Deck 10: Regression With Time Series Data: Stationary Variables

Question 1

If you have a times series data set with 100 years worth of data that you use to estimate a distributed lag model of order 3,how many degrees of freedom will you have for hypothesis testing on estimated coefficients?

A)93
B)95
C)99
D)100

Answer 1

A

Question 2

When a lagged dependent variable is included as a regressor,we must use a weaker form of assumption TSMR2 that allows the error term to be correlated with future values of explanatory variables,but not present or past values.What implications does this weaker assumption have for our regressors?

A)biased,but consistent
B)unbiased,but no longer BLUE
C)unbiased,but no longer linear
D)biased,but with minimum variance

Answer 2

A

Question 3

Which of the following is NOT a reason nonlinear least squares is used to estimate an AR(1)model?

A)linear least squares is not possible since the transformation that allows the new error term to be uncorrelated is no longer linear in parameters
B)using OLS to estimate the untransformed model provides incorrect standard errors
C)the algorithmic nonlinear optimization is less complicated to compute when error terms are correlated
D)minimizing the sum of squares of uncorrelated error terms produces an estimator that is unbiased and consistent

Answer 3

C

Question 4

When using the LM test for serial correlation,what is the null hypothesis?

A)it depends on the model specification
B)no serial correlation is present
C)statistically significant serial correlation with the first lag
D)statistically significant serial correlation with unspecified lag

Question 5

Using the notation ARDL(p,q)what does q represent?

A)the number of lagged dependent variables included as explanatory variables
B)the number of lagged explanatory variables included
C)the frequency of the time series
D)the degree or integration in the error term

Question 6

Which of the following is an example of an autoregressive distributed lag model?

A)y_t = f(x_t,x_t-1,x_t-2……. )
B)y_t = f(y_t-1,x_t,x_t-1,x_t-2…)
C)y_t = f(x_t,x²_t,x³_t)
D)y_t = f(x_t)+ g(e_t-1)

Question 7

Which of the following is an AR(3)model?

A)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
B)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
C)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ v_t
D)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + v_t

Question 8

Using the notation ARDL(p,q)what does p represent?

A)the number of lagged dependent variables included as explanatory variables
B)the number of lagged explanatory variables included
C)the frequency of the time series
D)the degree or integration in the error term

Question 9

Which of the following is an ARDL(3,3)model?

A)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
B)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
C)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ v_t
D)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + v_t

Question 10

Which of the following is not a valid criterion for choosing p and q in an ARDL model?

A)fewest number of lags that eliminates serial correlation
B)statistical significance of coefficient estimates
C)minimization of AIC and SC
D)maximization of R²

Question 11

If you use a times series data set with 100 years worth of data to estimate a distributed lag model of order 5,how many observations will you have for estimation?

A)100
B)5
C)95
D)105

Question 12

Which model below has an autocorrelated error term?

A)y_t = f(x_t,x_t-1,x_t-2……. )
B)y_t = f(y_t-1,x_t,x_t-1,x_t-2…)
C)y_t = f(x_t,x²_t,x³_t)
D)y_t = f(x_t)+ g(e_t-1)

Question 13

Which of the following is NOT true of Newey-West standard errors?

A)allows valid inference despite the presence of serial correlation
B)does not require knowledge of structure of serial correlation
C)valid when estimated using stationary data
D)always produce smaller standard error estimates,which makes them the BLUE estimator

Question 14

When autocorrelation is present,which assumption of the linear regression model is incorrect?

A)E(e_t)=0
B)var (e_t)= $\sigma$ ²
C)cov(e_t,e_s)=0,t≠s
D)e_t N(0, $\sigma$ ²)

Question 15

What are the consequences of ignoring or failing to recognize serial correlation?

A)biased,but consistent
B)unbiased,but no longer BLUE
C)unbiased,but no longer linear
D)biased,but with minimum variance

Question 16

Finite distributed lag models are most useful for

A)forecasting and economic policy analysis
B)testing hypotheses and measuring economic dynamics
C)measuring impacts and optimizing economic outcomes
D)measuring autocorrelation and autoregressive dynamics

Question 17

Which of the following is an ARDL (1,3)model?

A)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
B)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
C)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ v_t
D)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + v_t

Question 18

Which assumption is most likely to be violated with times series data:

A)E(e_t)=0
B)var (e_t)= $\sigma$ ²
C)cov(e_t,e_s)=0,t≠s
D)e_t N(0, $\sigma$ ²)

Question 19

What is second order sample autocorrelation?

A)correlation between a mean and the second moment of the sample distribution
B)a test statistic distributed N(0, $\sigma$ )
C)correlation between observations that are two time periods apart
D)correlation between the dependent variable and a squared explanatory variable

Question 20

When performing a LM test for serial correlation,how is the test statistic distributed when the null hypothesis is true?

A) $\chi$ ²
B)t_n-1
C)F
D)z

Question 21

AR models are primarily used for

A)forecasting
B)smoothing data over time
C)policy evaluation
D)hypothesis testing

Question 22

How are AR and exponential smoothing models similar?

A)both use only previous observations of the same variable for forecasting future values
B)both incorporate past information in the form of moving averages of multiple varaibles over time
C)both incorporate information on current values of all relevant variables
D)they generate forecasts with identically distributed expected values

Question 23

Which of the following is equivalent to L³y_t?

A)y _t-3
B)3L² y _t
C)Ly_t L²y_t
D)Ly³_t

Question 24

Which of the following is an ARDL(2,0)model?

A)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
B)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\delta$ ₀x_t + $\delta$ ₁x_t-1+ $\delta$ ₂x_t-2+ $\delta$ ₃x_t-3 + v_t
C)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + $\delta$ ₁x_t-1+ v_t
D)y_t = $\delta$ + $\theta$ ₁y_t-1+ $\theta$ ₂y_t-2 + $\theta$ ₃y_t-3 + $\delta$ ₀x_t + v_t