We extend and generalize an approach to conduct fitting models of periodically repeating data. Our method first detrends the data from a baseline function and then fits the data to a periodic (trigonometric, polynomial, or piecewise linear) function. The polynomial and piecewise linear functions are developed from assumptions of continuity and differentiability across each time period. We apply this approach to different datasets in the environmental sciences in addition to a synthetic dataset. Overall the polynomial and piecewise linear approaches developed here performed as good (or better) compared to the trigonometric approach when evaluated using statistical measures (R2 or the AIC). These results were consistent when the number of measurements decreased (through random removal of data). Future applications of the fitting method could account for higher-order terms in the polynomial function or refinements to the estimation of parameters in the piecewise linear function.
Bělík, Pavel; Hotchkiss, Andrew; Perez, Brandon; and Zobitz, John
"Empirical Fitting of Periodically Repeating Environmental Data,"
Spora: A Journal of Biomathematics: Vol. 7, 61–71.
Available at: https://ir.library.illinoisstate.edu/spora/vol7/iss1/8