Linear Smoothing of Noisy Spatial Temporal Series

Abstract

The main objective of the study is the development of a linear filter to extract the signal from a spatio-temporal series affected by measurement error. We assume that the evolution of the unobservable signal can be modelled by a space time autoregressive process. In its vectorial form, the model admits a state space representation allowing the direct application of the Kalman filter machinery to predict the unobservable state vector on the basis of the sample information. Having introduced 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. Consistent method 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 simulation studies and an investigation involving sulphur dioxide level monitoring.