Temporal autocorrelation measures how a time series relates to a lagged version of itself. In financial returns, autocorrelation of squared returns, Corr(r²ₜ₋₁, r²ₜ), tests whether large moves follow large moves and small moves follow small moves, regardless of direction. section 3.2.2
S&P 500 volatility clustering
Compute daily returns, square them, and calculate lag-one autocorrelation. The S&P 500 result is 0.2228, with standard error 0.0106 and t-statistic 21.03, providing strong evidence that volatility is not independent over time.
Interpret the statistic in context:
- Near-zero autocorrelation would be consistent with no volatility clustering; a materially positive value indicates that yesterday’s squared return helps forecast today’s. section 3.2.2
- GARCH models use this persistence to forecast future volatility rather than treating returns as identically distributed over time. section 3.2.2
