Research interview time-series round.
Is this series stationary?
The question
Why does stationarity matter before you model a price series, and what do you do about it?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
Most estimators assume a stable distribution. Prices are not stationary, returns are much closer to it.
Regression, correlation and most time-series estimators assume the underlying distribution is not drifting. On a trending price series they produce relationships that are artefacts of the trend.
Two independent random walks will show a high regression R-squared, which is spurious regression and the reason level-on-level modelling misleads.
Differencing to returns removes the unit root in most cases. Tests such as augmented Dickey-Fuller check what is left, though they have limited power on short samples.
Cointegration is the exception worth naming: two non-stationary series can have a stationary combination, which is the foundation of pairs trading.
What it is testing
Whether you know why the standard first step exists rather than just performing it.
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Preparing properly
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