In the periodogram approach to calculating the power spectra, the sample autocorrelation function is multiplied by some window function and then Fourier transformed. The window is applied to provide statistical stability as well as to avoid leakage from other parts of the spectrum. However, the window limits the spectral resolution.
Maximum entropy method attempts to improve the spectral resolution by extrapolating the correlation function beyond the maximum lag in such a way that the entropy of the corresponding probability density function is maximized in each step of the extrapolation.  
The maximum entropy rate stochastic process that satisfies the given empirical autocorrelation and variance constraints is an autoregressive model with independent and identically distributed zero-mean Gaussian input.
Therefore, the maximum entropy method is equivalent to least-squares fitting the available time series data to an autoregressive model 
where the  are independent and identically distributed as . The unknowns coefficients  are found using least-square method. Once the autoregressive coefficients have been determined, the spectrum of the time series data is estimated by evaluating the power spectral density function of the fitted autoregressive model
where  is the sampling period  and  is the imaginary unit.