Effective Sample Size

Effective sample size is the number of independent observations that would provide roughly the same estimation precision as a correlated sample.

A backtest can contain thousands of daily returns without containing thousands of independent pieces of information. Positive serial dependence makes nearby observations more alike, which can reduce effective information relative to the raw row count.

Correlation changes the information content of a sample

The Grizzly Bulls autocorrelation check models this through a variance-inflation factor. Under that framework:

1effective observations = raw observations / variance inflation factor

The exact factor depends on the assumed dependence structure. The public calculator currently uses an AR(1) model, so it should not be generalized into a universal estimator for every time series.

This concept complements return skewness and return kurtosis: skewness and kurtosis describe distribution shape, while effective sample size describes how dependence changes estimation precision.

Use the Backtest Autocorrelation calculator for the actual AR(1) sensitivity analysis.

Effective sample size is statistic-specific

Different estimands and dependence structures can imply different uncertainty adjustments. An ESS reported for one mean or one model should not automatically be reused for every performance statistic.

Andrew Lo's Sharpe-ratio work shows why serial correlation can invalidate simple square-root-of-time annualization, while general statistical treatments define ESS through the autocorrelation structure of dependent samples.

Sources: Andrew Lo, The Statistics of Sharpe Ratios and Stan Reference Manual, Effective Sample Size.

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