Skip to content

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

A DF regression ΔY_t = α + γY_{t-1} + ε_t is estimated on a series, giving α = 0.40 and γ = −0.08, with a t-statistic for γ of −1.70 against a 5% DF critical value of −2.86. A colleague wrongly concludes the series is stationary around a mean of 5.0 (= 0.40/0.08). Which statement is correct?

The unit root null is not rejected because −1.70 is not below the critical value of −2.86. Hence the series cannot be treated as mean-reverting, and the implied level of 5.0 is not reliable evidence, despite γ being negative.

  1. AThe unit root null is not rejected, so the implied mean of 5.0 is not meaningful evidence of mean reversionCorrect
  2. BThe null is rejected because γ is negative, so the series reverts to 5.0
  3. CThe null is rejected because 0.40 exceeds 0.08
  4. DThe test is invalid because a constant cannot be included in a DF regression

Explanation

The statistic −1.70 is not below −2.86, so the null of a unit root cannot be rejected at 5%. The ratio −α/γ = 5.0 would be the mean only if the process were stationary, which the test has not established. A negative γ alone is not sufficient, and constants are allowed (drift specification).

Did you get it right without looking?

One question tells you little. A timed set on Nonstationary Time Series shows your real accuracy, how long you take and where you lose marks.

Practise Nonstationary Time SeriesFree diagnostic mock

More Nonstationary Time Series questions