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...The loop is necessary, since you need to calculate recursive sequence. Is there a faster way to do this in R, without using loops? The model is such: r_t = \mu + \alpha_2 r_{t-2} + a_t a_t = \sigma_t\varepsilon_t \sigma_t^2 = \beta_1a_{t-1}^2+\beta_2\sigma_{t-1}^2+ 1_{\{a_{t-1}>0\}}(\gamma_0+ \gamma_1a_{t-1}^2+\gamma_2\sigma^2_{t-1}) It is asummed that \varepsilon_t are iid and normal with zero mean and variance one. The data given is r_t, and you have to estimate variables, \mu, \alpha, \beta and \gamma. Since \varepsilon_t=\frac{a_t}{\sqrt{sigma_t}} using the equations we calculate a_t and \s...