I got interested in this topic, after reading about Time Cycles from Murphy's book. Time cycle seems pretty much Fourier series analysis. Just to try it out, I took the monthly data for EURUSD for its entirety. First, this is the monthly EURUSD chart (x-axis is just data points). I take a Fourier Transform of this data, select the low-frequency components, and then Inverse Fourier Transform, to give this graph (red graph is the standard EURUSD Monthly data). The blue curve is showing an interesting cyclic pattern. It seems set to repeat a bullish wave. To make it cleaner, I pass the EURUSD monthly data through a Low-pass filter, set at cutoff frequency of 0.05 units (which is around 5 times the frequency step size), and then I get this graph. We are clearly seeing initiation of a bull run again. I was wondering if professionals consider this a reliable analysis of FX markets? All other forces of the market (ECB, Fed, rates, trade agreements/wars, Futures), they are perhaps unwittingly playing their part in helping this cycle evolve naturally? Or is this just a fluke?
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