Time Series Analysis Stationarity and Differencing

Question 1

A stationary time series is characterized by which of the following?

Accepted Answer

Constant mean, variance, and autocovariance over time

Answer

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)?

Accepted Answer

Augmented Dickey-Fuller (ADF) test

Answer

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)?

Accepted Answer

Constant mean and autocovariance that depends only on lag, not time

Answer

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?

Accepted Answer

Seasonal differencing subtracts the value from the same period in a prior season

Answer

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?

Accepted Answer

KPSS null hypothesis is stationarity; ADF null is non-stationarity

Answer

In KPSS, the null hypothesis is that the series is stationary, so a significant result means non-stationarity — the opposite of ADF.

Time Series Analysis Practice Test