Cosinor analysis uses the least squares method to fit a sine wave to a
time series. Cosinor analysis is often used in the analysis
of biologic time series that demonstrate predictible rhythms. This
method can be used with an unequally spaced time series.
Follows cosinor analysis of a time series as outlined by
Nelson et al. "Methods for Cosinor-Rhythmometry" Chronobiologica.
1979. Please consult reference.
t - time series
y - value of series at time t
w - cycle length, defined by user based on prior knowledge of time
alpha - type I error used for cofidence interval calculations. Usually
set to be 0.05 which corresponds with 95% cofidence intervals
Note: Statistics toolbox is necessary only to caculate t and F distributions for the number of samples at the specified alpha. These values could be obtained from a table and manually inserted in the code, thus negating the use of the statistics toolbox.