Spectral Estimation: An Overdetermined Rational Model Equation Approach.
Final technical rept.,
ARIZONA STATE UNIV TEMPE DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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In seeking rational models of time series, the concept of approximating second order statistical relationships i.e., the Yule-Walker equations is often explicitly or implicitly invoked. The parameters of the hypothesized rational model are typically selected so that these relationships best represent a set of autocorrelation lag estimates computed from time series observations. One of the objectives of the report will be that of establishing this fundamental approach to the generation of rational models. An examination of many popular contemporary spectral estimation methods reveals that the parameters of hypothesized rational model are estimated upon using a minimal set of Yule-Walker equation evaluations. This results in an undesired parameter hypersensitivity and a subsequent decrease in estimation performance. To counteract this parameter hypersensitivity, the concept of using more than the minimal number of Yule-Walker equation evaluations is herein developed. It is shown that by taking overdetermined parametric approach, a reduction in data induced model parameter hypersensitivity is obtained, and a corresponding improvement in modeling performance results.
- Statistics and Probability