Problems in the statistical analysis of short periodic time series∗∗

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Abstract
In biological rhythm research very short records are not uncommon, especially in medicine, covering only one cycle and with few sample points. After contrasting this with some rare examples of long time series, the main approaches to the analysis of short records are discussed. Fourier methods and other avenues are compared. The classical Fourier analysis is shown to be a special case of multiple regression, the latter must be used if the data are unequispaced. Comparisons are made on some model sines with varying amounts of noise added. The effect of spatial and temporal errors are discussed; that of the successive addition of sine terms are also explored on an example from the seasonal temperature rhythm in rats. The relations between polynomial curve fitting and periodic regression are studied using the McLaurin expansion in connection with a discussion of period estimation. Some major methods presently being used are discussed, the cosinor, periodic regression and pergressive harmonic analysis. The transient synchronization analysis for exploring biological synchronization is touched upon.

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