@vince.quant: How do you pick your indicators? Let's build a formula. Every systematic strategy is a function of the past path. Rough path theory gives that path a canonical description, its signature: the sequence of iterated integrals, where level one is the increment, level two the areas swept, against time the shape of the trend and between two assets the lead-lag, and higher levels finer shape shrinking like 1/n!. Hambly and Lyons (2010, Annals of Mathematics) proved the signature determines the path, and a universal approximation theorem says any continuous function of the path is, to any precision, a linear combination of signature terms. So every indicator, moving-average crossovers, RSI, Bollinger bands, even the Kalman filter, can be approximated arbitrarily well by a linear combination of signature terms. Futter, Horvath and Wiese (Quantitative Finance, 2025) make this a portfolio method. Regressing a MACD momentum strategy with a sigmoid, on the TLT ETF, onto the signature recovers it with R² of 66% at order 1, 89% at order 3 and 98% at order 11. Because the strategy is linear in the signature, the mean-variance optimum is closed-form: the weight vector is proportional to the inverse covariance of the terms' profit attributions times those attributions, both read off the expected lead-lag signature, with no neural network and no gradient descent. At order zero it is exactly Markowitz; each order adds path dependence and, because the criterion is over a horizon, a built-in drawdown control. For two assets, one signal and time at order two, that is 21 terms. The limits, from the paper: the expected signature is noisy to estimate and robustness is left to future work; the covariance needs signature terms of order six for an order-two strategy; market impact is not modelled; the real-data evidence is a three-ETF frontier and one momentum replication. Libraries: signatory, esig, iisignature. Futter, O., Horvath, B. & Wiese, M. (2025). Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals. Quantitative Finance, 25(2). arXiv 2308.15135. #finance #quant #machinelearning #roughpaths #algotrading

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Monday 14 September 2026 20:35:45 GMT