Computes the objective value minimized in the robust parameter estimation (RPE) procedure.
objective_func(parameters, Var_ests)A numeric scalar representing the objective value.
Numeric vector of length three, containing the parameters \((\sigma_{\eta}^2, \sigma_{\nu}^2, \phi)\) to be estimated.
Numeric vector of empirical variance estimates \(\{v^{(l)}\}_{l=1}^L\) obtained from the \(l\)-lagged differences of the data.
For each lag \(l = 1, \ldots, L\), the theoretical variance of the \(l\)-lagged difference \(z^{(l)}_t = y_{t+l} - y_t\) is calculated by $$V_l = l\sigma_{\eta}^2 + 2\,\sigma_{\nu}^2 \frac{1 - \phi^l}{1 - \phi^2}.$$ The function returns the sum of squared deviations between \(V_l\) and the empirical variance estimates \(v^{(l)}\): $$\sum_{l=1}^L \left(V_l - v^{(l)}\right)^2.$$