def _mean_prediction(self, lmda, Y, scores, h, t_params):
        """ Creates a h-step ahead mean prediction

        Parameters
        ----------
        lmda : np.array
            The past predicted values

        Y : np.array
            The past data

        scores : np.array
            The past scores

        h : int
            How many steps ahead for the prediction

        t_params : np.array
            A vector of (transformed) latent variables

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

        # Create arrays to iteratre over
        lmda_exp = lmda.copy()
        scores_exp = scores.copy()
        Y_exp = Y.copy()
        m1 = (np.sqrt(t_params[-2])*sp.gamma((t_params[-2]-1.0)/2.0))/(np.sqrt(np.pi)*sp.gamma(t_params[-2]/2.0))
        temp_theta = t_params[-1] + (t_params[-3] - (1.0/t_params[-3]))*np.exp(lmda_exp[-1]/2.0)*m1
        # Loop over h time periods          
        for t in range(0,h):
            new_value = t_params[0]

            if self.p != 0:
                for j in range(1,self.p+1):
                    new_value += t_params[j]*lmda_exp[-j]

            if self.q != 0:
                for k in range(1,self.q+1):
                    new_value += t_params[k+self.p]*scores_exp[-k]

            if self.leverage is True:
                m1 = (np.sqrt(t_params[-2])*sp.gamma((t_params[-2]-1.0)/2.0))/(np.sqrt(np.pi)*sp.gamma(t_params[-2]/2.0))
                new_value += t_params[1+self.p+self.q]*np.sign(-(Y_exp[-1]-temp_theta))*(scores_exp[-1]+1)

            temp_theta = t_params[-1] + (t_params[-3] - (1.0/t_params[-3]))*np.exp(new_value/2.0)*m1

            lmda_exp = np.append(lmda_exp,[new_value]) # For indexing consistency
            scores_exp = np.append(scores_exp,[0]) # expectation of score is zero
            Y_exp = np.append(Y_exp,[temp_theta])

        return lmda_exp
Creates a h-step ahead mean prediction

        Parameters
        ----------
        lmda : np.array
            The past predicted values

        Y : np.array
            The past data

        scores : np.array
            The past scores

        h : int
            How many steps ahead for the prediction

        t_params : np.array
            A vector of (transformed) latent variables

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