ISYE 6402 Official Midterm 1 MC | Questions and
ANSWERs - Spring 2026 | 100% Correct - GT
COMPREHENSIVE PRACTICE EXAM: 100+
QUESTIONS WITH RATIONALES
SECTION 1: STATIONARITY AND WHITE NOISE (Questions 1-20)
Q1. A time series is weakly stationary if:
A) Its mean and variance are constant over time, and autocovariance depends only on lag
B) Its joint probability distribution is time-invariant
C) It contains no trend or seasonality
D) All roots of the characteristic equation lie outside the unit circle
Correct ANSWER: A
Rationale: Weak stationarity (covariance stationarity) requires constant mean, constant variance, and
autocovariance that depends only on the time lag between observations, not on absolute time. Strict
stationarity requires the joint distribution to be time-invariant, which is a stronger condition .
Q2. For a stationary time series, the autocorrelation function at lag 0 is:
A) 0
B) Between -1 and 1
C) 1
D) Undefined
,Correct ANSWER: C
Rationale: By definition, the correlation of any series with itself at the same time point (lag 0) is always
1. This is true for all stationary processes .
Q3. True or False: A random walk process Yt = Yt-1 + εt is stationary.
Correct ANSWER: False
Rationale: The variance of a random walk grows linearly with time (Var(Yt) = tσ²), violating the constant
variance requirement for stationarity. Additionally, the autocovariance depends on time (t), not just lag .
Q4. Which of the following is NOT a necessary condition for weak stationarity?
A) Constant mean
B) Constant variance
C) Normal distribution of errors
D) Autocovariance depends only on lag
Correct ANSWER: C
Rationale: Weak stationarity does not require normality; it only requires constant first and second
moments (mean, variance, and covariance structure). Normality is a distributional assumption, not a
stationarity condition .
Q5. The AR(1) process Yt = 0.9Yt-1 + εt is:
A) Stationary
B) Non-stationary with a unit root
,Correct ANSWER: A
Rationale: For an AR(1) process, stationarity requires |φ| < 1. Since 0.9 < 1, this process is stationary.
The ACF decays exponentially, and the effects of past shocks diminish over time .
Q6. Which of the following statements about white noise is TRUE?
A) It has a constant mean, constant variance, and zero autocorrelation at all non-zero lags
B) It is always normally distributed
C) It is non-stationary
D) Its variance increases over time
Correct ANSWER: A
Rationale: A white noise process is characterized by E[at] = 0, Var(at) = σ² (constant), and Cov(at, at-k) =
0 for all k ≠ 0. White noise does NOT require normality (though i.i.d. normal white noise is common). It is
stationary by definition .
Q7. In an ACF plot, non-stationarity is typically indicated by:
A) A single significant spike at lag 1
B) Alternating positive and negative spikes
C) Slowly decaying spikes that remain significant for many lags
D) No significant spikes at any lag
Correct ANSWER: C
, Rationale: Non-stationary series typically show ACF patterns that decay very slowly, remaining
significant for many lags, indicating the need for differencing. Stationary series typically show ACF values
that decay exponentially to zero or cut off after a certain lag .
Q8. True or False: Differencing a non-stationary series once always makes it stationary.
Correct ANSWER: False
Rationale: Some non-stationary processes require multiple differences (e.g., quadratic trends).
Additionally, over-differencing can introduce non-invertibility and other problems. Some series with
deterministic trends are better handled by detrending rather than differencing .
Q9. The KPSS test has a null hypothesis of:
A) Stationarity
B) Unit root (non-stationarity)
C) No autocorrelation
D) Normality
Correct ANSWER: A
Rationale: The KPSS test is designed with a null hypothesis of stationarity. In contrast, the ADF test has a
null hypothesis of a unit root (non-stationarity). Using both tests together provides stronger evidence
about the stationarity properties of a series .
Q10. A Gaussian time series with time-varying mean:
A) Is always stationary
B) Cannot be Gaussian if the mean varies
C) Is non-stationary even though the distribution at each time may be normal
D) Is stationary if the variance is constant
ANSWERs - Spring 2026 | 100% Correct - GT
COMPREHENSIVE PRACTICE EXAM: 100+
QUESTIONS WITH RATIONALES
SECTION 1: STATIONARITY AND WHITE NOISE (Questions 1-20)
Q1. A time series is weakly stationary if:
A) Its mean and variance are constant over time, and autocovariance depends only on lag
B) Its joint probability distribution is time-invariant
C) It contains no trend or seasonality
D) All roots of the characteristic equation lie outside the unit circle
Correct ANSWER: A
Rationale: Weak stationarity (covariance stationarity) requires constant mean, constant variance, and
autocovariance that depends only on the time lag between observations, not on absolute time. Strict
stationarity requires the joint distribution to be time-invariant, which is a stronger condition .
Q2. For a stationary time series, the autocorrelation function at lag 0 is:
A) 0
B) Between -1 and 1
C) 1
D) Undefined
,Correct ANSWER: C
Rationale: By definition, the correlation of any series with itself at the same time point (lag 0) is always
1. This is true for all stationary processes .
Q3. True or False: A random walk process Yt = Yt-1 + εt is stationary.
Correct ANSWER: False
Rationale: The variance of a random walk grows linearly with time (Var(Yt) = tσ²), violating the constant
variance requirement for stationarity. Additionally, the autocovariance depends on time (t), not just lag .
Q4. Which of the following is NOT a necessary condition for weak stationarity?
A) Constant mean
B) Constant variance
C) Normal distribution of errors
D) Autocovariance depends only on lag
Correct ANSWER: C
Rationale: Weak stationarity does not require normality; it only requires constant first and second
moments (mean, variance, and covariance structure). Normality is a distributional assumption, not a
stationarity condition .
Q5. The AR(1) process Yt = 0.9Yt-1 + εt is:
A) Stationary
B) Non-stationary with a unit root
,Correct ANSWER: A
Rationale: For an AR(1) process, stationarity requires |φ| < 1. Since 0.9 < 1, this process is stationary.
The ACF decays exponentially, and the effects of past shocks diminish over time .
Q6. Which of the following statements about white noise is TRUE?
A) It has a constant mean, constant variance, and zero autocorrelation at all non-zero lags
B) It is always normally distributed
C) It is non-stationary
D) Its variance increases over time
Correct ANSWER: A
Rationale: A white noise process is characterized by E[at] = 0, Var(at) = σ² (constant), and Cov(at, at-k) =
0 for all k ≠ 0. White noise does NOT require normality (though i.i.d. normal white noise is common). It is
stationary by definition .
Q7. In an ACF plot, non-stationarity is typically indicated by:
A) A single significant spike at lag 1
B) Alternating positive and negative spikes
C) Slowly decaying spikes that remain significant for many lags
D) No significant spikes at any lag
Correct ANSWER: C
, Rationale: Non-stationary series typically show ACF patterns that decay very slowly, remaining
significant for many lags, indicating the need for differencing. Stationary series typically show ACF values
that decay exponentially to zero or cut off after a certain lag .
Q8. True or False: Differencing a non-stationary series once always makes it stationary.
Correct ANSWER: False
Rationale: Some non-stationary processes require multiple differences (e.g., quadratic trends).
Additionally, over-differencing can introduce non-invertibility and other problems. Some series with
deterministic trends are better handled by detrending rather than differencing .
Q9. The KPSS test has a null hypothesis of:
A) Stationarity
B) Unit root (non-stationarity)
C) No autocorrelation
D) Normality
Correct ANSWER: A
Rationale: The KPSS test is designed with a null hypothesis of stationarity. In contrast, the ADF test has a
null hypothesis of a unit root (non-stationarity). Using both tests together provides stronger evidence
about the stationarity properties of a series .
Q10. A Gaussian time series with time-varying mean:
A) Is always stationary
B) Cannot be Gaussian if the mean varies
C) Is non-stationary even though the distribution at each time may be normal
D) Is stationary if the variance is constant
