Financial Risk Manager Part 1
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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:
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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.
Explanation:
Explanation
A unit root in a time series indicates the presence of a stochastic or random trend, meaning the series is non-stationary. Linear regression assumes that the data is stationary - that the mean, variance, and autocorrelation structure do not change over time.
Key Issues with Unit Roots:
- Non-stationarity: When a time series has a unit root, its mean and variance change over time
- Spurious regression: Using linear regression on non-stationary data can lead to misleading results that appear statistically significant but are actually meaningless
- Violated assumptions: Linear regression's statistical properties (like t-statistics and R-squared) become unreliable with non-stationary data
Why Other Options Are Incorrect:
- Option A: While co-integration can sometimes allow for valid regression, this doesn't address the fundamental problem of the unit root in one series
- Option C: Changing significance levels doesn't solve the underlying non-stationarity issue
- Option D: Similar to A, this doesn't properly handle the unit root problem
Correct Approach:
The analyst should first difference the series to remove the trend and make it stationary before proceeding with any modeling. This transforms the non-stationary series into a stationary one suitable for regression analysis.
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