If the current value is above the mean‑reverting level, the next forecast will:
Select an option first.
Correct answer: B — Decrease
Explanation: Above mean → predicted decline. Wrong options: A/C/D: Incorrect.
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Explanation: Standard assumption: E(error) = 0. Wrong options: B/C/D: Incorrect.
Question 167
A high lag coefficient close to 1 indicates:
Select an option first.
Correct answer: A — Strong persistence
Explanation: High coefficient → strong dependence on past values. Wrong options: B/C/D: Incorrect. I. General Time‑Series Concepts
Question 168
A random walk is:
Select an option first.
Correct answer: B — Non‑stationary
Explanation: Random walks drift → non‑stationary. Wrong options: A/C/D: Incorrect.
Question 169
A time series with constant variance but changing mean is:
Select an option first.
Correct answer: B — Non‑stationary
Explanation: Changing mean violates stationarity. Wrong options: A/C/D: Incorrect.
Question 170
A model with serially correlated errors violates:
Select an option first.
Correct answer: A — Independence assumption
Explanation: Serial correlation means the errors are related across time. This directly violates the assumption that errors must be independent of one another. Why the others are wrong: B: Linearity refers to the model being linear in parameters, not error behavior. C: Errors can be serially correlated and still be normally distributed. D: Serial correlation is about correlation over time, not variance patterns.
Question 171
A time series with no predictable pattern and no autocorrelation is best described as:
Select an option first.
Correct answer: A — White noise
Explanation: White noise is defined as a series with zero mean, constant variance, and no autocorrelation — essentially pure randomness. Why the others are wrong: B: A trend model has a predictable pattern. C: AR(1) implies dependence on past values. D: Seasonality implies repeating patterns, not randomness.
Question 172
A stationary AR(1) series will eventually converge toward:
Select an option first.
Correct answer: B — Its mean‑reverting level
Explanation: A stationary AR(1) process has a long‑run mean equal to ( b_0 / (1 - b_1) ). Over time, forecasts converge toward this mean‑reverting level. Why the others are wrong: A: Only converges to zero if the mean‑reverting level happens to be zero. C: Stationary processes do not diverge. D: Seasonality is unrelated unless explicitly modeled.
Question 173
A time series with a unit root is best described as:
Select an option first.
Correct answer: B — Non‑stationary
Explanation: Why right: A unit root implies the series does not have a stable mean and can wander over time. Why wrong: A: Stationary series do not have unit roots. C: Mean‑reverting series require |coefficient| < 1. D: White noise has no persistence.
Question 174
First‑differencing a time series is typically used to:
Select an option first.
Correct answer: B — Remove a unit root
Explanation: Why right: Differencing can turn a non‑stationary series with a unit root into a stationary one. Why wrong: A: Differencing removes trends. C: Seasonality is not created by differencing. D: Variance often decreases.
Question 175
A covariance‑stationary time series must have:
Select an option first.
Correct answer: A — Constant mean and constant variance
Explanation: Why right: Stationarity requires that mean and variance do not change over time. Why wrong: B/D: Trends violate constant mean. C: Unit root implies non‑stationarity.
Question 176
A random walk is an example of a process that:
Select an option first.
Correct answer: B — Has a unit root
Explanation: Why right: A random walk has a lag coefficient of 1, which is a unit root. Why wrong: A/C: Random walks do not have a stable mean. D: They include shocks each period.
Question 177
A series that steadily increases over time is most likely:
Select an option first.
Correct answer: B — Non‑stationary
Explanation: Why right: A persistent upward trend indicates non‑stationarity. Why wrong: A/C/D: These imply no trend or reversion.
Question 178
A stationary series has autocovariances that depend only on:
Select an option first.
Correct answer: B — The lag between observations
Explanation: Why right: For stationarity, the covariance depends only on the time gap, not the specific time. Why wrong: A/C/D: These are not defining features of stationarity.
Question 179
Using a non‑stationary series directly in regression often leads to:
Select an option first.
Correct answer: B — Spurious relationships
Explanation: Why right: Non‑stationarity can create misleadingly significant relationships. Why wrong: A/C/D: These are not typical outcomes.
Question 180
A random walk with drift differs from a pure random walk because it:
Select an option first.
Correct answer: B — Has a constant average change each period
Explanation: Why right: Drift adds a constant expected increment each period. Why wrong: A: Both have errors. C/D: Both are non‑stationary and persistent.
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