Regression with Autocorrelated Errors (Prais-Winsten / Cochrane-Orcutt)

Prais-Winsten and Cochrane-Orcutt regression estimate a linear model whose errors follow a first-order autoregressive process by repeatedly estimating the autocorrelation and quasi-differencing the data.

Prais-Winsten·Cochrane-Orcutt 회귀는 오차가 1차 자기회귀를 따르는 선형모형을, 자기상관을 반복 추정하고 자료를 준차분해 추정합니다.

My time-series regression residuals are autocorrelated; how do I get valid coefficients and standard errors?

시계열 회귀의 잔차에 자기상관이 있는데, 올바른 계수와 표준오차를 어떻게 얻나요?

The autocorrelation rho is estimated from residuals, the outcome and predictors are transformed as y_t - rho y_{t-1}, and the regression is refitted until rho converges. Prais-Winsten keeps the first observation scaled by the square root of 1 - rho squared, while Cochrane-Orcutt drops it.

When to use Regression with Autocorrelated Errors (Prais-Winsten / Cochrane-Orcutt)

• A Durbin-Watson statistic far from 2 shows first-order serial correlation in a time-series regression.
• You want feasible GLS estimates rather than only autocorrelation-robust standard errors.
• The series is short enough that keeping the first observation (Prais-Winsten) matters.

When to use something else

• The predictors include a lagged outcome; use dynamic models or ARIMA with regressors.
• The series are non-stationary and possibly cointegrated; use unit-root and cointegration methods.

Assumptions and requirements

• Errors follow a stationary AR(1) process (|rho| < 1), or AR(p) with the iterated GLSAR option.
• Predictors are strictly exogenous.
• Observations are equally spaced and ordered by the time column.

What the analysis reports

• Converged rho
• FGLS coefficients and SEs alongside OLS
• Durbin-Watson before and after transformation
• Ljung-Box test on transformed residuals

How to report it

A Prais-Winsten regression of [outcome] on [predictors] (N = [value]) estimated rho = [value]; for [predictor], b = [value], SE = [value], p = [value]. The Durbin-Watson statistic was [value] for OLS and [value] after transformation.

Related methods

• Newey-West HAC Standard Errors
• ARIMA
• Autocorrelation Analysis (ACF, PACF, Ljung-Box)

Run Regression with Autocorrelated Errors (Prais-Winsten / Cochrane-Orcutt) on Quorant