Skip to content

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

A random walk with drift is Y_t = 0.5 + Y_{t-1} + e_t, where e_t has variance 4 and Y_0 = 10. Which statement about Y_{25}, viewed from time 0, is correct?

The mean is 22.5 and the variance is 100. The drift adds 0.5 for each of 25 periods to the starting value of 10, giving 22.5, while the independent shocks accumulate to 25 times 4, which is 100.

  1. AMean 22.5 and variance 100Correct
  2. BMean 22.5 and variance 4
  3. CMean 12.5 and variance 100
  4. DMean 35 and variance 10

Explanation

Mean = Y_0 + 25 x 0.5 = 10 + 12.5 = 22.5. Variance = 25 x 4 = 100. Option 3 omits the starting value; option 2 uses only one-period variance.

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