Covariance-stationary
Having a constant, finite mean and variance, and covariances with past values that depend only on the lag. Autoregressive models give valid results only for such series.
Where you will meet it
Covariance-stationary appears in 4 learning outcomes on the CFA syllabus. A few of them:
- Explain why a time series needs to be covariance stationary and what it means when a series lacks stationarity
“A series is covariance stationary when its expected value, its variance and its covariance with its own past values are constant and finite over time.”
- Say what mean reversion is and work out the level a series tends to revert to
“Every covariance-stationary series has a finite mean-reverting level.”
- Set out the features of a random walk and how it differs from a covariance stationary process
“It is therefore not covariance stationary, unlike an AR(1) with b1 below 1 in absolute value, which has a constant mean and variance.”
- Choose a suitable time-series model for a given investment problem and give reasons for the choice
“Before that, make the series covariance stationary, by differencing it, taking logs first if it grows exponentially.”
See also
Autoregressive model · Covariance · Variance
Practise it
Practise covariance-stationary until it is automatic: questions that explain every wrong option.
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