  The Wiener-Hopf equations are a Toeplitz system of linear equations that
naturally arise in several applications in time series. These include the
update and prediction step of the stationary Kalman filter equations and the
prediction of bivariate time series. The celebrated Wiener-Hopf technique is
usually used for solving these equations and is based on a comparison of
coefficients in a Fourier series expansion. However, a statistical
interpretation of both the method and solution is opaque. The purpose of this
note is to revisit the (discrete) Wiener-Hopf equations and obtain an
alternative solution that is more aligned with classical techniques in time
series analysis. Specifically, we propose a solution to the Wiener-Hopf
equations that combines linear prediction with deconvolution.
  The Wiener-Hopf solution requires the spectral factorization of the
underlying spectral density function. For ease of evaluation it is often
assumed that the spectral density is rational. This allows one to obtain a
computationally tractable solution. However, this leads to an approximation
error when the underlying spectral density is not a rational function. We use
the proposed solution with Baxter's inequality to derive an error bound for the
rational spectral density approximation.
