Durbin-Watson Test
A statistical test used to detect the presence of first-order autocorrelation in the residuals from a regression analysis.
What is Durbin-Watson Test?
The Durbin-Watson (DW) statistic assesses whether the error term at time t is correlated with the error term at time t-1. The statistic ranges from 0 to 4, where a value near 2 indicates no autocorrelation, values approaching 0 indicate positive autocorrelation, and values approaching 4 indicate negative autocorrelation.
Why Durbin-Watson Test Matters
Autocorrelation, common in time-series data, violates the standard OLS assumption that errors are independent. If left uncorrected, it causes the standard errors to be underestimated, artificially inflating t-statistics and making predictors appear more significant than they actually are.
Example
An economist analyzing the relationship between inflation and unemployment over 50 years calculates a DW statistic of 0.8, indicating strong positive autocorrelation. They must subsequently employ autoregressive models or Newey-West robust standard errors to correct for this.
Common Mistakes
- Using the Durbin-Watson test when the regression model includes a lagged dependent variable, which renders the test statistic invalid.
- Failing to check for higher-order autocorrelation (e.g., seasonality), as the DW test only detects correlation between immediate consecutive time periods.