Inverse of the covariance matrix of an MA(2) process

Abstract A component-wise formula for the inverse of the covariance matrix of an MA(2) process is provided in Shaman (1973) requiring O ( n 3 ) calculations per column. This paper simplifies his formula resulting in only O ( n ) calculations per column. Using a well-known result concerning the inverse of symmetric Toeplitz matrices, we show that the inverse of the covariance matrix of an MA(2) process may be written as a function of its first column, requiring only O ( n ) calculations to obtain instead of the O ( n 2 ) calculations required from the Levinson–Durbin algorithm (Levinson, 1947).