ARMA modeling

Abstract

This thesis estimates the frequency response of a network where the only data is the output obtained from an Autoregressive-moving average (ARMA) model driven by a random input. Models of random processes and existing methods for solving ARMA models are examined. The estimation is performed iteratively by using the Yule-Walker Equations in three different methods for the AR part and the Cholesky factorization for the MA part. The AR parameters are estimated initially, then MA parameters are estimated assuming that the AR parameters have been compensated for. After the estimation of each parameter set, the original time series is filtered via the inverse of the last estimate of the transfer function of an AR model or MA model, allowing better and better estimation of each model's coefficients. The iteration refers to the procedure of removing the MA or AR part from the random process in an alternating fashion allowing the creation of an almost pure AR or MA process, respectively. As the iteration continues the estimates are improving. When the iteration reaches a point where the coefficients converse the last VIA and AR model coefficients are retained as final estimates.