Skip to content

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

An analyst models a monthly price index as y_t = y_{t-1} + e_t, where e_t is white noise with variance 4. Which statement about this process is correct?

The process is a random walk with a unit root. Every shock persists permanently, so the variance of the level grows in proportion to time. The series is not covariance-stationary, although its first difference is white noise and therefore stationary.

  1. AIt is covariance-stationary because the shocks have constant variance
  2. BIt is a random walk, and the variance of y_t grows over timeCorrect
  3. CIt is trend-stationary, so detrending yields a stationary series
  4. DIt is mean-reverting toward zero with a half-life of one month

Explanation

With coefficient 1 on the lagged value, the process has a unit root. Shocks accumulate permanently, so Var(y_t) = t*4 (given a fixed starting value), which grows without bound. Constant shock variance does not make the level series stationary; only the differenced series is stationary.

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