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Answer: has heteroskedastic errors.
## Explanation The regression equation $\varepsilon_t^2 = a_0 + a_1 \varepsilon_{t-1}^2 + u_t$ is testing for **ARCH (Autoregressive Conditional Heteroskedasticity)** effects. Key points: - When $a_1$ is positive and statistically significant, it indicates that the variance of the error term depends on past squared errors - This is the definition of heteroskedastic errors in time series context - ARCH models specifically capture this phenomenon where volatility clusters over time **Why other options are incorrect:** - **Unit root (A)**: This relates to non-stationarity in the mean of the series, not the variance - **Mean-reverting (B)**: This refers to the series returning to its long-term mean, which is unrelated to variance behavior The positive and significant $a_1$ coefficient directly indicates the presence of heteroskedastic errors following an ARCH(1) process.
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An analyst is modeling a time series as an AR(1) process and performs the following regression on the errors of the model, :
where is an error term. If the coefficient is found to be positive and statistically significant, the analyst can conclude that :
A
has a unit root.
B
is mean-reverting.
C
has heteroskedastic errors.
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