Skip to content

FRM Part I · FRM Exam Part I · Stationary Time Series

A white noise process ε_t has variance σ² = 4. A series is built as Y_t = 3 + ε_t + 0.5 ε_{t-1}, where the ε_t are white noise. What is the variance of Y_t?

The variance is 5.0. Since white noise shocks at different dates are uncorrelated, variances add: the variance equals 4 times (1 plus 0.5 squared), which is 4 times 1.25. The constant 3 adds no variance, and the coefficient must be squared.

  1. A4.0
  2. B5.0Correct
  3. C6.0
  4. D4.5

Explanation

Because ε_t and ε_{t-1} are uncorrelated, Var(Y_t) = σ²(1 + 0.5²) = 4 × 1.25 = 5.0. Option A ignores the lagged shock. Option D uses 1 + 0.5 incorrectly scaled (4 + 0.5), and C adds 0.5×4 = 2 instead of 0.25×4 = 1.

Did you get it right without looking?

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

Practise Stationary Time SeriesFree diagnostic mock

More Stationary Time Series questions