Short Data Length Effects in an Asymptotically Efficient ARMA (AutoRegressive Moving Average) Spectral Estimator

摘要

The short data length behaviour of a recently proposed computationally efficient approximate maximum likelihood estimation algorithm is studied through Monte Carlo simulations. It is found that short data lengths combined with a large number of instruments results in very high variances, especially when the process being estimated has zeros near the unit circle. Several modifications of the algorithm are considered to reduce the problem mentioned above. First, a version which is recursive in the number of instruments and which adaptively chooses the number of instruments and postiterations is developed. A second modification uses a stabilized version of the estimated denominator polynomial. A version that forces the numerator estimate to non negative definite is considered, but it fails to give major improvements over the original algorithm. Finally, using overdetermined Yule Walker equations instead of the minimal number is found to markedly improve the quality of the estimates.