Autocorrelated errors and inflated t-stats

Question

You regress a strategy's daily returns on a factor using OLS. The residuals are positively autocorrelated: today's error tends to have the same sign as yesterday's, as is common in financial time series.

What happens to the coefficient, the standard errors, and your significance tests? How do you fix it?

Accepted Answer

The assumption that fails: no serial correlation (\operatorname{Cov}(\varepsiloni, \varepsilonj \mid X) = 0). The coefficient is fine. Like heteroskedasticity, autocorrelation does not violate exogeneity, so OLS stays unbiased and consistent. The point estimate of the factor loading is not the problem. The standard errors are the problem, and the direction matters. With positive autocorrelation, the OLS variance formula understates the true standard errors. Intuitively, correlated observations carry less independent information than their count suggests, so your effective sample size is small…

Autocorrelated errors and inflated t-stats

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