2. Consider the following \( \operatorname{GARCH}(1,1) \) model \[ \begin{array}{l} Y_{t}=\gamma+u_{t} u_{t} \sim N\left[0, h_{t} ight] \\ h_{t}=\lambda_{0}+\lambda_{1} u_{t-1}^{2}+\lambda_{2} h_{t-1} \end{array} \] [Mean equation] [Variance equation]

If \( y \), is a daily stock return series, what range of values are likely for the coefficients \( \gamma, \lambda_{0}, \lambda_{1} \) and \( \lambda_{2} \) ?

Suppose that a researcher wanted to test the null hypothesis that \( \lambda_{1}+\lambda_{2}<1 \) in the model. Explain how this might be achieved within the maximurn likelihood framework.