Unit root
A lag coefficient of one in an autoregressive model, as in a random walk. A series with one is not covariance stationary, so regression results on it cannot be trusted until it is differenced.
Where you will meet it
Unit root appears in 5 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 with a trend in its mean, a variance that changes over time, or a unit root is not stationary, and regressions on it can produce impressive but meaningless t-statistics and R².”
- Explain what unit roots mean for time-series work, when they tend to arise and how to detect them, and show how to transform a series with a unit root so that an AR model can be used on it
“A series has a unit root when its lag coefficient b1 equals 1.”
- Set out the stages of testing a series for a unit root (nonstationarity) and explain how the test connects to autoregressive models
“The null hypothesis is a unit root, with g1 equal to 0, and the alternative is stationarity, with g1 below 0.”
- Explain how to check time-series variables for cointegration and/or nonstationarity before putting them into a linear regression
“Before regressing one time series on another, test each for a unit root.”
See also
Autoregressive model · Covariance · Covariance-stationary · Random walk
Practise it
Practise unit root until it is automatic: questions that explain every wrong option.
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