Question 1

Under adaptive expectations,the expected current value of a variable does not depend on a recently observed value of the variable.

Accepted Answer

Under adaptive expectations, the expected current value of a variable does depend on a recently observed value of the variable. This is in contrast to rational expectations, where expected values are based on a more sophisticated analysis of all available information.

Question 2

A process is stationary if:
A)any collection of random variables in a sequence is taken and shifted ahead by h time periods;the joint probability distribution changes.
B)any collection of random variables in a sequence is taken and shifted ahead by h time periods,the joint probability distribution remains unchanged.
C)there is serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance.
D)there is no serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance.

Accepted Answer

Stationarity refers to a time series process where the statistical properties such as mean, variance, and autocorrelation are constant over time. A stationary process does not depend on time, hence the joint distribution of a sequence of random variables will remain unchanged when shifted by h time periods. Therefore, choice B is the correct option. Choices A, C, and D are incorrect as they do not describe the characteristics of a stationary process.

Question 3

Which of the following statements is true?
A)A model with a lagged dependent variable cannot satisfy the strict exogeneity assumption.
B)Stationarity is critical for OLS to have its standard asymptotic properties.
C)Efficient static models can be estimated for nonstationary time series.
D)In an autoregressive model,the dependent variable in the current time period varies with the error term of previous time periods.

Accepted Answer

A

Question 4

Suppose u_t is the error term for time period 't' in a time series regression model the explanatory variables are x_t = (x_t1,x_t2 …. ,x_tk).The assumption that the errors are contemporaneously homoskedastic implies that: A)Var(u_t|x_t)= √σ. B)Var(u_t|x_t)= ∞. C)Var(u_t|x_t)= σ². D)Var(u_t|x_t)= σ.

Accepted Answer

Contemporaneous homoskedasticity implies that the variance of the error term given the explanatory variables is constant, denoted as σ².

Question 5

Which of the following statements is true?
A)A random walk process is stationary.
B)The variance of a random walk process increases as a linear function of time.
C)Adding a drift term to a random walk process makes it stationary.
D)The variance of a random walk process with a drift decreases as an exponential function of time.

Accepted Answer

A random walk process is not stationary as it does not have a constant mean and variance. Adding a drift term to a random walk process can make it stationary, but it would no longer be a random walk. The variance of a random walk process increases as a function of time, specifically as a quadratic function, not a linear function. The variance of a random walk process with a drift still increases over time, but at a slower rate, so it does not decrease and is not an exponential function.

Question 6

Covariance stationarity focusses only on the first two moments of a stochastic process.

Accepted Answer

Covariance stationarity (also known as weak stationarity) is a property of a stochastic process where the mean and covariance of the process do not depend on time. It only considers the first two moments (i.e., mean and covariance) and not higher order moments.

Question 7

Which of the following is assumed in time series regression?
A)There is no perfect collinearity between the explanatory variables.
B)The explanatory variables are contemporaneously endogenous.
C)The error terms are contemporaneously heteroskedastic.
D)The explanatory variables cannot have temporal ordering.

Accepted Answer

Time series regression assumes that there is no perfect collinearity between the explanatory variables. This means that the independent variables are not highly correlated with each other, as this can lead to issues with estimation and interpretation of the coefficients. The other choices are not assumed in time series regression: contemporaneously endogeneity of explanatory variables is a concern, contemporaneous heteroskedasticity of error terms is a violation, and explanatory variables can have temporal ordering (as in lagged variables).

Question 8

Which of the following statements is true of dynamically complete models?
A)There is scope of adding more lags to the model to better forecast the dependent variable.
B)The problem of serial correlation does not exist in dynamically complete models.
C)All econometric models are dynamically complete.
D)Sequential endogeneity is implied by dynamic completeness..

Accepted Answer

The answer of Which of the following statements is true...

Question 9

Sequential exogeneity is implied by dynamic completeness.

Accepted Answer

Sequential exogeneity means that the current value of a variable is only dependent on past values of that variable and exogenous variables. Dynamic completeness implies that all variables in a system are included and specified accurately, therefore ruling out the possibility of simultaneous endogeneity. Hence, dynamic completeness implies sequential exogeneity.

Question 10

Weakly dependent processes are said to be integrated of order zero.

Accepted Answer

Weakly dependent processes have correlations that decay to zero at a slow rate, but they are still stationary. Such processes are integrated of order zero.

Question 11

Consider the model: y_t = α₀ + α₁r_t1 + α₂r_t2 + u_t.Under weak dependence,the condition sufficient for consistency of OLS is: A)E(r_t1|r_t2)= 0. B)E(y_t |r_t₁,r_t₂)= 0. C)E(u_t |r_t₁,r_t₂)= 0. D)E(u_t |r_t₁,r_t₂)= ∞.

Accepted Answer

Under weak dependence, the sufficient condition for consistency of OLS is that the errors (residuals) are uncorrelated with the regressors. Therefore, choice C is the correct answer as it represents the condition that the error term u is uncorrelated with the regressors r1 and r2. Choice A and B are not correct because they involve conditional expectations of the dependent variable, while the sufficient condition for consistency depends on the error term. Choice D is not correct as the error term should have a finite expected value.

Question 12

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²)< ∞] is covariance stationary if: A)E(x_t)is variable,Var(x_t)is variable,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 'h' and not on 't'. B)E(x_t)is variable,Var(x_t)is variable,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 't' and not on h. C)E(x_t)is constant,Var(x_t)is constant,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 'h' and not on 't'. D)E(x_t)is constant,Var(x_t)is constant,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 't' and not on 'h'.

Accepted Answer

A stochastic process is said to be covariance stationary if its mean and variance are constant over time, and the covariance between any two time points only depends on the time lag between them and not on the actual time points. Therefore, option C is the correct option as it satisfies all the conditions for a covariance stationary process. Options A and B have a variable mean and variance, making them non-stationary, and option D has a covariance that depends only on time and not on the lag, which is also not stationary.

Question 13

The homoskedasticity assumption in time series regression suggests that the variance of the error term cannot be a function of time.

Accepted Answer

Homoskedasticity assumption requires that the variance of the error term is constant over time and not a function of time. Therefore, the statement is true.

Question 14

In the model y_t = α₀ + α₁x_t1 + α₂x_t2 + …..+ α?_kx_tk + u_t,the explanatory variables,x_t = (x_t1,x_t2 …. ,x_tk),are sequentially exogenous if: A)E(u_t|x_t,x_t-1,……)= E(u_t)= 0,t = 1,2,…. B)E(u_t|x_t,x_t-1,……)≠ E(u_t)= 0,t = 1,2,…. C)E(u_t|x_t,x_t-1,……)= E(u_t)> 0,t = 1,2,…. D)E(u_t|x_t,x_t-1,……)= E(u_t)= 1,t = 1,2,….

Accepted Answer

Sequential exogeneity means that the conditional expectation of the error term at time t, given the explanatory variables up to time t and all lagged values of the explanatory variables, is equal to 0. Choice A reflects this definition. Choice B indicates that the conditional expectation of the error term is not equal to 0, which contradicts the definition. Choice C suggests that the conditional expectation of the error term is positive, which is also not in line with the definition. Choice D is incorrect because the conditional expectation of the error term cannot be equal to 1.

Question 15

If u_t refers to the error term at time 't' and y_{t - 1}refers to the dependent variable at time 't - 1',for an AR(1)process to be homoskedastic,it is required that: A)Var(u_t|y_{t - 1})> Var(y_t|y_t-1)= σ². B)Var(u_t|y_{t - 1})= Var(y_t|y_t-1)> σ². C)Var(u_t|y_{t - 1})< Var(y_t|y_t-1)= σ². D)Var(u_t|y_{t - 1})= Var(y_t|y_t-1)= σ².

Accepted Answer

For an AR(1) process to be homoskedastic, the variance of the error term at time 't' conditional on the dependent variable at time 't - 1' should be constant and independent of the value of the dependent variable at time 't - 1', i.e., Var(u_t|y_t-1) = σ^2. Additionally, the variance of the dependent variable at time 't' conditional on the dependent variable at time 't - 1' should also be constant and independent of the value of the dependent variable at time 't - 1', i.e., Var(y_t|y_t-1) = σ^2/(1 - ϕ^2). Therefore, the correct choice is D because it satisfies both conditions.

Question 16

The model x_t_? = α₁x_{t - 1} + e_t ,t =1,2,…. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_e represents a(n): A)moving average process of order one. B)moving average process of order two. C)autoregressive process of order one. D)autoregressive process of order two.

Accepted Answer

The given model is an autoregressive process of order one (AR(1)) because it expresses the current value x_t as a function of its immediately preceding value x_(t-1) and a random error term e_t.

Question 17

The model y_t = y_{t - 1}+ e_t,t = 1,2,… represents a: A)AR(2)process. B)MA(1)process. C)random walk process. D)random walk with a drift process.

Accepted Answer

The y_t model represents a random walk process, as it shows a constant drift () and a random error term (e_{t). It does not have any autoregressive or moving average terms.}

Question 18

A covariance stationary time series is weakly dependent if:
A)the correlation between the independent variable at time 't' and the dependent variable at time 't + h' goes to ∞ as h → 0.
B)the correlation between the independent variable at time 't' and the dependent variable at time 't + h' goes to 0 as h → ∞.
C)the correlation between the independent variable at time 't' and the independent variable at time 't + h' goes to ∞ as h → 0.
D)the correlation between the independent variable at time 't' and the independent variable at time 't + h' goes to 0 as h → ∞.

Accepted Answer

In a weakly dependent time series, the correlation between values at different times decreases as the time gap increases, meaning it approaches zero as h approaches infinity.

Question 19

If a process is said to be integrated of order one,or I(1),_____.
A)it is stationary at level
B)averages of such processes already satisfy the standard limit theorems
C)the first difference of the process is weakly dependent
D)it does not have a unit root

Accepted Answer

An I(1) process means that the first difference of the process is stationary, implying weak dependence over time. This does not necessarily mean it is stationary at level (A), nor does it imply that averages of such processes satisfy standard limit theorems (B), or that it does not have a unit root (D), as having a unit root is actually a characteristic of I(1) processes before differencing.

Question 20

The model y_t = e_t + β₁e_{t -}₁+ β₂e_{t - 2},t = 1,2,….. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_erepresents a(n): A)static model. B)moving average process of order one. C)moving average process of order two. D)autoregressive process of order two.

Accepted Answer

The given model is a moving average process of order two, as it depends on the past two error terms (eS1U1B1t-1S1U1B0 and eS1U1B1t-2S1U1B0) with corresponding coefficients (βS1U1B11 and βS1U1B12).

Quiz 11: Further Issues in Using Ols With Time Series Data

Under adaptive expectations,the expected current value of a variable does not depend on a recently observed value of the variable.

A process is stationary if:

Which of the following statements is true?

Suppose u_t is the error term for time period 't' in a time series regression model the explanatory variables are x_t = (x_t1,x_t2 …. ,x_tk) .The assumption that the errors are contemporaneously homoskedastic implies that:

Which of the following statements is true?

Covariance stationarity focusses only on the first two moments of a stochastic process.

Which of the following is assumed in time series regression?

Which of the following statements is true of dynamically complete models?

Sequential exogeneity is implied by dynamic completeness.

Weakly dependent processes are said to be integrated of order zero.

Consider the model: y_t = α₀ + α₁r_t1 + α₂r_t2 + u_t.Under weak dependence,the condition sufficient for consistency of OLS is:

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²) < ∞] is covariance stationary if:

The homoskedasticity assumption in time series regression suggests that the variance of the error term cannot be a function of time.

In the model y_t = α₀ + α₁x_t1 + α₂x_t2 + …..+ α?_kx_tk + u_t,the explanatory variables,x_t = (x_t1,x_t2 …. ,x_tk) ,are sequentially exogenous if:

If u_t refers to the error term at time 't' and y_{t - 1}refers to the dependent variable at time 't - 1',for an AR(1) process to be homoskedastic,it is required that:

The model x_t_? = α₁x_{t - 1} + e_t ,t =1,2,…. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_e represents a(n) :

The model y_t = y_{t - 1}+ e_t,t = 1,2,… represents a:

A covariance stationary time series is weakly dependent if:

If a process is said to be integrated of order one,or I(1) ,_____.

The model y_t = e_t + β₁e_{t -}₁+ β₂e_{t - 2},t = 1,2,….. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_erepresents a(n) :

Quiz 11: Further Issues in Using Ols With Time Series Data

Under adaptive expectations,the expected current value of a variable does not depend on a recently observed value of the variable.

A process is stationary if:

Which of the following statements is true?

Suppose ut is the error term for time period 't' in a time series regression model the explanatory variables are xt = (xt1,xt2 …. ,xtk) .The assumption that the errors are contemporaneously homoskedastic implies that:

Which of the following statements is true?

Covariance stationarity focusses only on the first two moments of a stochastic process.

Which of the following is assumed in time series regression?

Which of the following statements is true of dynamically complete models?

Sequential exogeneity is implied by dynamic completeness.

Weakly dependent processes are said to be integrated of order zero.

Consider the model: yt = α0 + α1rt1 + α2rt2 + ut.Under weak dependence,the condition sufficient for consistency of OLS is:

A stochastic process {xt: t = 1,2,….} with a finite second moment [E(xt2) < ∞] is covariance stationary if:

The homoskedasticity assumption in time series regression suggests that the variance of the error term cannot be a function of time.

In the model yt = α0 + α1xt1 + α2xt2 + …..+ α?kxtk + ut,the explanatory variables,xt = (xt1,xt2 …. ,xtk) ,are sequentially exogenous if:

If ut refers to the error term at time 't' and yt - 1 refers to the dependent variable at time 't - 1',for an AR(1) process to be homoskedastic,it is required that:

The model xt? = α1xt - 1 + et ,t =1,2,…. ,where et is an i.i.d.sequence with zero mean and variance σ2e represents a(n) :

The model yt = yt - 1 + et,t = 1,2,… represents a:

A covariance stationary time series is weakly dependent if:

If a process is said to be integrated of order one,or I(1) ,_____.

The model yt = et + β1et - 1 + β2et - 2 ,t = 1,2,….. ,where et is an i.i.d.sequence with zero mean and variance σ2erepresents a(n) :

Suppose u_t is the error term for time period 't' in a time series regression model the explanatory variables are x_t = (x_t1,x_t2 …. ,x_tk) .The assumption that the errors are contemporaneously homoskedastic implies that:

Consider the model: y_t = α₀ + α₁r_t1 + α₂r_t2 + u_t.Under weak dependence,the condition sufficient for consistency of OLS is:

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²) < ∞] is covariance stationary if:

In the model y_t = α₀ + α₁x_t1 + α₂x_t2 + …..+ α?_kx_tk + u_t,the explanatory variables,x_t = (x_t1,x_t2 …. ,x_tk) ,are sequentially exogenous if:

If u_t refers to the error term at time 't' and y_{t - 1}refers to the dependent variable at time 't - 1',for an AR(1) process to be homoskedastic,it is required that:

The model x_t_? = α₁x_{t - 1} + e_t ,t =1,2,…. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_e represents a(n) :

The model y_t = y_{t - 1}+ e_t,t = 1,2,… represents a:

The model y_t = e_t + β₁e_{t -}₁+ β₂e_{t - 2},t = 1,2,….. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_erepresents a(n) :