Multidimensional autoregression

Multidimensional autoregression

Jon Claerbout

The many applications of least squares to the one-dimensional convolution operator constitute the subject known as ``time-series analysis.'' The autoregression filter, also known as the prediction-error filter (PEF), gathers statistics for us, not the autocorrelation or the spectrum directly but it gathers them indirectly as the inverse of the amplitude spectrum of its input. The PEF plays the role of the so-called ``inverse-covariance matrix'' in statistical estimation theory. Given the PEF, we use it to find missing portions of signals.