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.