Deck 18: Advanced Time Series Topics

Question 1

Let {(yt,zt): t = …,2,1,0,1,2,…} be a bivariate time series process.The model: y_t= α + β_oz_t + β₁z_{t - 1} + β₂z_{t - 2} + …..+ u_t,where t = ….. ,-2,-1,0,1,2,……,represents a(n):

A)moving average model.
B)ARIMA model.
C)finite distributed lag model.
D)infinite distributed lag model.

Answer 1

D

Question 2

Two series are said to be cointegrated if:

A)both series are I(1)but a linear combination of them is I(0).
B)both series are I(0)but a linear combination of them is I(1).
C)both series have the same set of explanatory variables but a different dependent variable.
D)both series have the same dependent variable but a different set of explanatory variables.

Answer 2

B

Question 3

Which of the following statements is true of spurious regressions?

A)The OLS estimates of the population parameters are efficient and unbiased and the t statistic is valid.
B)Even if the explanatory variables and the dependent variable are independent times series processes,the R² can large.
C)Spurious regressions are limited to I(0)processes,and are not possible in case of I(1)processes.
D)Spurious regressions are limited to I(1)processes,and are not possible in case of I(0)processes.

Answer 3

B

Question 4

Which of the following tests can be used to check for cointegration between two series?

A)Wald test
B)Breush-Pagan test
C)White test
D)Engle-Granger test

Question 5

A spurious correlation refers to a situation where:

A)two variables are related through their correlation with a third variable.
B)the correlation coefficient between two variables cannot be estimated.
C)there is direct causal relationship between two variables but tests for correlations reject this relationship.
D)the correlation between two variables is positive till the sample size reaches a threshold,and negative after the sample size crosses the threshold.

Question 6

The model: y_t? = α₀ + γ_0?z_t +ρy_{t - 1} + γ_1?z_{t - 1} +v_t,where v_t= u_t - ρu_{t - 1} ?represents a:

A)finite distributed lag model.
B)simultaneous equations model.
C)rational distributed lag model.
D)vector error correction model.

Question 7

Which of the following is true of squared forecast errors?

A)An error of +4 yields a greater loss than an error of -4.
B)An error of -4 yields a greater loss than an error of +4.
C)An error of -4 or +4 yields the same loss.
D)Loss from positive and negative forecast errors cannot be compared.

Question 8

A spurious regression refers to a situation where:

A)the direction of the relationship between the dependent variable and the explanatory variables is uncertain.
B)even though two variables are independent,the OLS regression of one variable on the other indicates a relationship between them.
C)a few important and necessary explanatory variables are left out of a regression equation,thus leading to inefficient and inconsistent forecasts.
D)at least one of the variables used in a regression equation does not have a unit root and the error terms are heteroskedastic.

Question 9

In the given AR(1)model,y_t = α + ρy_{t - 1},t = 1,2…… ,the Dickey-Fuller distribution refers to the:

A)asymptotic distribution of the t statistic under the hypothesis ρ - 1 = 0.
B)asymptotic distribution of the F statistic under the hypothesis ρ - 1 = 0.
C)asymptotic distribution of the χ² statistic under the hypothesis ρ - 1 = 0.
D)asymptotic distribution of the z statistic under the hypothesis ρ - 1 = 0.

Question 10

Vector autoregressive models should be used for forecasting if the series being studied are cointegrated.

Question 11

In calculation of squared forecast errors,an error of +3 yields a loss three times greater than an error of -1.

Question 12

Which of the following statements correctly identifies the difference between an autoregressive model and a vector autoregressive model?

A)In an autoregressive model,the dependent variable is expressed as a function of its own lag,whereas in a vector autoregressive model,the dependent variable is expressed as a function of the lag of an explanatory variable.
B)In an autoregressive model,the dependent variable is expressed as a function of the lag of an explanatory variable,whereas in a vector autoregressive model,the dependent variable is expressed as a function of its own lag.
C)In an autoregressive model several series are modelled in terms of their own past,whereas in a vector autoregressive model only one series is modelled in terms of its own past.
D)In an autoregressive model one series is modelled in terms of its own past,whereas in a vector autoregressive model several series are modelled in terms of their past.

Question 13

Which of the following is used to test whether a time series follows a unit root process?

A)Wald test
B)White test
C)Augmented Dickey-Fuller test
D)Johansen test

Question 14

If the t statistic for the presence of a unit root in a variable is -7.22 and the 5% critical value is -2.86,there is strong evidence against a unit root in the variable.

Question 15

Exponential smoothing is a forecasting method where the weights on the lagged dependent variable decline to zero exponentially.

Question 16

In case of forecasts,the root mean squared error is the:

A)average of the forecast errors divided by the variance of the errors.
B)average of the absolute forecast errors.
C)standard deviation of the forecast errors without any degrees of freedom adjustment.
D)standard deviation of the forecast errors with a degrees of freedom adjustment.

Question 17

The Koyck distributed lag model is an example of:

A)a moving average model.
B)an autoregressive conditional heteroskedasticity model.
C)an infinite distributed lag model.
D)a finite distributed lag model.

Question 18

If f_t denotes the forecast of y_t+1made at time t,then the forecast error is given by:

A)e_t+1 = f_t/y_t+1.
B)e_t+1 =y_t+1/f_t?.
C)e_t+1 = y_t+1+ f_t?.
D)e_t+1= y_t+1- f_t.

Question 19

Which of the following statements is true?

A)The calculated t statistic is valid and efficient in case of a spurious regression.
B)If an explanatory variable or a dependent variable is integrated of the order one,the OLS estimators are asymptotically normally distributed.
C)An error correction model can be used to study the short-run dynamics in the relationship between the dependent variable and the explanatory variables in a time series model.
D)The Dickey-Fuller test can be used to test for heteroskedasticity in the error terms.

Question 20

The R²calculated in a spurious regression is a valid and efficient estimate of the goodness-of-fit of the regression equation.