A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters

A good approximation of the Gaussian likelihood of simultaneous autoregressive (SAR) model is proposed. The approximation yields us an asymptotically efficient estimate of the parameters. No integration of the spectral density nor any other expensive calculation is necessary, so that our estimation procedure is applicable for any SAR model without restriction. Numerical experiments show that our estimate has less bias and variance than the other estimate, although our comparison is limited to the case where random number generation and the calculation of the other estimate are both feasible.