ISYE 6402 Exam 4: Time Series Analysis Verified
and Latest Questions and Answers - Georgia Tech
1. What is the primary motivation for using ARCH and GARCH models in
finance?
A. To model linear trends in the mean of the series
B. To eliminate seasonality from monthly data
C. To account for volatility clustering and time-varying variance
D. To model the relationship between two non-stationary variables
Answer: C
Explanation: ARCH and GARCH models are designed to capture ‘volatility clustering’,
where large changes tend to be followed by large changes, reflecting time-varying
conditional variance.
2. In a GARCH(1,1) model, defined as σ²_t = ω + αε²_{t-1} + βσ²_{t-1}, what is the
condition for the process to be wide-sense stationary?
A. α + β = 1
B. ω = 0
C. α < 1 and β > 1
D. α + β < 1
Answer: D
Explanation: For a GARCH(1,1) process to be covariance stationary, the sum of the ARCH
coefficient (α) and the GARCH coefficient (β) must be less than 1.
,3. Which of the following describes the ‘Leverage Effect’ in financial time series?
A. Volatility increases more after a positive shock than a negative shock
B. Volatility increases more after a negative shock than a positive shock
C. Returns are always positive when volatility is low
D. The mean of the series is dependent on the variance
Answer: B
Explanation: The leverage effect refers to the empirical observation that negative shocks
(bad news) often increase volatility more than positive shocks of the same magnitude.
4. Which model is specifically designed to handle the leverage effect?
A. ARCH(1)
B. GARCH(1,1)
C. EGARCH (Exponential GARCH)
D. VAR(1)
Answer: C
Explanation: EGARCH models the log of variance and includes a term that allows for
asymmetric responses to positive and negative shocks.
5. In a VAR(p) model, how many equations are estimated if there are ‘k’
variables?
A. k
B. p
C. 1
D. k * p
Answer: A
Explanation: A Vector Autoregression (VAR) model consists of a system of equations, one
for each variable in the system.
, 6. What is the primary purpose of an Impulse Response Function (IRF) in VAR
analysis?
A. To trace the effect of a one-time shock to one innovation on the current and future values of the
endogenous variables
B. To determine the optimal lag length
C. To test for stationarity of the vector process
D. To calculate the correlation between variables at lag 0
Answer: A
Explanation: IRFs are used to visualize how a shock to one variable propagates through
the system of equations over time.
7. If two variables are integrated of order 1, I(1), but a linear combination of
them is I(0), the variables are said to be:
A. Autoregressive
B. Cointegrated
C. Spuriously correlated
D. Differenced
Answer: B
Explanation: Cointegration occurs when non-stationary variables share a common long-
term equilibrium, resulting in a stationary linear combination.
8. The Vector Error Correction Model (VECM) is appropriate when:
A. Variables are I(0) and not cointegrated
B. Variables are I(1) and not cointegrated
C. Variables have different orders of integration
D. Variables are I(1) and cointegrated
Answer: D
Explanation: VECM is used for I(1) variables that are cointegrated, as it allows for both
short-run dynamics and long-run equilibrium adjustments.
and Latest Questions and Answers - Georgia Tech
1. What is the primary motivation for using ARCH and GARCH models in
finance?
A. To model linear trends in the mean of the series
B. To eliminate seasonality from monthly data
C. To account for volatility clustering and time-varying variance
D. To model the relationship between two non-stationary variables
Answer: C
Explanation: ARCH and GARCH models are designed to capture ‘volatility clustering’,
where large changes tend to be followed by large changes, reflecting time-varying
conditional variance.
2. In a GARCH(1,1) model, defined as σ²_t = ω + αε²_{t-1} + βσ²_{t-1}, what is the
condition for the process to be wide-sense stationary?
A. α + β = 1
B. ω = 0
C. α < 1 and β > 1
D. α + β < 1
Answer: D
Explanation: For a GARCH(1,1) process to be covariance stationary, the sum of the ARCH
coefficient (α) and the GARCH coefficient (β) must be less than 1.
,3. Which of the following describes the ‘Leverage Effect’ in financial time series?
A. Volatility increases more after a positive shock than a negative shock
B. Volatility increases more after a negative shock than a positive shock
C. Returns are always positive when volatility is low
D. The mean of the series is dependent on the variance
Answer: B
Explanation: The leverage effect refers to the empirical observation that negative shocks
(bad news) often increase volatility more than positive shocks of the same magnitude.
4. Which model is specifically designed to handle the leverage effect?
A. ARCH(1)
B. GARCH(1,1)
C. EGARCH (Exponential GARCH)
D. VAR(1)
Answer: C
Explanation: EGARCH models the log of variance and includes a term that allows for
asymmetric responses to positive and negative shocks.
5. In a VAR(p) model, how many equations are estimated if there are ‘k’
variables?
A. k
B. p
C. 1
D. k * p
Answer: A
Explanation: A Vector Autoregression (VAR) model consists of a system of equations, one
for each variable in the system.
, 6. What is the primary purpose of an Impulse Response Function (IRF) in VAR
analysis?
A. To trace the effect of a one-time shock to one innovation on the current and future values of the
endogenous variables
B. To determine the optimal lag length
C. To test for stationarity of the vector process
D. To calculate the correlation between variables at lag 0
Answer: A
Explanation: IRFs are used to visualize how a shock to one variable propagates through
the system of equations over time.
7. If two variables are integrated of order 1, I(1), but a linear combination of
them is I(0), the variables are said to be:
A. Autoregressive
B. Cointegrated
C. Spuriously correlated
D. Differenced
Answer: B
Explanation: Cointegration occurs when non-stationary variables share a common long-
term equilibrium, resulting in a stationary linear combination.
8. The Vector Error Correction Model (VECM) is appropriate when:
A. Variables are I(0) and not cointegrated
B. Variables are I(1) and not cointegrated
C. Variables have different orders of integration
D. Variables are I(1) and cointegrated
Answer: D
Explanation: VECM is used for I(1) variables that are cointegrated, as it allows for both
short-run dynamics and long-run equilibrium adjustments.
