What is autocorrelation and why does it matter for time-series analysis?

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AcadiFi · Accepted Answer

Autocorrelation (also called serial correlation) is the correlation of a time-series with its own lagged values. Formally, the lag-k autocorrelation is ρₖ = Cov(Xₜ, Xₜ₋ₖ) / Var(Xₜ).

Durbin-Watson (DW) approximates 2(1 - ρ₁). A DW of 1.1 implies ρ₁ ≈ 0.45 — strong positive serial correlation in your residuals. Critical interpretations:

- DW ≈ 2: no first-order autocorrelation (ideal).
- DW < 2: positive autocorrelation (residuals are persistent).
- DW > 2: negative autocorrelation (residuals oscillate).

Why it matters in finance:

1. Smoothed returns: hedge funds, private equity, and real estate often report returns that are artificially smoothed. Serial correlation is a fingerprint of this smoothing. The reported volatility understates true volatility and the Sharpe ratio is flattered.
2. Biased OLS standard errors: coefficient estimates remain unbiased, but their standard errors are understated, leading to over-rejection of null hypotheses (false significance).
3. Model misspecification: autocorrelated residuals often signal that an important lag or variable is missing.

Remedies on the CFA exam:

- Newey-West standard errors: adjust for both heteroskedasticity and autocorrelation.
- AR(1) model: explicitly model the persistence in residuals.
- Unsmoothed returns: back out the implied true returns before running performance analytics.

For hedge funds, a useful rule of thumb: if ρ₁ > 0.2 in monthly returns, reported Sharpe ratios should be deflated by √(1 + 2ρ₁) to reflect the true standard deviation. This is especially relevant when evaluating illiquid strategies for inclusion in diversified portfolios.

What is autocorrelation and why does it matter for time-series analysis?

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