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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