Scalograms are like piano-roll sheet-music, therefore I like to investigate a dynamical system's data not by human intuition and cognitive observations e.g. 12 month periodicity known to all of us, rather by looking at the scalograms which are basically the time-frequency map of a 1D time-series.

These are difficult to obtain from FFT and therefore as motivation the new field of Wavelet Theory was developed. FFT basis are cos and sin like with no compact support, but the wavelets' compact support allow for such Scalograms. We will use this property later on for forecast algorithms via the Kernel Mathematics (I will publish a tutorial very soon).

Also I do multiple decompositions (since they are approximate in nature) to render a clearer understanding of the time-frequency map.

I have converted the frequency to periods (months) i.e. the y-axis is periods in months.

Dara