Presentation and inspection of results

A simple way to graphically present the results of a TSA is to plot the test statistics S against its parameter $\nu$ or l, depending on whether the analysis was performed in the frequency or time domain. Plots in the frequency domain are called periodograms. In them, oscillations are revealed by the presence of spectral lines. However, some (often many) lines are spurious and simply arise from random fluctuations of the signal. By means of the confidence level $\alpha$and the probability distribution of S one can find the critical value S_crit for significant features. Examples of statistics used in the time domain are covariance and correlation functions. The correlation of a signal with itself or with another signal produces maxima in these functions at particular lags. Detection of genuine lags then consists of testing the significance of such maxima.