2.26 The Frequency Response of Trading Indicators
Every linear indicator is a filter with a unique frequency response. RSI(14), MACD(12,26), Stochastic(14) read the same 15-40 bar cycle band three different ways. The confluence is redundancy.
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2.25 Why Moving Averages Can Lie at Turning Points
At a turning point, the MA reports the prior regime as the present. EMA(50) signaled the SPX March 2020 bottom 27 bars late; cycle-mode detectors fired in 2-5 bars. Structural lag, not a tuning bug.
2.24 Decyclers: Extracting Trend by Removing Cycle Energy
The decycler extracts trend by subtracting the cycle, not by smoothing. On SPX, decycler at T=30 cuts EMA(50)'s 18% cycle leakage to 4% with less lag. Specify the cycle to cancel, not a lookback.
2.23 Band-Pass Filters: The Most Underused Tool in Technical Analysis
The band-pass rejects both trend and noise, keeping only the cycle band. Direct second-order form has two parameters (T, δ). On SPX at T = 20, δ = 0.3, BPF MI is 1.9 vs 1.2 for close-minus-MA.
2.22 High-Pass Filters for Traders
HPF output = input − LPF. Each pole adds 6 dB/octave rolloff and one bar of lag. The 2-pole HPF at critical period T is the cleanest detrender for daily mean-reversion features.
2.21 The Trader's Guide to Low-Pass Filters
Each pole adds 6 dB/oct rolloff and one bar of lag at critical period T. 1-pole EMA: 6 dB/oct. 2-pole and super-smoother: 12 dB/oct. The super-smoother is critically damped with clean step response.
2.20 EMA vs SMA: Why Simplicity Still Matters
EMA is the 1-pole IIR low-pass: y_t = α x_t + (1−α) y_{t−1}. One state, one parameter, no sidelobes. EMA wins on O(1) state and composability — the building block for HPF, BPF, AGC, decycler.
2.19 Why the SMA Is Often a Terrible Smoother
SMA's sinc response has the worst sidelobes of any common smoother: −13.3 dB (22% leakage) regardless of N. Same lag, Hann leaks 2.6%, Blackman 0.12%. Critical period ~2N. Use Hann or Blackman.
2.18 The Hidden Cost of Every Moving Average: Lag
Every MA pays a lag tax. Symmetric FIR length N has lag (N−1)/2. On SPX, 200-day SMA captures 18% of a 10% move; 50-day captures 56%. WMA buys lag with phase distortion. Structural trade.
2.17 No Filter Is Predictive: What Traders Misunderstand About Smoothing
Every linear filter is y(t)=Σ b_k x(t−k)−Σ a_k y(t−k). H(z) has only negative powers, no z⁺¹. Filters summarize the past; they don't extrapolate. SMA(50) on next-day return: R²≈0.0002.
2.16 Feature Engineering Before Machine Learning
Feature engineering contributes 90-95% of the edge; model selection 5-10%. Same XGBoost: raw OHLC → SPX AUC 0.502; full statistical pipeline → 0.524. Features are IP. The model is a commodity.
2.15 Why the Median Often Beats the Mean in Trading Features
Mean breakdown 1/n; median 0.5. On SPX 100-bar center through March 2020, mean spikes 5σ; median moves 0.4. Median for centering, MAD/IQR for spread, Spearman for correlation, LAD for regression.