Statistics
Statistics in trading is not about p-hacking your way to a publishable result. I write about the applied methods I actually use: bootstrap confidence intervals, permutation tests for strategy comparison, autocorrelation diagnostics, and deflated Sharpe ratios. These articles focus on getting honest answers from noisy financial data.
Finding Signal in Market Noise: I Stopped Reading the Tape and Started Measuring It
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 …
Monte Carlo Permutation Tests for Strategy Significance: Is Your Alpha Real or Random?
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 …
Bootstrap Methods for Strategy Robustness: Resampling When You Can't Get More Data
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 …
A Taxonomy of Backtest Lies: Survival Bias, Lookahead Bias, and the Rest
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 Optimization: Anchored vs. Rolling Windows and When Each Fails
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 …
Autocorrelation and What It Means for Your Backtest P&L
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 …
Stationarity Testing for Strategy Signals: ADF, KPSS, and Why Your Backtest Depends on It
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 Meets Financial Data: Turning Market Invariants into Executable Specifications
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 …