Estimation of Parameters in the ARMA Model When the Characteristic Polynomial of the MA Operator Has a Unit Zero
移动平均算子特征多项式具有单位零点时的ARMA参数估计
We consider the estimation of parameters in the time series model $X(t) = \sum^q_{j = 1}a_jX(t - j) + \varepsilon(t) - \varepsilon(t - j) - \sum^p_{j = 1} c_j\{\varepsilon(t - j) - \varepsilon(t - j - 1)\}$ where the $\varepsilon(t)$ are independently identically distributed random variables with zero mean and variance $\sigma^2$. We compute the exact $\log$ likelihood of the model, propose and justify an asymptotic approximation of it. The latter will be used to derive…