Time Series Analysis Stationarity and Differencing 2 — Questions and Answers
Question 1: What does the Augmented Dickey-Fuller test add compared to the simple Dickey-Fuller test?
- Lagged difference terms to account for serial correlation in residuals (Correct answer)
- A seasonal component
- Multiple unit root testing
- Variance stabilization
Correct answer: Lagged difference terms to account for serial correlation in residuals
The ADF augments the basic test with lagged first differences to ensure residuals are white noise, correcting for serial correlation.
Question 2: A time series with a deterministic trend is best handled by:
- Detrending (subtracting a fitted trend) (Correct answer)
- First differencing
- Log transformation alone
- Seasonal decomposition
Correct answer: Detrending (subtracting a fitted trend)
A deterministic trend can be removed by fitting and subtracting a regression trend line, leaving a stationary residual.
Question 3: What is the Phillips-Perron (PP) test used for?
- Testing for unit roots with non-parametric correction for serial correlation (Correct answer)
- Testing for seasonality
- Measuring forecast accuracy
- Detecting outliers
Correct answer: Testing for unit roots with non-parametric correction for serial correlation
The PP test is a unit root test that uses a non-parametric correction for serial correlation, making it robust to heteroscedasticity.
Question 4: If a time series requires differencing twice (d=2) to become stationary, it is said to be:
- Integrated of order 2, I(2) (Correct answer)
- Integrated of order 1, I(1)
- Stationary in levels
- Seasonally integrated
Correct answer: Integrated of order 2, I(2)
A series requiring two differences is I(2), meaning it has two unit roots and is second-order integrated.
Question 5: Which visual tool is most helpful for an initial stationarity assessment?
- Time series plot showing mean and variance over rolling windows (Correct answer)
- Histogram of values
- Scatter plot of y vs x
- Box plot of all values
Correct answer: Time series plot showing mean and variance over rolling windows
Plotting rolling mean and variance reveals whether the series has shifting central tendency or spread, indicating non-stationarity.
Question 6: What is 'cointegration' in the context of multiple non-stationary time series?
- Two non-stationary series share a long-run equilibrium relationship (Correct answer)
- Both series are stationary
- The series have identical variances
- Differencing one series makes the other stationary
Correct answer: Two non-stationary series share a long-run equilibrium relationship
Cointegrated series are individually I(1) but their linear combination is stationary, implying a stable long-run relationship.
Time Series Analysis Stationarity and Differencing 2
What does the Augmented Dickey-Fuller test add compared to the simple Dickey-Fuller test?