Likelihood Ratio Test for the Equivalence of Two Autoregressive Moving-Average Time Series
NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV RI
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To passively detect quiet sources, future sonar systems will require more sensors, which may contribute to operator overload. The methods described in this report have the potential to automatically determine if two sonar tracks, for example, correspond to the same source, thereby improving operator performance. Specifically, a likelihood ratio test for the equivalence of two autoregressive moving average ARMA time series is derived. This test investigates the structural characteristics of the two time series through the ARMA parameters. Four cases of this test are presented for examining the ARMA parameters, series means, andor innovations variances. The autoregressive AR time series is treated separately, not only because AR parameters are easier to estimate, but also because many time series can be characterized by an AR process. Monte Carlo analysis has shown that the likelihood ratio test has a good fit to the chi square distribution, with degrees of freedom equal to the number of parameters being tested.
- Statistics and Probability
- Acoustic Detection and Detectors