Everyone knows the market data are fractal. You can look at a chart of daily data, look at a chart of weekly data, and the charts basically look the same if the scales are removed. In other words, the amplitude of the cyclic swings scale in direct proportion to the cycle period. I call this effect Spectral Dilation because longer cycle periods have larger swings. The Hurst Coefficient is directly related to the degree of dilation. Fibonccians use the Golden Spiral to show the dilation factor is 1.618. The exact degree of dilation is not important. The fact that dilation exists is beyond question. So, in round numbers, the spectrum amplitude increases 6 dB per octave of cycle period. This “1/F” phenomena seems to be almost universal in physical systems.
Here was my epiphany regarding market data: Like everyone, I knew the market data was fractal. However I completely disregarded this fact when looking at oscillator type indicators such as the Momentum, Stochastic, RSI, MACD, or CCI. In a nutshell, all these indicators are first order differentiators. That is, they all take just one difference in their calculation. A basic principle of filtering is that simple differencing has an attenuation rolloff of 6 dB per octave per order of the filter in the attenuation band of the filter. Therefore, all of these indicators roll off at the rate of 6 dB per octave like a simple HighPass filter. Since the data amplitude swings are increasing at the rate of 6 dB per octave, the best these indicators can do is to flatten the response of the data spectrum in the indicator output.
Figure 1 shows the practical effect of a simple HighPass filter when applied to some sample market data. Note that during the period of the long uptrend the oscillator does not have a zero mean. That is, the wiggles are not centered on zero. The interpretation is that the data has not been fully detrended and that the longer cycle period signals are “leaking through” the rejection band of the filter.
Figure 1. A Simple HighPass Filter Does Not Accommodate Spectral Dilation
The attenuation rate is increased 12 dB per octave in the attenuation band by using a second order HighPass Filter. The filter attenuation exceeds the 6 dB per octave Spectral Dilation in the data and therefore effective filtering of the longer cycle components is accomplished. Figure 2 shows the contrast between using a first order HighPass filter and second order HighPass filter. The dotted red line is the original response given in Figure 1 and the solid blue line is the second order response. Note the second order response provides a nominal zero mean for the oscillator and that much of the lag induced by the “leaking” longer cyclic components is eliminated.
Figure 2. The Second Order HighPass Filter Establishes a Zero Mean and Reduces Lag of the Oscillator
I call the combination of my SuperSmoother filter and the second order HighPass filter a “Roofing Filter” because it provides a roof over the data spectrum so the data is preprocessed for use with any indicator that may follow. The Roofing filter is not a bad indicator in its own right. In a sense, the Roofing filter is a kind of BandPass filter. The Roofing filter differs from a BandPass filter because the rejection response on the high frequency side is specifically designed to reject aliasing noise and the second order rejection response on the low frequency side is specifically designed to eliminate the effects of Spectral Dilation.
The MESA Stochastic is just a standard Stochastic calculation preceded by a Roofing filter, and is just one example of the use of the Roofing filter. The two indicators are compared in Figure 3. I rememberGeorge Lane, a bombastic speaker, list the myriad of rules in the use of the Stochastic. Some depended on %D crossing %K on the right side or left side. Also one rule was “In an uptrend, don’t go short until %D crossed below 80 three times”. As we now see, all those rules are just plain silly. The distortion of the Stochastic in an uptrend is due solely to Spectral Dilation. When the Roofing filter precedes the Stochastic, the result is an easy-to-use oscillator whose swings are nearly in synchronization with the swings in the prices.
Figure 3. Roofing Filter Removes Spectral Dilation Effects from Indicators