1. Consider the simple linear population model without intercept:
$y_i = \beta x_i + \varepsilon_i$
$\varepsilon_i = \rho \varepsilon_{i-1} + u_i,$
where $u_i \sim i.i.d(0, \sigma^2)$. We use OLS method to estimate parameter $\hat{\beta}$. After we obtain the $\hat{\beta}$, we use OLS residuals to generate Durbin-Watson statistic. Which approximation value does Durbin-Watson statistic converge under $T \to \infty$?
(A) \( 2 - \hat{\rho} \)
(B) \( 1 - 2\hat{\rho} \)
(C) \( 2(1 - \hat{p}) \)
(D) \( 1 - \hat{p} \)
(E) \( 2 - 3\hat{p} \)

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