Time Series Analysis Stationarity and Differencing 1 — Questions and Answers
Question 1: A stationary time series is characterized by which of the following?
- Constant mean, variance, and autocovariance over time (Correct answer)
- Increasing mean over time
- Decreasing variance over time
- Random seasonal patterns
Correct answer: Constant mean, variance, and autocovariance over time
Stationarity requires that the statistical properties — mean, variance, and covariance structure — do not change with time.
Question 2: Which statistical test is most widely used to test for a unit root (non-stationarity)?
- Augmented Dickey-Fuller (ADF) test (Correct answer)
- Ljung-Box test
- Breusch-Pagan test
- Shapiro-Wilk test
Correct answer: Augmented Dickey-Fuller (ADF) test
The ADF test checks for the presence of a unit root; a low p-value (< 0.05) allows rejection of the null hypothesis of non-stationarity.
Question 3: What is 'weak stationarity' (also called covariance stationarity)?
- Constant mean and autocovariance that depends only on lag, not time (Correct answer)
- Constant distribution at every time point
- No autocorrelation at any lag
- Constant variance but non-constant mean
Correct answer: Constant mean and autocovariance that depends only on lag, not time
Weak stationarity requires a constant mean and covariances that depend only on the time lag between observations, not their absolute positions.
Question 4: How does seasonal differencing differ from regular differencing?
- Seasonal differencing subtracts the value from the same period in a prior season (Correct answer)
- Seasonal differencing uses consecutive observations
- Seasonal differencing removes trend only
- They are identical operations
Correct answer: Seasonal differencing subtracts the value from the same period in a prior season
Seasonal differencing subtracts the observation from the same period s steps ago, removing periodic (seasonal) patterns.
Question 5: The KPSS test differs from the ADF test in which fundamental way?
- KPSS null hypothesis is stationarity; ADF null is non-stationarity (Correct answer)
- KPSS tests for seasonality; ADF tests for trend
- They are the same test with different names
- KPSS only works on daily data
Correct answer: KPSS null hypothesis is stationarity; ADF null is non-stationarity
In KPSS, the null hypothesis is that the series is stationary, so a significant result means non-stationarity — the opposite of ADF.
Question 6: Which transformation is commonly applied to stabilize variance before differencing?
- Logarithmic transformation (Correct answer)
- Z-score normalization
- Min-max scaling
- Fourier transformation
Correct answer: Logarithmic transformation
A log transform compresses large values and reduces heteroscedasticity, stabilizing the variance before trend removal.
Time Series Analysis Stationarity and Differencing 1
A stationary time series is characterized by which of the following?