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Answer: Not use linear regression
When a time series has a unit root, it is non-stationary and exhibits a stochastic trend. Using linear regression with non-stationary time series leads to spurious regression results, where the error term is not covariance stationary. This violates the assumptions of classical linear regression and can produce misleading statistical inferences, such as artificially high R-squared values and t-statistics that appear significant when there is no true relationship. The presence of a unit root indicates that the series has a stochastic trend, making standard regression techniques inappropriate regardless of co-integration considerations.
Author: Nikitesh Somanthe
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An analyst intends to use linear regression to model the relationship between two-time series. After some testing, she finds out that one of the time series has a unit root. She should:
A
Not use linear regression if the two time series are not co-integrated
B
Not use linear regression
C
Perform another test on a higher level of significance before proceeding to use linear regression
D
Only use linear regression if the time series are co-integrated