Stationarity and Differencing Quiz

Answers and explanations appear as you take the quiz.

1. Under weak stationarity, how may autocovariance depend on time?
   • On lag, but not on the calendar time of the pair
   • On the later time index only
   • It must equal zero at every lag
   • It must grow linearly each year
2. What does first differencing compute?
   • The current value divided by the seasonal mean
   • The current value minus the immediately prior value
   • The rolling average over the full series
   • The residual after a classification threshold
3. Which null does the Augmented Dickey-Fuller test evaluate?
   • The errors are normally distributed
   • The series is stationary around a level
   • The series has a unit root
   • The series contains no seasonal component
4. Which null is used by the usual KPSS test?
   • A zero forecast error
   • A unit root in every model
   • No autocorrelation at any lag
   • Stationarity, under a level or trend specification
5. What does seasonal differencing subtract?
   • The immediately previous value regardless of period
   • The value one seasonal period earlier
   • The entire sample mean
   • The forecast error at lag one
6. What does failure to reject the ADF null establish?
   • It proves the trend is deterministic
   • It proves strict stationarity
   • It is evidence insufficient to reject a unit root, not proof of one
   • It means KPSS must reject stationarity
7. Why can over-differencing be harmful?
   • It removes the need to validate forecasts
   • It guarantees constant variance
   • It always increases test power
   • It can add unnecessary noise and dependence patterns
8. Which approach is appropriate after differencing a series?
   • Check transformed plots and forecast behavior before adding another difference
   • Difference repeatedly until every p-value is zero
   • Assume the series is stationary by definition
   • Use only the original-level ADF statistic