2.38 Causal Wavelet Filters and the Mexican Hat
A wavelet is a band-pass whose width scales, so one Mexican Hat (the 2nd derivative of a Gaussian) scans every cycle at once. Compact support makes it usable; the resolution tradeoff makes it honest.
Independent research on systematic & quantitative trading
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 →The ten pillars
Read in order. Each pillar walks you out of one trap with one new ability. The newest article is the worst place to begin.
- 1 The Scientific Trader Rebuild what you accept as evidence. Every rule becomes a hypothesis, every backtest an experiment you can falsify. 26
- 2 Indicator Engineering The input decides the ceiling. Build features with measurable properties that survive the tests. 82
- 3 Robust Systems Lab A strategy is not robust for surviving one friendly backtest. Here it survives hostile testing. 37
- 4 Market Structure Notes The same rule is edge on one instrument and noise on another. Read a market's personality before you deploy. 70
- 5 Microstructure Alpha The order-book layer. The same signal is worthless as taker flow and valuable as a maker improvement. 45
- 6 Portfolio Construction & System Death A real signal still loses if the size and correlations are wrong. Sizing is part of the signal. 48
- 7 Python Research Notebooks Stop taking results on faith. Re-run every claim on your own data and see whether it holds. 3
- 8 Physics, Geometry & Event-Driven Markets The frontier. Markets as event-driven nonlinear systems, not fixed-time price series. Read it last. 8
- 9 Prediction Market Arbitrage The cleanest money on Polymarket and Kalshi comes from prices that contradict each other, not prices that turn out wrong. 33
- 10 Cross-Sectional & Factor Investing Stop timing one asset. Rank the whole cross-section and let relative value, not direction, carry the return. 15
Latest articles
2.37 Cubic-Velocity Modified EMA and Skipped Convolution
Estimate slope from a 4-point cubic with skipped taps and the modified EMA turns faster and lags less. But a derivative is no low-pass: the output is not smooth, and that is the real trade.
2.36 Zero-Lag EMA: The Kalman Filter, Simplified
The zero-lag EMA borrows the Kalman predict step: smooth Price + kappa*velocity, so the slope cancels lag in trends. The same guess overshoots reversals, so it is no turn detector.
2.35 Frequency-Adaptive EMA: Smoothing That Reacts to Noise
A fixed EMA smooths the same in calm and chaos. The adaptive EMA ties alpha to cycle speed: track tight when clean, smooth hard when noisy, at most one bar lag, if you can estimate omega.
2.34 Sinc / Scaling Functions: The Closest Thing to a Brick-Wall Filter
The sinc is the exact brick-wall low-pass: full pass below the cutoff, nothing above. But it runs infinitely long and needs future bars, so you build only a truncated, windowed version that rings.
2.33 The Butterworth Filter for Traders
The Butterworth is the maximally flat low-pass: slow cycles pass with no ripple, each pole cuts noise harder. The bill is lag, about one EMA's worth per pole, so two poles is the sweet spot.
2.32 The Transfer Function View: Characterizing Any Indicator with the Z-Transform
Write any linear indicator as a transfer function H(z), a ratio of two short polynomials, and its full behavior reads out: gain at every cycle, lag in bars, and the poles that make it ring.
8.5 Markets Are Getting More Random: Non-Stationarity of Randomness Itself
The market's randomness itself drifts: competition arbitrages structure away, so recent data is more random than old and your backtest edge is an upper bound that decays, not a stable estimate.
8.4 Long-Range Dependence: Real Memory or Just Short-Range Echo?
Market "long memory" is mostly short-range autocorrelation in disguise: correct for it and the Hurst signal collapses toward random. Kill a striking statistic with the boring explanation first.
8.3 Log-Normal Prices and the Price/Volume Trick
Bachelier's normal-price model lets prices go negative; putting the walk on log price fixes it. The twist: raw price fits a log-normal badly, but price divided by volume fits one cleanly.
8.2 The Omori Law: Why Aftershocks Follow Market Crashes
After a crash the violent days keep coming, dense then fading along the same power-law curve geologists use for aftershocks. Independent returns can't do that, so size down for weeks, not days.
6.42 Stable Paretian / Fractal Distributions: Infinite Variance Markets
Mandelbrot's stable Paretian family fits markets better than the Gaussian: fat-tailed, fractal, with infinite variance that breaks volatility sizing, Sharpe, and every variance-based risk number.