# Quantitative Analysis > Use when applying statistical methods to financial data. Covers return distributions, stationarity, correlation versus causation, the multiple-testing problem, and the statistical traps specific to financial time series. - Skill: `nimadorostkar/quantitative-analysis` (Agent Skill) - Install (CLI): `npx skillmds@latest add nimadorostkar/quantitative-analysis` - Raw SKILL.md: https://api.skillmd.com/api/skills/nimadorostkar/quantitative-analysis/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - Author: nimadorostkar (https://skillmd.com/u/nimadorostkar) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/nimadorostkar/quantitative-analysis --- # Quantitative Analysis ## Purpose Apply statistics to financial data without being fooled by it. Financial time series violate nearly every assumption of standard statistical methods, and the tools will produce confident, well-formatted, wrong answers without complaint. ## When to Use - Testing whether a signal has predictive value. - Modeling returns, volatility, or correlations. - Evaluating a quantitative claim someone else has made. - Building a factor model or a risk model. ## Capabilities - Return distributions and their fat tails. - Stationarity, unit roots, and spurious regression. - Correlation, causation, and confounding. - Multiple-testing correction and data snooping. - Volatility modeling and clustering. ## Inputs - The data, and an honest account of how it was selected. - The hypothesis — stated before the data was examined. - The number of hypotheses that have already been tested on this data. ## Outputs - A result with its assumptions stated. - A significance level corrected for the number of tests actually run. - An honest statement of what the result does and does not support. ## Workflow 1. **Look at the distribution before assuming one** — Financial returns are not normal. They have fat tails and skew, and every method that assumes normality will underestimate the probability of a large move — which is the only probability that matters for survival. 2. **Test for stationarity** — Regressing one non-stationary series on another produces a high R-squared and a significant t-statistic between two entirely unrelated things. This is spurious regression, and it is the most common error in financial statistics. 3. **Work in returns, not prices** — Prices are non-stationary by construction. Returns are approximately stationary. Almost every meaningful analysis operates on returns. 4. **Count the hypotheses you have tested** — If you tried a hundred signals and one has a p-value of 0.01, you have found exactly what pure chance predicts. A p-value not adjusted for the search is not evidence. 5. **Distinguish correlation from causation, and both from coincidence** — With enough series, something will correlate with anything. A mechanism stated in advance is what separates a finding from a coincidence. 6. **Validate out of sample** — On data that was not available when the hypothesis was formed. Everything else is description. ## Best Practices - Financial returns have fat tails. A "six-sigma" event under a normal distribution should occur once in several million years; in markets it occurs every few years. Any model built on normality is quietly understating tail risk. - Non-stationarity produces spurious regressions with astonishing reliability. Two random walks will regress on each other with a significant t-statistic roughly 70% of the time. Always difference or test first. - Correlation between financial series is unstable. A correlation estimated over three years describes those three years, and it will not hold in the crisis you are trying to protect against. - The multiple-testing problem is the single largest source of false discovery in quantitative finance. The published anomaly literature is substantially a record of it. - In-sample fit is not evidence. Any sufficiently flexible model fits any dataset. The only test that means anything is out of sample. - Report the effect size, not just the p-value. A statistically significant edge of 0.02% per trade is not tradable after costs. ## Examples **Spurious regression — the error that produces the most confident wrong answers:** ```python import numpy as np, statsmodels.api as sm # Two independent random walks. There is no relationship whatsoever. np.random.seed(1) a = np.cumsum(np.random.randn(500)) b = np.cumsum(np.random.randn(500)) model = sm.OLS(a, sm.add_constant(b)).fit() print(f"R-squared: {model.rsquared:.3f} t-stat: {model.tvalues[1]:.2f}") # R-squared: 0.681 t-stat: 32.71 # # An R-squared of 0.68 and a t-statistic of 33 between two series with NO # relationship at all. This is not a fluke of the seed; it happens most of the # time with non-stationary series. Any conclusion drawn from this is fiction. # The correct procedure: test for stationarity, and work in returns. from statsmodels.tsa.stattools import adfuller for name, series in [("a", a), ("b", b)]: p = adfuller(series)[1] print(f"{name}: ADF p={p:.3f} -> {'non-stationary' if p > 0.05 else 'stationary'}") # a: ADF p=0.712 -> non-stationary # b: ADF p=0.884 -> non-stationary # # Differencing to returns removes the spurious relationship entirely. model_returns = sm.OLS(np.diff(a), sm.add_constant(np.diff(b))).fit() print(f"R-squared: {model_returns.rsquared:.4f} t-stat: {model_returns.tvalues[1]:.2f}") # R-squared: 0.0004 t-stat: -0.44 <- the truth: no relationship ``` **Multiple testing — why most published anomalies are not real:** ```python def corrected_significance(p_values: list[float], n_tested: int) -> Report: """A p-value of 0.01 means nothing if you tested 100 hypotheses.""" best_p = min(p_values) # Bonferroni: the family-wise error rate. bonferroni = min(1.0, best_p * n_tested) # The probability that the best of n random signals looks this good by chance. prob_by_chance = 1 - (1 - best_p) ** n_tested return Report( raw_p=best_p, bonferroni_p=bonferroni, prob_at_least_one_by_chance=prob_by_chance, verdict=( "Not distinguishable from chance." if bonferroni > 0.05 else "Survives correction. Now validate out of sample." ), ) # Tested 120 signal variants. The best has p = 0.008. # raw p : 0.008 "significant!" # Bonferroni-corrected p : 0.96 # P(at least one this good # by chance among 120) : 0.62 # Verdict: not distinguishable from chance. # # The signal is exactly as good as the best of 120 random signals would be # expected to be. It is a discovery about the search, not about the market. ``` ## Notes - The spurious-regression demonstration above is the single most important thing in this skill. An R-squared of 0.68 between two unrelated random walks is not a corner case — it is the typical result, and it has produced a great many published findings. - Fat tails mean that variance is a poor risk measure for financial returns. Maximum drawdown and expected shortfall describe what actually hurts. - This is educational material about quantitative methodology, not financial advice, and none of it constitutes a recommendation.