Miha Kralj
90d5638008
- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
4.1 KiB
MSTOCH: Ehlers MESA Stochastic
The MESA Stochastic applies John Ehlers' Roofing Filter as a preprocessing stage before computing a stochastic oscillator, then smooths the stochastic output with a Super Smoother. The Roofing Filter removes both low-frequency trend components (via highpass) and high-frequency noise (via Super Smoother), isolating the dominant cycle. The stochastic calculation on this filtered data produces a clean 0-to-1 oscillator that responds to cycle turning points rather than trend or noise, with substantially reduced whipsaw compared to conventional stochastic indicators.
Historical Context
John Ehlers introduced the MESA Stochastic in his 2013 book Cycle Analytics for Traders, as part of his systematic framework for applying digital signal processing to market data. The "MESA" prefix references Maximum Entropy Spectral Analysis, Ehlers' preferred technique for estimating dominant cycle periods. The key innovation is the Roofing Filter preprocessing: by bandpass-filtering the data before applying the stochastic calculation, the oscillator responds to cycle extremes rather than trend extremes. Conventional stochastic indicators on raw price tend to saturate at 0 or 100 during trends (the "stochastic pop" failure mode), but the Roofing Filter removes the trend component entirely, so the stochastic operates on stationary cycle data. Ehlers demonstrated that this produces fewer false signals in trending markets while maintaining responsiveness at genuine cycle turning points. The Super Smoother stages use 2-pole Butterworth-derived coefficients that provide superior smoothing characteristics compared to simple or exponential moving averages.
Architecture & Physics
Three-Stage Pipeline
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Stage 1: Roofing Filter (Highpass + Super Smoother). The highpass is a 2-pole Butterworth filter that removes cycles longer than
hpLength, eliminating trend. The Super Smoother is a 2-pole lowpass filter that removes cycles shorter thanssLength, eliminating noise. Together they form a bandpass that isolates the dominant cycle band. -
Stage 2: Stochastic on filtered data. A standard highest-high / lowest-low stochastic over
stochLengthbars of the roofing-filtered output. Because the input is zero-mean (trend removed), the stochastic operates on cycle oscillations rather than trending prices. -
Stage 3: Super Smoother of stochastic. The same 2-pole smoothing filter applied to the raw stochastic, removing stochastic noise while preserving the timing of overbought/oversold transitions. Output is clamped to
[0, 1].
IIR Filter Coefficients
Both the highpass and Super Smoother stages use coefficients derived from 2-pole Butterworth prototypes:
\text{arg} = \frac{\sqrt{2}\pi}{P}, \quad e^{-\text{arg}}, \quad c_2 = 2 e^{-\text{arg}} \cos(\text{arg}), \quad c_3 = -e^{-2\text{arg}}
The highpass uses c_1 = (1 + c_2 - c_3)/4 with a second-difference input (x - 2x_{-1} + x_{-2}).
The Super Smoother uses c_1 = 1 - c_2 - c_3 with an averaged input (x + x_{-1})/2.
Mathematical Foundation
Roofing Filter highpass (removes trend, cutoff period P_{hp}):
HP_t = c_1^{hp}(x_t - 2x_{t-1} + x_{t-2}) + c_2^{hp} \cdot HP_{t-1} + c_3^{hp} \cdot HP_{t-2}
where c_1^{hp} = \frac{1 + c_2^{hp} - c_3^{hp}}{4}
Super Smoother (removes noise, cutoff period P_{ss}):
F_t = c_1^{ss} \cdot \frac{HP_t + HP_{t-1}}{2} + c_2^{ss} \cdot F_{t-1} + c_3^{ss} \cdot F_{t-2}
where c_1^{ss} = 1 - c_2^{ss} - c_3^{ss}
Stochastic on filtered data:
S_t = \frac{F_t - \min(F_{t-k}, \ldots, F_t)}{\max(F_{t-k}, \ldots, F_t) - \min(F_{t-k}, \ldots, F_t)}
where k = \text{stochLength} - 1. If range is zero, S_t = 0.5.
Final smoothing:
MSTOCH_t = c_1^{ss} \cdot \frac{S_t + S_{t-1}}{2} + c_2^{ss} \cdot MSTOCH_{t-1} + c_3^{ss} \cdot MSTOCH_{t-2}
\text{Output} = \text{clamp}(MSTOCH_t, 0, 1)
Default parameters: stochLength = 20, hpLength = 48, ssLength = 10.
Resources
- Ehlers, J.F. (2013). Cycle Analytics for Traders. Wiley, Chapter 6
- Ehlers, J.F. (2004). Cybernetic Analysis for Stocks and Futures. Wiley
- PineScript reference:
mstoch.pine