MESA, Fourier Analysis of Maximum Entropy Spectra and Correlation Function Analysis

1 - Description of problem or function: The MESA program determines periodic components from input data which represent a time series. Transformations may be performed on the raw data before doing the spectral analysis. Routines are included to calculate both the Fourier spectrum and maximum entropy spectrum, the Yule-Walker estimates of the autocovariance function, the periodogram ordinates, the cumulative periodogram, the autocorrelation function resulting from the maximum entropy computations, and the final prediction error, if desired. 2 - Method of solution: A test for white noise is performed using the cumulative periodogram. The Fourier power spectrum and the maximum entropy spectrum are used for estimating the period of the time series. The maximum entropy spectral analysis is based on the spectrum that corresponds to the most random and least predictable time series whose autocorrelation function agrees with the given input values. 3 - Restrictions on the complexity of the problem: Maxima of: 5 spectra, 5 transformations, 600 data points, 599 frequencies