Estimation of autoregressive parameters by the constrained total least square algorithm using a bootstrap method

Modified Yule-Walker (MYW) equations are often used to estimate autoregressive parameters of an autoregressive moving average (ARMA) model. Commonly used algorithms, i.e., the least square (LS) algorithm, the total least square (TLS) algorithm, cannot give an optimal estimate because they do not exploit the Toeplitz property and covariance of the perturbation matrix. In this paper, a constrained total least squares (CTLS) algorithm is applied to solve modified Yule-Walker equations. The perturbation covariance matrix of the autocorrelation functions required by the CTLS algorithm is estimated by introducing the bootstrap method. By utilizing the Toeplitz property and the covariance of perturbation matrix, a Newton method based CTLS algorithm is shown to outperform TLS and LS solutions.