Autocorrelation
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
Correlation of a time series with its own lagged values: ρ_k = Corr(X_t, X_t-k). Equity returns show near-zero autocorrelation at daily-to-monthly horizons (weak-form efficiency), but volatility (|R_t| or R_t^2) is strongly positively autocorrelated — the volatility-clustering stylised fact that motivates GARCH. Ljung-Box and Durbin-Watson are standard significance tests; positive return autocorrelation in fund NAVs is the smoking gun for stale-price marking (a Madoff-detection diagnostic).
Autocorrelation in plain English
Autocorrelation asks whether a sequence of numbers echoes its own past — does today's value tell you anything about a value from a few steps back? For stock returns the answer is basically no over short horizons (you can't predict tomorrow's move from today's, which is what 'efficient market' means), but the *size* of the moves clumps together: wild days cluster near other wild days, and calm near calm. It's like weather — you can't guess if tomorrow will be warmer or cooler than today, but stormy stretches and calm stretches each tend to run in streaks. This tool also catches fraud: if a fund's supposedly independent monthly returns are suspiciously smooth and predictable from month to month, it hints the prices are being faked or 'smoothed' — one of the red flags that exposed the Madoff scandal.
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