Consistent Parameter Estimation of ARMA with Measurement Noises

This paper studies the problem of estimating parameters of ARMA(p,q) with the observed data corrupted by an unknown white noise. A modified recursive instrumental variables(RIV) method is developed to provide consistent estimates for the parameters of AR(p) and variance of the white noise. With these obtained results, estimates of the parameters in MA(q) can be determined by using the welldeveloped Newton-Raphson algorithm.