300;
Date: 2005;
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Keywords: Gaussian markov random field | image analysis | maximum likelihood estimation | measurement error | Kalman filter | STARMA model | STARG model | state space model

ABSTRACT
The main objective of the study is the development of a linear filter to extract the signalfrom a spatio-temporal series affected by measurement error. We assume that the evolution of theunobservable signal can be modelled by a space time autoregressive process. In its vectorial form, themodel admits a state space representation allowing the direct application of the Kalman filtermachinery to predict the unobservable state vector on the basis of the sample information. Havingintroduced the model, referred to as a STARG+Noise model, the study discusses Maximum Likelihood(ML) parameter estimation assuming knowledge of the variance of the noise process. Consistentmethod of moments estimators of the autoregressive coefficients and noise variance are also derived,primarily to be used as inputs in the ML estimation procedure. Finally, we consider some simulationstudies and an investigation involving sulphur dioxide level monitoring.

Tango Jona
Tangokurs Rapperswil-Jona

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