Fixed parameter models for time series and longitudinal data

Abstract

The methods of the foregoing sections are mainly appropriate for modelling and analyzing a broad class of non-normal cross-sectional data. Extensions to time-dependent data are possible in a variety of ways. Time series are repeated observations (y _t , x _t ) on a response variable y of primary interest and on a vector of covariates taken at times t = 1,...,T. Discrete time longitudinal or panel data are repeated observations (y _it , x _it ) taken for units i = 1,..., n at times t = 1,..., T _i . The restriction to integral times is made to simplify notation but is not necessary for most of the approaches. Longitudinal data may be viewed as a cross section of individual time series, reducing to a single time series for n = 1, or as a sequence of cross-sectional observations where units are identifiable over time. If a comparably small number of longer time series is observed, models and methods will be similar to those for single time series. If, however, many short time series have been observed, models, and often the scientific obiective, can be different.