Question 1

Unit root tests
A)use the standard normal distribution since they are based on the t-statistic.
B)cannot use the standard normal distribution for statistical inference.As a result the ADF statistic has its own special table of critical values.
C)can use the standard normal distribution only when testing that the level variable is stationary, but not the difference variable.
D)can use the standard normal distribution but only if HAC standard errors were computed.

Accepted Answer

Unit root tests, such as the Augmented Dickey Fuller (ADF) test, cannot use the standard normal distribution for statistical inference. Instead, the ADF statistic has its own special table of critical values. This is because the null hypothesis of the test assumes the presence of a unit root, which violates the assumptions of standard statistical tests.

Question 2

The coefficients of the VAR are estimated by
A)using a simultaneous estimation method such as TSLS.
B)maximum likelihood.
C)panel methods.
D)estimating each of the equations by OLS.

Accepted Answer

D

Question 3

A VAR with five variables, 4 lags and constant terms for each equation will have a total of
A)21 coefficients.
B)100 coefficients.
C)105 coefficients.
D)84 coefficients.

Accepted Answer

For each variable, there are 4 lags and a constant term, giving a total of 5 coefficients per equation. Since there are 5 variables in the VAR, there will be a total of 5 equations. Therefore, the total number of coefficients will be: 5 equations x (4 lags + 1 constant) x 5 variables = 105 coefficients.

Question 4

One advantage of forecasts based on a VAR rather than separately forecasting the variables involved is
A)that VAR forecasts are easier to calculate.
B)you typically have knowledge of future values of at least one of the variables involved.
C)it can help to make the forecasts mutually consistent.
D)that VAR involves panel data.

Accepted Answer

VAR can help to make the forecasts mutually consistent, ensuring that the relationship between the variables is taken into account in the forecasting process. This can lead to more accurate forecasts overall. Additionally, neither A, B nor D are true advantages of VAR over separate variable forecasting.

Question 5

A VAR allows you to test joint hypothesis that involve restrictions across multiple equations by
A)computing a z-statistic.
B)computing the BIC but not the AIC.
C)using a stability test.
D)computing an F-statistic.

Accepted Answer

To test joint hypothesis involving restrictions across multiple equations in a VAR model, we compute an F-statistic. This is because the null hypothesis is a joint hypothesis that involves restrictions and we want to compare the explained variation in the restricted versus unrestricted model. The F-statistic is used to test the significance of those restrictions.

Question 6

A multiperiod regression forecast h periods into the future based on an AR(p)is computed a. the same way as the iterated AR forecast.
b. by estimating the multiperiod regression $Y _ { t } = \delta _ { 0 } + \delta _ { 1 } Y _ { t - h } + \ldots + \delta _ { p } Y _ { t - p - h + 1 } + u _ { t }$, then using the estimated coefficients to compute the forecast $h$ periods in advance.
c. by estimating the multiperiod regression $Y _ { t } = \delta _ { 0 } + \delta _ { 1 } Y _ { t - h } + u _ { t }$, then using the estimate coefficients to comput the forecast h period in advance.
d. by first computing the one-period ahead forecast, next using that to compute the two-period ahead forecast, and so forth.

Accepted Answer

The answer of A multiperiod regression forecast h periods into...

Question 7

If Yt is I(2), then a. $\Delta ^ { 2 } Y _ { t }$ is stationary.
b. $Y _ { t }$ has a unit autoregressive root.
c. $\Delta Y _ { t }$ is stationary.
d. $Y _ { t }$ is stationary.

Accepted Answer

The answer of If Yt is I(2), then a. \(\Delta...

Question 8

The following is not a consequence of X_t and Y_t being cointegrated: A) if $X _ { t }$ and Y_t are both I(1) , then for some $\theta , Y _ { t } - \theta X _ { t } \text { is } I ( 0 )$ B) $X _ { t } \text { and } Y _ { t }$ have the same stochastic trend. C) in the expression $Y _ { t } - \theta X _ { t } , \theta$ is called the cointegrating coefficient. D) if $X _ { t } \text { and } Y _ { t }$ are cointegrated then integrating one of the variables gives you the same result as integrating the other.

Accepted Answer

Cointegration implies that a linear combination of the variables is stationary, not that integrating one variable gives the same result as integrating the other.

Question 9

Multiperiod forecasting with multiple predictors a. is the same as the iterated AR forecast method.
b. can use the iterated VAR forecast method.
c. will yield superior results when using the multiperiod regression forecast $h$ periods into the future based on $p$ lags of each $Y _ { t }$, rather than the iterated VAR forecast method.
d. will always yield superior results using the interated VAR since it takes all equations into account.

Accepted Answer

The answer of Multiperiod forecasting with multiple predictors a. is...

Question 10

In a VECM, a. past values of $Y _ { t } - \theta X _ { t }$ help to predict future values of $\Delta Y _ { t }$ and/or $\Delta X _ { t }$.
b. errors are corrected for serial correlation using the Cochrane-Orcutt method.
c. current values of $Y _ { t } - \theta X _ { t }$ help to predict future values of $\Delta Y _ { t }$ and/or $\Delta X _ { t }$.
d. VAR techniques, such as information criteria, no longer apply.

Accepted Answer

The answer of In a VECM, a. past values of...

Question 11

You can determine the lag lengths in a VAR
A)by using confidence intervals.
B)by using critical values from the standard normal table.
C)by using either F-tests or information criteria.
D)with the help from economic theory and institutional knowledge.

Accepted Answer

Lag lengths in a VAR can be determined through either F-tests or information criteria. Confidence intervals and critical values from the standard normal table are not used to determine lag lengths in a VAR. While economic theory and institutional knowledge may be helpful, they are not a systematic method for determining lag lengths.

Question 12

The biggest conceptual difference between using VARs for forecasting and using them for structural modeling is that
A)you need to use the Granger causality test for structural modeling.
B)structural modeling requires very specific assumptions derived from economic theory and institutional knowledge, of what is exogenous and what is not.
C)you can no longer use the information criteria to decide on the lag length.
D)structural modeling only allows a maximum of three equations in the VAR.

Accepted Answer

Structural modeling with VARs requires specific assumptions about exogenous and endogenous variables based on economic theory and institutional knowledge. Forecasting with VARs does not require these assumptions and can use information criteria for lag length selection. The Granger causality test may be used in both types of modeling. There is no maximum limit to the number of equations in a VAR, but the complexity of the model may make it difficult to estimate and interpret.

Question 13

The error term in a multiperiod regression
A)is serially correlated.
B)causes OLS to be inconsistent.
C)is serially correlated, but less so the longer the forecast horizon.
D)is serially uncorrelated.

Accepted Answer

The error term in a multiperiod regression is often serially correlated because past errors can influence future errors, especially in time series data.

Question 14

To test the null hypothesis of a unit root, the ADF test
A)has higher power than the so-called DF-GLS test.
B)uses complicated interative techniques.
C)cannot be calculated if the variable is integrated of order two or higher.
D)uses a t-statistic and a special critical value.

Accepted Answer

The ADF test uses a t-statistic and a special critical value to test the null hypothesis of a unit root. Choice A is incorrect because DF-GLS test has higher power than the ADF test. Choice B is incorrect because ADF test does not involve complicated iterative techniques. Choice C is incorrect because the ADF test can be used to test the null hypothesis of a unit root when the variable is integrated up to order two.

Question 15

The following is not an appropriate way to tell whether two variables are cointegrated
A)see if the two variables are integrated of the same order.
B)graph the series and see whether they appear to have a common stochastic trend.
C)perform statistical tests for cointegration.
D)use expert knowledge and economic theory.

Accepted Answer

The answer of The following is not an appropriate way...

Question 16

If $X _ { t } \text { and } Y _ { t }$ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is
A) BLUE
B) unbiased when using HAC standard errors.
C) unbiased even in small samples.
D) consistent.

Accepted Answer

The OLS estimator in a cointegrating regression is consistent, meaning it converges to the true parameter value as the sample size increases. However, it may not be unbiased in small samples.

Question 17

Under the VAR assumptions, the OLS estimators are
A)consistent and have a joint normal distribution even in small samples.
B)BLUE.
C)consistent and have a joint normal distribution in large samples.
D)unbiased.

Accepted Answer

The answer of Under the VAR assumptions, the OLS estimators...

Question 18

A vector autoregression a. is the ADL model with an AR process in the error term.
b. is the same as a univariate autoregression.
c. is a set of $k$ time series regressions, in which the regressors are lagged values of all $k$ series.
d. involves errors that are autocorrelated but can be written in vector format.

Accepted Answer

The answer of A vector autoregression a. is the ADL...

Question 19

The order of integration a. can never be zero.
b. is the number of times that the series needs to be differenced for it to be stationary.
c. is the value of $\phi _ { 1 }$ in the quasi difference $\left( \Delta Y _ { t } - \phi _ { 1 } Y _ { t - 1 } \right)$.
d. depends on the number of lags in the VAR specification.

Accepted Answer

The answer of The order of integration a. can never...

Question 20

$\Delta ^ { 2 } Y _ { t }$
A) $= \Delta Y _ { t } - \Delta Y _ { t-1 }$
B) $= Y _ { t } ^ { 2 } - Y _ { t - 1 } ^ { 2 }$
C) $= \Delta Y _ { t } - \Delta Y _ { t - 2 }$
D) $= Y _ { t } - Y _ { t - 2 }$

Accepted Answer

The second difference $\Delta ^ { 2 } Y _ { t }$ is defined as the difference of consecutive first differences: $\Delta Y _ { t } - \Delta Y _ { t-1 }$.

Quiz 16: Additional Topics in Time Series Regression

Unit root tests

The coefficients of the VAR are estimated by

A VAR with five variables, 4 lags and constant terms for each equation will have a total of

One advantage of forecasts based on a VAR rather than separately forecasting the variables involved is

A VAR allows you to test joint hypothesis that involve restrictions across multiple equations by

If Yt is I(2), then a. Δ2Yt\Delta ^ { 2 } Y _ { t }Δ2Yt​ is stationary. b. YtY _ { t }Yt​ has a unit autoregressive root. c. ΔYt\Delta Y _ { t }ΔYt​ is stationary. d. YtY _ { t }Yt​ is stationary.

The following is not a consequence of Xt and Yt being cointegrated:

You can determine the lag lengths in a VAR

The biggest conceptual difference between using VARs for forecasting and using them for structural modeling is that

The error term in a multiperiod regression

To test the null hypothesis of a unit root, the ADF test

The following is not an appropriate way to tell whether two variables are cointegrated

If Xt and YtX _ { t } \text { and } Y _ { t }Xt​ and Yt​ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is

Under the VAR assumptions, the OLS estimators are

Δ2Yt\Delta ^ { 2 } Y _ { t }Δ2Yt​

If Yt is I(2), then a. $\Delta ^ { 2 } Y _ { t }$ is stationary. b. $Y _ { t }$ has a unit autoregressive root. c. $\Delta Y _ { t }$ is stationary. d. $Y _ { t }$ is stationary.

The following is not a consequence of X_t and Y_t being cointegrated:

If $X _ { t } \text { and } Y _ { t }$ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is

$\Delta ^ { 2 } Y _ { t }$