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FRM Part I · FRM Exam Part I · Nonstationary Time Series

An analyst applies the Augmented Dickey-Fuller (ADF) test instead of the basic DF test to a quarterly series. What is the purpose of the added lagged difference terms?

The lagged difference terms soak up serial correlation in the errors, which would otherwise distort the basic Dickey-Fuller test. The null is still a unit root and the nonstandard critical values still apply; the augmentation only corrects for higher-order dynamics.

  1. ATo absorb serial correlation in the residuals so the test statistic is validCorrect
  2. BTo convert the null hypothesis into one of stationarity
  3. CTo remove the need for special critical values
  4. DTo guarantee that the series is stationary after differencing

Explanation

If the series follows a higher-order autoregression, the DF residuals are autocorrelated and the test is distorted. Adding lagged ΔY terms captures this dynamic. The null remains a unit root and the nonstandard DF-type critical values still apply.

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