Question 1

What type of model is most useful for modeling volatility of financial data?&#10;A)VEC&#10;B)VAR&#10;C)ARCH(1)&#10;D)ARDL(1)

Accepted Answer

ARCH (Autoregressive Conditional Heteroskedasticity) model is most useful for modeling the volatility of financial data as it takes into account the error term volatility, which is found to be time-varying in financial data. VEC and VAR models are useful for modeling time-series data with multiple variables and their causal relationships, but they do not account for volatility specifically. ARDL (Auto-Regressive Distributed Lag) model is useful for analyzing the long-run relationships between variables in a time-series context, but it does not address volatility specifically.

Question 2

In an ARCH(1)model E(y_t|x_t-1)has a _____________ distribution while E(y_t)has a ____________ distribution. A)leptokuric,normal B)binomial,leptokuric C)normal,binomial D)normal,leptokuric

Accepted Answer

In an ARCH(1) model, the conditional mean function E(y_t|x_t-1) follows a normal distribution as it is a linear combination of the dependent variable and the lagged residuals, which are also normally distributed. On the other hand, the unconditional mean function E(y_t) follows a leptokurtic distribution as it involves the variance of the error term that is heteroscedastic and exhibits heavy tails. Therefore, the best choice is D, where the first blank is filled with normal and the second blank is filled with leptokuric.

Question 3

Suppose there is a series,Y_t,modeled by the following three equations: y_t = $\phi$ +e_t
E_t|I_t-1 N(0h_t)
H_t = $\alpha$ ₀ + $\alpha$ ₁ e²_t-1, $\alpha$ ₀ $\gt$ 0 ≤ $\alpha$ ₁ $\lt$ 1
This model is classified as a(n)

A)ARCH(1)
B)ECM
C)ARDL(1)
D)VAR

ARCH(1)

Accepted Answer

The model described is an ARCH(1) model, which stands for Autoregressive Conditional Heteroskedasticity. It is characterized by the variance of the error term being dependent on past squared errors, as shown in the equation for H_t.

Question 4

How are ARCH models estimated?&#10;A)OLS&#10;B)2SLS&#10;C)GLS&#10;D)ML

Accepted Answer

ARCH models are estimated using Maximum Likelihood (ML) estimation.

Question 5

If you reject the null hypothesis when testing for ARCH effects,what should you conclude?&#10;A)the variance changes over time&#10;B)the variance is constant&#10;C)the mean is constant&#10;D)the mean varies over time

Accepted Answer

If the null hypothesis (that there are no ARCH effects) is rejected, it means that the variance is not constant and changes over time.

Question 6

What is the primary advantage of a GARCH model rather than an ARCH model?&#10;A)fewer parameters to be estimated&#10;B)fewer assumptions required&#10;C)normally distributed estimators&#10;D)lower variance of estimates

Accepted Answer

GARCH models (Generalized Autoregressive Conditional Heteroskedasticity) include lagged conditional variances in addition to lagged squared errors, allowing for fewer parameters to be estimated compared to ARCH (Autoregressive Conditional Heteroskedasticity) models, which only include lagged squared errors. This efficiency in parameter estimation is a primary advantage of GARCH models.

Question 7

In a GARCH(p,q)model,what does the q indicate? A)the number of lagged h terms B)the number of lagged e² terms C)the number of endogenous variables in a system D)the number of excluded exogenous variables that can be instruments

Accepted Answer

In a GARCH(p,q) model, the q indicates the number of lagged e² terms. These terms capture the information about the past squared error terms and past variances, which are used to model the time-varying volatility in the series. The number of lagged h terms is indicated by p, which captures the information about the past conditional variances. The other options (C and D) are not relevant to the GARCH model.

Question 8

What does the T in T-ARCH stand for and when is it used?&#10;A)threshold,used to model asymmetric effects&#10;B)two stage,used to model indirect effects&#10;C)time,used to model time varying heteroskedasticity&#10;D)total,used to model total variance

Accepted Answer

The T in T-ARCH stands for "threshold" and is used to model asymmetric effects.

Question 9

Suppose there is a series,Y_t,modeled by the following three equations: y_t = $\phi$ +e_t
E_t|I_t-1 N(0h_t)
H_t = $\alpha$ ₀ + $\alpha$ ₁ e²_t-1, $\alpha$ ₀ $\gt$ 0 ≤ $\alpha$ ₁ $\lt$ 1
This model is classified as a(n)

A)ARCH(1)
B)ECM
C)ARDL(1)
D)VAR

ARCH(1)

Accepted Answer

Equation 2 specifies that the error term follows a normal distribution conditioned on the information available at time t-1, hence it is conditionally normal.

Question 10

When compared to a normal distribution,what does it mean for a distribution to be leptokuric?&#10;A)flatter around the mean and fatter tails&#10;B)more peaked around mean and fatter tails&#10;C)more peaked around mean and larger variance&#10;D)flatter around mean and larger variance

Accepted Answer

A leptokurtic distribution has a higher peak and thicker tails than a normal distribution, which means it is more peaked around the mean and has fatter tails.

Question 11

What does ARCH abbreviate?&#10;A)autoregressive conditional heteroskedastic&#10;B)alternative regression creating homoscedasticity&#10;C)all regression characteristic hierarchy&#10;D)abbreviated regular consistent hypothesis

Accepted Answer

The answer of What does ARCH abbreviate?&#10;A)autoregressive conditional heteroskedastic&#10;B)alternative regression...

Question 12

What does it mean for a model to be GARCH-in-mean?&#10;A)the mean and variance both move over time but are independent&#10;B)the mean is constant but variance changes over time&#10;C)the mean increases while variance is constant&#10;D)the mean increases with the variance

Accepted Answer

The answer of What does it mean for a model...

Question 13

Which test is commonly performed to check for the presence of ARCH effects?&#10;A)Chow test&#10;B)Wald test&#10;C)LM&#10;D)F-test

Accepted Answer

The answer of Which test is commonly performed to check...

Question 14

A model with the following conditional variance function is what type of model? h_t= $\alpha$ ₀ +$\alpha$₁ e²_t-1 + $\alpha$ ₂ e²_t-2 + +$\alpha$₃ e²_t-3 A)ARCH(3) B)ARDL(2) C)ARDL(3) D)VAR

Accepted Answer

The answer of A model with the following conditional variance...

Question 15

In a GARCH(p,q)model,what does the p indicate? A)the number of lagged h terms B)the number of lagged e² terms C)the number of endogenous variables in a system D)the number of excluded exogenous variables that can be instruments

Accepted Answer

The answer of In a GARCH(p,q)model,what does the p indicate?&#10;A)the...

Deck 15: Time-Varying Volatility and Arch Models