Fourier Analysis is useful, if you have a reason to believe that there are cyclical components in your time series and if you can identify the frequencies and eliminate the noise.
However, futures and stock prices mostly exhibit a non-linear behaviour, which means there are few such cyclical components to be identified.
If I look at your first chart, it shows a curve retro-fitted to data. At the right border - that is the place, where we want to predict price action and use the prediction for our trading - your curve exhibits a downward slope. If you please check what the market really did: it went up.
Curve fitting is a nice mathematical exercise. If you use a sufficient number of parameters, you can fit your curve to any past price action. But the curve has no predictive value. You can use it for interpolation but not for extrapolation.
Taking that data and drawing a simple trendline and wait until it is broken is more helpful. If you want to apply mathematics to trading, better look at volatility and autocorrelation than analyze supposed, but inexistant cyclical components.
Fat i have a knowledge who uses this type of analysis (Fourier Analysis) to fine tune the parameters of his indicators and according to him this is the cream of the cream. For example, finding the optimal range per bar to use as interval for the ES or TF to name one. So to fine-tune our indicators would you consider it or do you think it's a lost of time ?
Not sure that a naked DFT will reveil much of a cycle. You could have a look at the Corona Indicators developped by John F. Ehlers. He detrends the time series before analyzing for cycles. I have put the indicators on a 3 min chart for ES for last Friday.
If you look at the cyclical component, there was a dominant cycle with a period of around 28 in the beginning of the session. The lows were tradeable because of the trend that developped later in the day, the highs predicted were not impressive. The problem here is that the cycle amplitude was too small compared to the noise. The signal-to-noise stayed below 4DB during the first two hours, with a large corona, which means that the cyclical signal was week and the noise dominant.
Also to note that the cyclical component, which can barely be identified within price action, changed its period during noon - increased period - and then again prior to the close of the session. if I take into account the daily volatility smile, it is possible that the cycle analysis works better on range charts than time based charts. This is what the shorter cycle in the beginning and the end and the longer cycle in the middle suggest.
But this is just one day of observation. I do not think that cycle analysis is an easy route to success. But it is the sexiest indicator I have ever seen.
Please register on futures.io to view futures trading content such as post attachment(s), image(s), and screenshot(s).
Indicators courtesy of @sefstrat can be downloaded here. They work with both NT 6.5. and NT 7.0