Financial Risk Manager Part 1

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.