def _mean_prediction(self, mu, Y, h, t_z):
        """ Creates a h-step ahead mean prediction

        Parameters
        ----------
        mu : np.ndarray
            The past predicted values

        Y : np.ndarray
            The past data

        h : int
            How many steps ahead for the prediction

        t_z : np.ndarray
            A vector of (transformed) latent variables

        Returns
        ----------
        h-length vector of mean predictions
        """     

        # Create arrays to iteratre over
        Y_exp = Y.copy()

        # Loop over h time periods          
        for t in range(0,h):

            if self.ar != 0:
                Y_exp_normalized = (Y_exp[-self.ar:][::-1] - self._norm_mean) / self._norm_std
                new_value = self.predict_new(np.append(1.0, Y_exp_normalized), self.latent_variables.get_z_values())

            else:  
                new_value = self.predict_new(np.array([1.0]), self.latent_variables.get_z_values())

            Y_exp = np.append(Y_exp, [self.link(new_value)])

        return Y_exp