class_docstr: Inherits time series methods from TSM class.
  
  **** GENERALIZED AUTOREGRESSIVE SCORE (GAS) MODELS ****
  
  Parameters
  ----------
  data : pd.DataFrame or np.array
      Field to specify the univariate time series data that will be used.
  
  ar : int
      Field to specify how many AR lags the model will have.
  
  sc : int
      Field to specify how many score lags terms the model will have.
  
  family : GAS family object
      Which distribution to use, e.g. GASNormal()
  
  integ : int (default : 0)
      Specifies how many time to difference the time series.
  
  target : str (pd.DataFrame) or int (np.array)
      Specifies which column name or array index to use. By default, first
      column/array will be selected as the dependent variable.
docstr: Creates a h-step ahead mean prediction
  
  Parameters
  ----------
  theta : 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
  ----------
  Y_exp : np.array
      Vector of past values and predictions 
docstr_tok: ["Creates","a","h-step","ahead","mean","prediction","Parameters","--","--","--","--","--","theta",":","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","--","--","--","--","--","Y_exp",":","np.array","Vector","of","past","values","and","predictions"]
code: def _mean_prediction(self, theta, Y, scores, h, t_params):
      """Creates a h-step ahead mean prediction
  
      Parameters
      ----------
      theta : 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
      ----------
      Y_exp : np.array
          Vector of past values and predictions
      """
  
      Y_exp = Y.copy()
      theta_exp = theta.copy()
      scores_exp = scores.copy()
  
      # TODO: vectorize the inner construction here)
      for t in range(0, h):
          new_value = t_params[0]
  
          if self.ar != 0:
              for j in range(1, self.ar + 1):
                  new_value += t_params[j] * theta_exp[-j]
  
          if self.sc != 0:
              for k in range(1, self.sc + 1):
                  new_value += t_params[k + self.ar] * scores_exp[-k]
  
          if self.model_name2 == "Exponential":
              Y_exp = np.append(Y_exp, [1.0 / self.link(new_value)])
          else:
              Y_exp = np.append(Y_exp, [self.link(new_value)])
  
          theta_exp = np.append(
              theta_exp, [new_value]
          )  # For indexing consistency
          scores_exp = np.append(
              scores_exp, [0]
          )  # expectation of score is zero
  
      return Y_exp
  
imports: import sys
  import numpy
  import pandas
  import scipy.stats
  import scipy.special
  from ..None import families
  from ..None import tsm
  from ..None import data_check
  from .gas_core_recursions import gas_recursion
label_desc: Use image node_id 10 for calling the GAS obj's underlying member method code with example usage: obj._mean_prediction(theta, Y, scores, h, t_params) and returns: Y_exp