Time series analysis

This paper begins with a discussion of the properties of the noise occurring in the structures considered. This noise is taken to be generated by a stationary, ergodic, purely nondeterministic process. In case the observed vector sequence is generated by an autoregressive-moving average process then (a little more than) the additional requirement that the best predictor be the best linear predictor suffices for the development of an asymptotic inference theory. Signal measurement problems are considered, first where the signal is directly observed except for some unknown parameters and second where the signal is not directly observable and some characteristics, such as the velocity of propagation, have to be measured. Finally nonstationary models, nonlinear models for prediction, transient signals, and irregularly spaced samples are briefly discussed. Throughout, the methods are based on the use of the fast Fourier transforms of the data and their relation to the use of quasimaximum likelihoods in terms of those transforms is discussed.