I would use DSP.periodogram or welch_pgram rather than fft directly, they use fft internally. And you typically want to look at the magnitude of the fft rather than the real part. This is exactly what the periodigram does. Another alternative is to look at the cross correlation, e.g. StatsBase.crosscorr or ControlSystemIdentification.crosscorrplot.
An amplitude histogram is simply a histogram of the values, I think StatsBase fits a histogram for you.
AR models can be fit with many different packages, I use my package ControlSystemIdentification.jl, but there are many others. I would look at the fraction of variance explained by an AR model. But the periodigram might be easier for you to reason about if you’re new to this.
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