Testing for Autocorrelation

Tests to check for autocorrelation include

Durbin-Watson test

• Wikipedia D-W test

Lagged scatterplot

• A scatterplot of y_t against y_t-k

• Example: Lagged Scatter Plot - Example 1 (R)

• NIST - lag plot

acf and pacf

• acf = autocorrelation function

  • NIST - acf plot

• pacf = partial autocorrelation function

  • Wikipedia - partial autocorrelation function

  • NIST - pacf plot

Box-Pierce statistic

The distribution of the sample acf is r_k ~ N(0,1/T)

Q_BP = T*sum(r_k²) which has a chi-square distribution

Ljung-Box statistic

• NIST - Box-Ljung test

From NIST: