Random walk
A series in which each value equals the previous one plus an unpredictable error, an AR(1) with b1 = 1. It has no finite mean-reverting level and is not covariance stationary.
Where you will meet it
Random walk appears in 2 learning outcomes on the CFA syllabus. A few of them:
- Say what mean reversion is and work out the level a series tends to revert to
“A random walk has none, because its b1 is 1 and the formula divides by zero.”
- Set out the features of a random walk and how it differs from a covariance stationary process
“A random walk is a series whose value each period equals the previous value plus an unpredictable error: x(t) = x(t − 1) + ε.”
See also
Covariance · Covariance-stationary · Mean reversion
Practise it
Practise random walk until it is automatic: questions that explain every wrong option.
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