Skip to content

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

A series follows Y_t = 2 + 0.6t + e_t, where e_t is white noise. An analyst first-differences this trend-stationary series. Which statement describes the consequence?

Differencing gives ΔY_t = 0.6 + e_t − e_{t−1}: constant mean 0.6 but a non-invertible moving-average error with a unit root. This is over-differencing of a trend-stationary series; detrending is the appropriate remedy.

  1. AThe differenced series has constant mean 0.6 but a moving-average error with a unit root, so it is over-differencedCorrect
  2. BThe differenced series has mean 2 and is properly stationary
  3. CThe differenced series is a random walk with drift 0.6
  4. DThe differenced series has a time-varying mean of 0.6t

Explanation

ΔY_t = 0.6 + e_t - e_{t-1}. The mean is constant at 0.6, but the MA(1) error has coefficient -1 (a unit root in the MA part), which signals over-differencing. The proper treatment is to detrend by regressing on time.

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