ARMA modeling

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Author
Kayahan, Gurhan
Date
1988-12Advisor
Hippenstiel, Ralph
Second Reader
Tummala, Murali
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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.
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