Autocorrelation, ACF and PACF Quiz

Answers and explanations appear as you take the quiz.

1. What does the ACF at lag k describe?
   • Correlation between observations k time steps apart
   • Correlation after removing all predictor effects
   • The partial regression slope at every lag
   • The forecast variance at horizon k
2. How does PACF at lag k differ from ACF?
   • It measures only seasonal frequencies
   • It accounts for linear effects of shorter lags
   • It is a correlation between two different series
   • It is always zero for nonstationary data
3. Repeated ACF spikes at lags 12, 24 and 36 in monthly data suggest what?
   • That all seasonal effects are removed
   • A guaranteed AR order of 36
   • Possible annual seasonal dependence
   • A perfect moving-average fit
4. Why can a slowly decaying ACF reflect trend rather than short-memory dependence?
   • A trend is identical to an MA term
   • The ACF omits all time information
   • Trend makes every lag exactly zero
   • Nonstationary level changes can induce broad persistence across lags
5. Which textbook pattern is associated with a pure AR(p) process under ideal conditions?
   • ACF cuts off after p while PACF is always one
   • PACF cuts off after p while ACF decays
   • Both functions are exactly zero at lag one
   • Both cut off at the sample size
6. Why are isolated spikes across many lags not definitive evidence?
   • Confidence bands equal exact causal tests
   • ACF values are always deterministic
   • Multiple approximate comparisons and finite-sample noise can create them
   • A lag plot cannot include uncertainty
7. Which ACF is useful after fitting an ARIMA candidate?
   • The seasonal ACF after labels are removed
   • Only the original series ACF because residuals are never diagnostic
   • The predictor ACF to estimate accuracy
   • The residual ACF to inspect remaining serial dependence
8. How should ACF/PACF plots guide model selection?
   • Suggest candidate orders that are then validated with diagnostics and forecasts
   • Set exact p and q without further checks
   • Prove stationarity whenever confidence bands are crossed
   • Replace a time-ordered test set