Estimation of non-integer lags in a subset of cyclic time series models

In this Dissertation, a new methodology is developed for the estimation of non-integer lags of deterministic as well as random time series. A graphical method, Lissajous figures, which traditionally is employed in electrical engineering, is expanded and applied in our analysis. Algorithms are developed to measure the accuracy of the estimates of the non-integer lags. Models with one and two lags are treated in detail. The traditional areas of model building, estimation, and verification are discussed for time series models with non-integer lags.; A deterministic linear time series model is considered where the exogenous (independent) variable is assumed to be from a subset of cyclic models. In particular, the case where the independent variable is a finite sum of sinusoids is considered. The bisection root-finding method is employed to approximate or estimate the non-integer lag. A measure of accuracy and related quasi-statistic are developed in detail for the case of a single lag. The methods developed in this dissertation are applied to a test data set from Box-Jenkins (1976). It turned out that our methods compare favorably to the classic time-domain and frequency domain methods.; Excursions are investigated for the cases where the deterministic time series models (1) are not linear or (2) have an independent variable not describable by a finite sum of sinusoids.