Methods for the Analysis of Non-Stationary Time Series with Applications to Oceanography

摘要

The probability structure for a type of real, mean zero, second order non-stationary stochastic process is shown to depend upon a non-stationary spectral density rho(lambda, tau) (if it exists). This dissertation treats the problem of estimating rho(lambda, tau) from a finite part of a sample function of the process. Two methods are developed: the case where rho(lambda, tau) is locally 'slowly varying', and the case where rho(lambda, tau) is 'linearly separable'. The statistical properties of these methods are investigated and approximations to the sampling distribution of the estimators are obtained for the Gaussian case. 'Spectral representations' for the estimates and their variances are obtained. A non-stationary version of the pseudo-integral representation investigated by Tukey and used by Pierson is shown to be rigorously definable and to correspond to a strongly normal non-stationary process of the type considered above. Several examples of the use of the methods are shown. In particular, the time varying spectral density of the Crescent City tsunami of May 23, 1960 is estimated. (Author)