def _advance_window(self):
        """Update values in current window and the current window means and variances."""
        x_to_remove, y_to_remove = self._x_in_window[0], self._y_in_window[0]

        self._window_bound_lower += 1
        self._update_values_in_window()
        x_to_add, y_to_add = self._x_in_window[-1], self._y_in_window[-1]

        self._remove_observation(x_to_remove, y_to_remove)
        self._add_observation(x_to_add, y_to_add)