statistics

You can’t quantify what you haven’t observed. I paper traded order flow as a deliberate research step, building the intuition needed to formalize concepts like absorption, iceberg …

Shuffle your signal, re-run the backtest 10,000 times, see if your strategy beats random. Permutation tests provide a distribution-free way to assess strategy significance. This article covers the …

You have one history of market data. Your strategy was designed on that history. How do you estimate performance on data you haven’t seen? Bootstrap resampling generates synthetic histories that …

Every backtest is biased. The question is how badly and in which direction. This article catalogs the biases that corrupt backtesting results, from survivorship and lookahead to time-period, …

Walk-forward validation is the backbone of out-of-sample testing for trading strategies. But the choice of window type, window length, and step size introduces meta-parameters that can themselves be …

Autocorrelated returns inflate Sharpe ratios, invalidate standard significance tests, and make backtests look better than reality. This article explains why strategy returns are almost always …

A strategy built on a non-stationary signal is a strategy built on sand. This article covers the statistical tests that detect non-stationarity (ADF, KPSS, Phillips-Perron, Zivot-Andrews), explains …

Property-based testing generates random inputs and checks invariants. Financial markets are full of invariants: non-negative spreads, consistent OHLC bars, monotonic timestamps. This article shows how …