Aligrithm is an independent research publication on systematic trading, quantitative research, market microstructure, and adaptive systems. Long-form essays, code notebooks, and architecture breakdowns across eight pillars, built for traders who care more about how markets behave than about hype.
More about the publication →Read in order. Each pillar walks you out of one trap with one new ability. The newest article is the worst place to begin.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
A wrong-scale sigmoid destroys the signal. Center on training median; scale α so IQR lands in the linear region (α≈1.2 for tanh). On SPX Range/Close, α=1.2 lifts AUC 0.503 → 0.519.
The histogram is the primary diagnostic. Scalars (R/IQR, RE, MI, TCR) confuse shapes needing different fixes. Identical scalars hide light-tail, heavy-tail, or bimodal — only bimodal needs a split.