ISYE 6402 Final Exam: Time Series Analysis Verified
and Latest Questions and Answers - Georgia Tech
1. Which of the following is a condition for a time series to be weakly
stationary?
A. The autocovariance depends only on the absolute time points.
B. The variance increases linearly with time.
C. The mean is constant over time.
D. The series must follow a normal distribution.
Answer: C
Explanation: Weak stationarity requires a constant mean, constant variance, and an
autocovariance that depends only on the lag, not the specific time point.
2. In an AR(p) model, which tool is primarily used to identify the order p?
A. Partial Autocorrelation Function (PACF)
B. Autocorrelation Function (ACF)
C. Periodogram
D. Q-Q Plot
Answer: A
Explanation: The PACF of an AR(p) process cuts off after lag p, making it the ideal tool for
identifying the order of an autoregressive process.
,3. For a Moving Average process of order q, MA(q), what is the behavior of the
ACF?
A. It decays exponentially to zero.
B. It shows a sine wave pattern.
C. It remains constant for all lags.
D. It cuts off after lag q.
Answer: D
Explanation: An MA(q) process has an ACF that is zero for all lags greater than q.
4. What does the Augmented Dickey-Fuller (ADF) test evaluate?
A. Whether the residuals are white noise.
B. The lag length of a VAR model.
C. Whether the series has a constant variance.
D. The presence of a unit root in the series.
Answer: D
Explanation: The ADF test is a standard statistical test used to determine if a time series is
non-stationary due to a unit root.
5. In the context of model selection, how does BIC differ from AIC?
A. BIC does not penalize the number of parameters.
B. BIC has a heavier penalty for the number of parameters than AIC.
C. AIC is only used for AR models, while BIC is for MA models.
D. BIC always selects more complex models than AIC.
Answer: B
Explanation: The Bayesian Information Criterion (BIC) uses a penalty term based on the
logarithm of the sample size, which is usually stricter than the AIC penalty.
, 6. What is the effect of applying a first-difference transformation to a Random
Walk process?
A. It becomes a Moving Average process.
B. The variance becomes infinite.
C. It results in a deterministic trend.
D. It becomes a White Noise process.
Answer: D
Explanation: A Random Walk is defined as Y_t = Y_{t-1} + e_t. Subtracting Y_{t-1} leaves
e_t, which is white noise.
7. In a SARIMA(p,d,q)x(P,D,Q)s model, what does the ‘s’ represent?
A. The seasonal period (e.g., 12 for monthly).
B. The significance level of the test.
C. The smoothing constant.
D. The number of exogenous variables.
Answer: A
Explanation: ‘s’ denotes the seasonal frequency or period of the time series data.
8. Which property ensures that an MA process can be represented as an infinite-
order AR process?
A. Stationarity
B. Causality
C. Ergodicity
D. Invertibility
Answer: D
Explanation: Invertibility allows an MA process to be written as an AR(infinity) process,
provided the roots of the MA polynomial lie outside the unit circle.
and Latest Questions and Answers - Georgia Tech
1. Which of the following is a condition for a time series to be weakly
stationary?
A. The autocovariance depends only on the absolute time points.
B. The variance increases linearly with time.
C. The mean is constant over time.
D. The series must follow a normal distribution.
Answer: C
Explanation: Weak stationarity requires a constant mean, constant variance, and an
autocovariance that depends only on the lag, not the specific time point.
2. In an AR(p) model, which tool is primarily used to identify the order p?
A. Partial Autocorrelation Function (PACF)
B. Autocorrelation Function (ACF)
C. Periodogram
D. Q-Q Plot
Answer: A
Explanation: The PACF of an AR(p) process cuts off after lag p, making it the ideal tool for
identifying the order of an autoregressive process.
,3. For a Moving Average process of order q, MA(q), what is the behavior of the
ACF?
A. It decays exponentially to zero.
B. It shows a sine wave pattern.
C. It remains constant for all lags.
D. It cuts off after lag q.
Answer: D
Explanation: An MA(q) process has an ACF that is zero for all lags greater than q.
4. What does the Augmented Dickey-Fuller (ADF) test evaluate?
A. Whether the residuals are white noise.
B. The lag length of a VAR model.
C. Whether the series has a constant variance.
D. The presence of a unit root in the series.
Answer: D
Explanation: The ADF test is a standard statistical test used to determine if a time series is
non-stationary due to a unit root.
5. In the context of model selection, how does BIC differ from AIC?
A. BIC does not penalize the number of parameters.
B. BIC has a heavier penalty for the number of parameters than AIC.
C. AIC is only used for AR models, while BIC is for MA models.
D. BIC always selects more complex models than AIC.
Answer: B
Explanation: The Bayesian Information Criterion (BIC) uses a penalty term based on the
logarithm of the sample size, which is usually stricter than the AIC penalty.
, 6. What is the effect of applying a first-difference transformation to a Random
Walk process?
A. It becomes a Moving Average process.
B. The variance becomes infinite.
C. It results in a deterministic trend.
D. It becomes a White Noise process.
Answer: D
Explanation: A Random Walk is defined as Y_t = Y_{t-1} + e_t. Subtracting Y_{t-1} leaves
e_t, which is white noise.
7. In a SARIMA(p,d,q)x(P,D,Q)s model, what does the ‘s’ represent?
A. The seasonal period (e.g., 12 for monthly).
B. The significance level of the test.
C. The smoothing constant.
D. The number of exogenous variables.
Answer: A
Explanation: ‘s’ denotes the seasonal frequency or period of the time series data.
8. Which property ensures that an MA process can be represented as an infinite-
order AR process?
A. Stationarity
B. Causality
C. Ergodicity
D. Invertibility
Answer: D
Explanation: Invertibility allows an MA process to be written as an AR(infinity) process,
provided the roots of the MA polynomial lie outside the unit circle.
