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

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

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

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

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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:

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