Exam 11: Further Issues in Using Ols With Time Sries Data

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Covariance stationary sequences where Corr(xt + xt+h) Covariance stationary sequences where Corr(xt + xt+h)   0 as   are said to be: 0 as Covariance stationary sequences where Corr(xt + xt+h)   0 as   are said to be: are said to be:

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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:

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Sequential exogeneity is implied by dynamic completeness.

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Consider the model: yt = Consider the model: y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>z<sub>t</sub><sub>1</sub> +   <sub>2</sub>z<sub>t</sub><sub>2</sub> + u<sub>t</sub>. Under weak dependence, the condition sufficient for consistency of OLS is: 0 + Consider the model: y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>z<sub>t</sub><sub>1</sub> +   <sub>2</sub>z<sub>t</sub><sub>2</sub> + u<sub>t</sub>. Under weak dependence, the condition sufficient for consistency of OLS is: 1zt1 + Consider the model: y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>z<sub>t</sub><sub>1</sub> +   <sub>2</sub>z<sub>t</sub><sub>2</sub> + u<sub>t</sub>. Under weak dependence, the condition sufficient for consistency of OLS is: 2zt2 + ut. Under weak dependence, the condition sufficient for consistency of OLS is:

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If a process is a covariance stationary process, then it will have a finite second moment.

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The model yt = et + The model y<sub>t</sub> = e<sub>t</sub> +   <sub>1</sub>e<sub>t -</sub> <sub>1</sub> +   <sub>2</sub>e<sub>t -</sub> <sub>2</sub> , t = 1, 2, ….. , where e<sub>t</sub> is an i.i.d. sequence with zero mean and variance   <sup>2</sup>e represents a(n): 1et - 1 + The model y<sub>t</sub> = e<sub>t</sub> +   <sub>1</sub>e<sub>t -</sub> <sub>1</sub> +   <sub>2</sub>e<sub>t -</sub> <sub>2</sub> , t = 1, 2, ….. , where e<sub>t</sub> is an i.i.d. sequence with zero mean and variance   <sup>2</sup>e represents a(n): 2et - 2 , t = 1, 2, ….. , where et is an i.i.d. sequence with zero mean and variance The model y<sub>t</sub> = e<sub>t</sub> +   <sub>1</sub>e<sub>t -</sub> <sub>1</sub> +   <sub>2</sub>e<sub>t -</sub> <sub>2</sub> , t = 1, 2, ….. , where e<sub>t</sub> is an i.i.d. sequence with zero mean and variance   <sup>2</sup>e represents a(n): 2e represents a(n):

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

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In the model yt = In the model y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>x<sub>t</sub><sub>1</sub> +   <sub>2</sub>x<sub>t</sub><sub>2</sub> + ….. +   <sub>k</sub>x<sub>tk</sub> + u<sub>t</sub>, the explanatory variables, x<sub>t</sub> = (x<sub>t</sub><sub>1</sub>, x<sub>t</sub><sub>2</sub> …., x<sub>tk</sub>), are sequentially exogenous if: 0 + In the model y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>x<sub>t</sub><sub>1</sub> +   <sub>2</sub>x<sub>t</sub><sub>2</sub> + ….. +   <sub>k</sub>x<sub>tk</sub> + u<sub>t</sub>, the explanatory variables, x<sub>t</sub> = (x<sub>t</sub><sub>1</sub>, x<sub>t</sub><sub>2</sub> …., x<sub>tk</sub>), are sequentially exogenous if: 1xt1 + In the model y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>x<sub>t</sub><sub>1</sub> +   <sub>2</sub>x<sub>t</sub><sub>2</sub> + ….. +   <sub>k</sub>x<sub>tk</sub> + u<sub>t</sub>, the explanatory variables, x<sub>t</sub> = (x<sub>t</sub><sub>1</sub>, x<sub>t</sub><sub>2</sub> …., x<sub>tk</sub>), are sequentially exogenous if: 2xt2 + ….. + In the model y<sub>t</sub> =   <sub>0</sub> +   <sub>1</sub>x<sub>t</sub><sub>1</sub> +   <sub>2</sub>x<sub>t</sub><sub>2</sub> + ….. +   <sub>k</sub>x<sub>tk</sub> + u<sub>t</sub>, the explanatory variables, x<sub>t</sub> = (x<sub>t</sub><sub>1</sub>, x<sub>t</sub><sub>2</sub> …., x<sub>tk</sub>), are sequentially exogenous if: kxtk + ut, the explanatory variables, xt = (xt1, xt2 …., xtk), are sequentially exogenous if:

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