Fitting nonlinear models with ARMA errors to biological rhythm data

Many behavioural and physiological processes are periodic with a period of approximately 24 hours. For descriptive purposes, linear regression using a simple sinusoid with a fixed 24 hour period is sometimes an adequate tool for analysing data from such processes. Inference based on regression models under the assumption of independent and identically distributed errors, however, can often mislead seriously. In this paper we present a general class of models for fitting biological rhythms, with use of higher-order harmonic terms of one or more unknown fundamentals and ARMA processes for the errors. We describe the procedures for model specification and estimation and give the theoretical justification for these procedures. Analysis of a series of human core body temperature illustrates the methodology.