ISYE 6402: Time Series Analysis — Midterm 2
Practice Exam
Section 1: Fundamentals of Time Series Analysis (Questions 1–20)
1. A time series is stationary if its mean and variance are constant over time.
Answer: True
Explanation: Weak stationarity (covariance stationarity) requires constant mean, constant variance,
and autocovariance that depends only on the lag, not on time. Strict stationarity requires the full
joint distribution to be time‑invariant. Both definitions include constant mean and variance as key
conditions.
2. A random walk process Yt = Yt−1 + εt has a constant variance.
Answer: False
Explanation: The variance of a random walk grows linearly with time: Var(Yt) = tσ². This violates
the stationarity assumption of a finite, constant variance.
3. Consecutive observations in a white noise process are always independent.
Answer: False
Explanation: White noise is defined as a sequence of uncorrelated random variables with zero
mean and constant variance. Uncorrelated does not necessarily imply independence unless the
process is also Gaussian (normal).
4. The sample ACF at lag 0 is always equal to 1.
Answer: True
Explanation: By definition, the autocorrelation at lag 0 is the correlation of a variable with itself,
which equals 1.
5. A white noise process has zero auto-covariance for all lags including lag zero.
Answer: False
,Explanation: A white noise process has zero auto‑covariance for all nonzero lags, but at lag zero
the auto‑covariance equals the variance, which is non‑zero.
6. If a time series is Gaussian then it is non‑stationary.
Answer: False
Explanation: A Gaussian process can be either stationary or non‑stationary; the distributional form
(Gaussian) does not dictate whether the mean and variance are constant over time. Many stationary
processes (e.g., Gaussian white noise) are Gaussian.
7. The fairly regular fluctuations that occur within each year would be contained in the seasonal
component of a time series.
Answer: True
Explanation: Seasonal patterns are regular, repeating fluctuations that occur within fixed periods
such as days, weeks, months, or years.
8. A time series is defined as a sequence of data points measured at equally spaced time intervals.
Answer: True
Explanation: Time series data are characterized by observations taken sequentially at equally
spaced points in time.
9. Regression coefficients are considered a component of time series data.
Answer: False
Explanation: The classical components of a time series are trend, seasonality, cyclic variations,
and irregular (noise). Regression coefficients are parameters estimated in a regression model, not
a time series component.
10. Irregularity (or noise) in time series refers to random fluctuations that cannot be explained by
trend, seasonality, or cycles.
Answer: True
Explanation: The irregular component captures unpredictable, random variation after removing
systematic components such as trend, seasonality, and cycles.
,11. A time series plot is used to visualize data over time and identify patterns such as trend,
seasonality, and outliers.
Answer: True
Explanation: Time series plots (line plots) are the primary visual tool for examining temporal
patterns, including long‑term trends, repeating seasonal patterns, cyclic behavior, and unusual
observations.
12. Cross‑sectional data is the same as time series data.
Answer: False
Explanation: Cross‑sectional data captures multiple subjects at a single point in time, whereas time
series data tracks a single subject over many time points. The two are fundamentally different.
13. The decomposition of a time series separates it into trend, seasonality, and residual
components.
Answer: True
Explanation: Decomposition methods (e.g., classical decomposition, STL) partition a time series
into three components: trend‑cycle, seasonal, and remainder (residual).
14. STL decomposition stands for Seasonal and Trend decomposition using Loess.
Answer: True
Explanation: STL is a robust decomposition method that uses locally weighted regression (Loess)
to estimate the seasonal and trend components.
15. Granger causality is a method used to check if one time series can predict another.
Answer: True
Explanation: Granger causality tests whether past values of one series provide statistically
significant information about future values of another series beyond the information contained in
its own past.
16. The Box‑Jenkins methodology is primarily used to identify parameters of ARIMA models.
Answer: True
, Explanation: The Box‑Jenkins approach is a systematic method for identifying, estimating, and
diagnosing ARIMA models for time series forecasting.
17. ARIMA stands for Autoregressive Integrated Moving Average.
Answer: True
Explanation: ARIMA combines autoregressive (AR), integration (differencing), and moving
average (MA) components to model non‑stationary time series.
18. A time series with a clear upward trend over time is considered stationary.
Answer: False
Explanation: Stationarity requires a constant mean over time. A trending time series violates this
assumption and is non‑stationary.
19. The variance of a stationary time series must be finite and constant over time.
Answer: True
Explanation: Weak stationarity (covariance stationarity) requires the variance to be constant and
finite, and the autocovariance to depend only on the lag.
20. Autocovariance measures the linear relationship between a time series and its lagged values.
Answer: True
Explanation: Autocovariance at lag k is defined as γ(k) = Cov(Yt, Yt−k), capturing the linear
dependence between observations separated by k time periods.
Section 2: Stationarity, Unit Roots & Differencing (Questions 21–40)
21. Differencing the data might not make the series stationary in the presence of cointegration.
Answer: True
Practice Exam
Section 1: Fundamentals of Time Series Analysis (Questions 1–20)
1. A time series is stationary if its mean and variance are constant over time.
Answer: True
Explanation: Weak stationarity (covariance stationarity) requires constant mean, constant variance,
and autocovariance that depends only on the lag, not on time. Strict stationarity requires the full
joint distribution to be time‑invariant. Both definitions include constant mean and variance as key
conditions.
2. A random walk process Yt = Yt−1 + εt has a constant variance.
Answer: False
Explanation: The variance of a random walk grows linearly with time: Var(Yt) = tσ². This violates
the stationarity assumption of a finite, constant variance.
3. Consecutive observations in a white noise process are always independent.
Answer: False
Explanation: White noise is defined as a sequence of uncorrelated random variables with zero
mean and constant variance. Uncorrelated does not necessarily imply independence unless the
process is also Gaussian (normal).
4. The sample ACF at lag 0 is always equal to 1.
Answer: True
Explanation: By definition, the autocorrelation at lag 0 is the correlation of a variable with itself,
which equals 1.
5. A white noise process has zero auto-covariance for all lags including lag zero.
Answer: False
,Explanation: A white noise process has zero auto‑covariance for all nonzero lags, but at lag zero
the auto‑covariance equals the variance, which is non‑zero.
6. If a time series is Gaussian then it is non‑stationary.
Answer: False
Explanation: A Gaussian process can be either stationary or non‑stationary; the distributional form
(Gaussian) does not dictate whether the mean and variance are constant over time. Many stationary
processes (e.g., Gaussian white noise) are Gaussian.
7. The fairly regular fluctuations that occur within each year would be contained in the seasonal
component of a time series.
Answer: True
Explanation: Seasonal patterns are regular, repeating fluctuations that occur within fixed periods
such as days, weeks, months, or years.
8. A time series is defined as a sequence of data points measured at equally spaced time intervals.
Answer: True
Explanation: Time series data are characterized by observations taken sequentially at equally
spaced points in time.
9. Regression coefficients are considered a component of time series data.
Answer: False
Explanation: The classical components of a time series are trend, seasonality, cyclic variations,
and irregular (noise). Regression coefficients are parameters estimated in a regression model, not
a time series component.
10. Irregularity (or noise) in time series refers to random fluctuations that cannot be explained by
trend, seasonality, or cycles.
Answer: True
Explanation: The irregular component captures unpredictable, random variation after removing
systematic components such as trend, seasonality, and cycles.
,11. A time series plot is used to visualize data over time and identify patterns such as trend,
seasonality, and outliers.
Answer: True
Explanation: Time series plots (line plots) are the primary visual tool for examining temporal
patterns, including long‑term trends, repeating seasonal patterns, cyclic behavior, and unusual
observations.
12. Cross‑sectional data is the same as time series data.
Answer: False
Explanation: Cross‑sectional data captures multiple subjects at a single point in time, whereas time
series data tracks a single subject over many time points. The two are fundamentally different.
13. The decomposition of a time series separates it into trend, seasonality, and residual
components.
Answer: True
Explanation: Decomposition methods (e.g., classical decomposition, STL) partition a time series
into three components: trend‑cycle, seasonal, and remainder (residual).
14. STL decomposition stands for Seasonal and Trend decomposition using Loess.
Answer: True
Explanation: STL is a robust decomposition method that uses locally weighted regression (Loess)
to estimate the seasonal and trend components.
15. Granger causality is a method used to check if one time series can predict another.
Answer: True
Explanation: Granger causality tests whether past values of one series provide statistically
significant information about future values of another series beyond the information contained in
its own past.
16. The Box‑Jenkins methodology is primarily used to identify parameters of ARIMA models.
Answer: True
, Explanation: The Box‑Jenkins approach is a systematic method for identifying, estimating, and
diagnosing ARIMA models for time series forecasting.
17. ARIMA stands for Autoregressive Integrated Moving Average.
Answer: True
Explanation: ARIMA combines autoregressive (AR), integration (differencing), and moving
average (MA) components to model non‑stationary time series.
18. A time series with a clear upward trend over time is considered stationary.
Answer: False
Explanation: Stationarity requires a constant mean over time. A trending time series violates this
assumption and is non‑stationary.
19. The variance of a stationary time series must be finite and constant over time.
Answer: True
Explanation: Weak stationarity (covariance stationarity) requires the variance to be constant and
finite, and the autocovariance to depend only on the lag.
20. Autocovariance measures the linear relationship between a time series and its lagged values.
Answer: True
Explanation: Autocovariance at lag k is defined as γ(k) = Cov(Yt, Yt−k), capturing the linear
dependence between observations separated by k time periods.
Section 2: Stationarity, Unit Roots & Differencing (Questions 21–40)
21. Differencing the data might not make the series stationary in the presence of cointegration.
Answer: True
