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Correcting for Serial Correlation

There are two routes to valid inference under serial correlation. The modern default is Newey-West (HAC) standard errors, which leave the OLS coefficients untouched and simply compute standard errors robust to both autocorrelation and heteroskedasticity up to a chosen lag. The classical route is feasible GLS, implemented as Cochrane-Orcutt or Prais-Winsten, which estimates ρ\rho, quasi-differences the data, and re-estimates to gain efficiency when the AR(1) model is correct. FGLS can be more efficient but relies on strict exogeneity and a correctly specified error process, so Newey-West is the safer, lower-assumption fix in applied work.

Why it matters

Newey-West takes one line. Trust the estimates, fix the uncertainty. It widens the standard errors to account for errors that move in runs, much as robust standard errors handle heteroskedasticity, and you choose how many lags of autocorrelation to allow for. FGLS instead tries to transform away the autocorrelation by quasi-differencing, which can buy efficiency but only if you have modeled the error dynamics correctly.

Formulas

AR(1) quasi-differencing (FGLS)
yt−ρ^ yt−1=β0(1−ρ^)+β1(xt−ρ^ xt−1)+ety_t - \hat{\rho}\, y_{t-1} = \beta_0(1 - \hat{\rho}) + \beta_1 (x_t - \hat{\rho}\, x_{t-1}) + e_t
Cochrane-Orcutt and Prais-Winsten estimate the rho and run OLS on these quasi-differenced data.
Newey-West lag choice
g≈4(n100)2/9g \approx 4\left(\tfrac{n}{100}\right)^{2/9}
A common rule of thumb for the truncation lag g in the HAC variance estimator.

Worked examples

Scenario

Your time-series regression has serially correlated errors and you want trustworthy standard errors without changing the model.

Solution

Use HAC standard errors: `newey y x, lag(4)`. The coefficients match OLS, but the standard errors are now robust to serial correlation up to four lags (and to heteroskedasticity). Increase `lag()` if autocorrelation is more persistent.

Note`newey` requires `tsset` data and keeps the OLS point estimates, fixing only the standard errors.
Scenario

You prefer the classical efficiency gain and believe the AR(1) error model is appropriate.

Solution

Run feasible GLS with `prais y x`. Prais-Winsten estimates rho, quasi-differences the data, and retains the first observation, unlike Cochrane-Orcutt which drops it. This can be more efficient than OLS when the AR(1) assumption holds.

NoteFGLS relies on strict exogeneity and a correctly specified error process, so it is less robust than Newey-West.

Common mistakes

  • ✗Newey-West changes the regression coefficients. It leaves the OLS estimates unchanged and only adjusts the standard errors.
  • ✗FGLS is always better than robust standard errors. FGLS gains efficiency only if the error model is correct and strict exogeneity holds; otherwise Newey-West is safer.
  • ✗Newey-West requires choosing the true lag length exactly. You pick a truncation lag; rules of thumb guide the choice, and results are usually not sensitive to small changes.
  • ✗Cochrane-Orcutt and Prais-Winsten are identical. They differ in the first observation: Prais-Winsten keeps it via a special transformation, Cochrane-Orcutt drops it.

Revision bullets

  • •Newey-West (HAC) standard errors are the modern default fix
  • •HAC keeps OLS coefficients, fixing only the standard errors
  • •FGLS (Cochrane-Orcutt / Prais-Winsten) quasi-differences for efficiency
  • •Prais-Winsten keeps the first observation; Cochrane-Orcutt drops it
  • •Stata: `newey y x, lag(4)` for HAC, `prais y x` for FGLS

Quick check

Newey-West standard errors differ from ordinary OLS standard errors in that they:

The main difference between Cochrane-Orcutt and Prais-Winsten estimation is:

Connected topics

Robust SEWLS / FGLSTS.1-TS.6Serial Corr.Test Serial

Sources

  1. Wooldridge (2019), §12.3 and §12.5
    Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 7th ed. Cengage, 2019.
    Covers FGLS (Cochrane-Orcutt, Prais-Winsten) and serial-correlation-robust (Newey-West) standard errors.
  2. Newey & West (1987)
    Newey, W.K., and K.D. West. A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55 (1987): 703-708.
    Original derivation of the HAC standard errors implemented by Stata’s newey command.
How to cite this page
Dr. Phil's Quant Lab. (2026). Correcting for Serial Correlation. Derivatives Atlas. https://phucnguyenvan.com/concept/efm-correcting-serial-correlation
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