ISYE 6402 Midterm 2 TF and MC Questions and Answers |
spring 2026 | 100% Correct – GT.
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Section 1: Stationarity, Autocorrelation, and Seasonal Adjustment
Instructions: Review each statement and the provided answer. Study the technical rationale to deepen
your understanding of time series statistical theory.
1. Strong stationarity implies weak (second-order) stationarity, provided that the first and second moments of the process exis
Answer: True Rationale: Strong stationarity implies that the joint distribution is invariant to time shifts, which includes the first two
moments (mean and variance) if they exist.
2. For a stationary process, the Autocorrelation Function (ACF) at lag kkk is always equal to the ACF at lag −k-k−k .
Answer: True Rationale: The ACF is an even function, meaning ρ(k)=ρ(−k)\rho(k) = \rho(-k)ρ(k)=ρ(−k). This symmetry is a
fundamental property of the autocovariance of stationary processes.
3. If a time series follows a Pure Seasonal AR(1) process with period sss , the non-seasonal PACF will show significant spikes at
lags 1,2,...,s−11, 2, ..., s-11,2,...,s−1 .
spring 2026 | 100% Correct – GT.
_
Section 1: Stationarity, Autocorrelation, and Seasonal Adjustment
Instructions: Review each statement and the provided answer. Study the technical rationale to deepen
your understanding of time series statistical theory.
1. Strong stationarity implies weak (second-order) stationarity, provided that the first and second moments of the process exis
Answer: True Rationale: Strong stationarity implies that the joint distribution is invariant to time shifts, which includes the first two
moments (mean and variance) if they exist.
2. For a stationary process, the Autocorrelation Function (ACF) at lag kkk is always equal to the ACF at lag −k-k−k .
Answer: True Rationale: The ACF is an even function, meaning ρ(k)=ρ(−k)\rho(k) = \rho(-k)ρ(k)=ρ(−k). This symmetry is a
fundamental property of the autocovariance of stationary processes.
3. If a time series follows a Pure Seasonal AR(1) process with period sss , the non-seasonal PACF will show significant spikes at
lags 1,2,...,s−11, 2, ..., s-11,2,...,s−1 .
