Statistical Inferencing for Quantitative Trading Strategies

Learn hypothesis testing for quantitative trading strategies with Monte Carlo and permutation methods to build distribution-free tests of backtested performance metrics such as the Sharpe ratio.

Explore prices, returns (gross, net, logarithmic), and portfolio construction with weights and leverage, and understand risk as volatility and variance in time series.

Explore foundations of probability and statistics, including the sample space omega, events, random variables, and estimators, with examples from dice, card decks, and the normal distribution.

Formulate null and alternative hypotheses for hypothesis testing and select a test statistic like the sample mean. Compute the p-value and compare to a significance level to decide rejection.

Explore how to manage type one and type two errors in hypothesis testing, quantify alpha, beta, and power, and apply strong familywise error rate control when evaluating quantitative trading strategies.

Explore parametric tests for portfolio returns using the t test to assess whether mean returns exceed zero, including normal versus student t assumptions and key robustness caveats.

Explore nonparametric tests for median returns, including the sign test and Wilcoxon signed rank test under symmetry, compare to parametric tests, and apply Monte Carlo methods for null distribution.

Introduce the Python code for backtesting strategies and demonstrate location tests, generating a realistic portfolio returns sample via a simulated trading strategy.

Learn to compute portfolio returns from weights, returns, and leverage, filter valid samples, and perform t tests, sign tests, and Wilcoxon signed rank tests with both manual and library approaches.

Explore Monte Carlo permutation tests to test trading strategies by comparing original results to permuted price paths, using a nonparametric null distribution and a permutation algorithm.

Demonstrates permutation of log differences to generate a univariate null distribution, preserving endpoints and asset correlations, and extends to multivariate feature permutations for hypothesis testing.

Explore preserving intra-bar and inter-bar distributions when permuting multivariate candlestick data, using open high low close deltas and log transforms to reconstruct price paths via region-based joint-distribution permutation.

Apply a Python permutation algorithm to prices and bars, generate a null distribution for hypothesis tests, and visualize permuted price paths and Japanese candlesticks with NumPy and pandas.

Combine nonparametric and Monte Carlo permutation testing to formalize hypothesis testing, compute p values under permutation-invariant null distributions, and assess trading strategy Sharpe ratios against nulls.

Construct hypothesis tests and p-values to detect overfitting by comparing real data and permuted data, using holdout and in-sample versus out-of-sample testing.

Investigate hypothesis tests for out-of-sample trading strategies, using regression-based alpha and beta to attribute performance, and apply permutation tests to assess timing and stock-picking ability.

Run Monte Carlo permutation tests to evaluate trend-following strategies like Bollinger using Sharpe ratio, null distributions, and cross-sectional and time-axis shuffles.

Examine selection bias in a family of trading strategies using permutation-based hypothesis tests and step-down resampling to assess the statistical significance of top strategies while controlling the familywise error rate.

Explore the python implementation of the romano-wolf stepdown for controlling false discoveries in multiple testing for quantitative trading strategies, with permutation p-values, exact vs bounded values, and practical evaluation.