Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation fun ction are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a method which is more re liable than traditional techniques, and is able to make clear identificatio n of periodic behavior when traditional techniques do not. This technique i s based on an information theoretic reduction of linear (autoregressive) mo dels so that only the essential features of an autoregressive model are ret ained. These models we call reduced autoregressive models (RARM). The essen tial features of reduced autoregressive models include any periodicity pres ent in the data. We provide theoretical and numerical evidence from both ex perimental and artificial data to demonstrate that this technique will reli ably detect periodicities if and only if they are present in the data. Ther e are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques a re used to ensure the converse. Furthermore, our calculations demonstrate t hat RARM is more robust, more accurate, and more sensitive than traditional spectral techniques.