One of the most often used methods in the spectral analysis of climatic time series is the parametric method of maximum entropy based on an autoregressive model. The method of maximum entropy is particularly appealing because of its high resolution and its good performance with short time series. Its main drawback is that the statistical significance of the spectral peaks is difficult to assess; consequently, there is a risk of accepting spurious peaks as having a physical origin. We propose to use a computer intensive method, the permutation test, for assessing the statistical significance of the spectral peaks, showing its implementation and the results using simulated and real data. With the simulated data we illustrate the applicability to a short time series but with rich signal content, while with the time series of the Southern Oscillation Index (SOI) we illustrate how it may be used in the estimation of the spectrogram.