Functional estimation incorporating prior correlation information (Q964621)

The problem of least mean-square error (MSE) prediction of a stochastic process \(z(s)\) by observations of \(y(t_i)=x(t_i)+\nu(t_i)\), \(i=1,\dots,N\), is considered, where \(\nu(t)\) is a centered white noise, \(x(t)\), \(y(t)\), \(z(t)\) are zero mean second order stationary processes, \(\nu\), \(z\) and \(x\) are correlated with each other and their cross-correlations are known. To overcome the computational difficulties in solving the Wienner-Hopf equations, the authors propose a sub-optimal algorithm based on functional principal components analysis. A recursive formula for the MSE of the obtained prediction is proposed. An example with \(x\) being an Ornstein-Uhlenbeck process is presented.