class_docstr: Inherits time series methods from the TSM parent class.
  
  **** AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODELS ****
  
  Parameters
  ----------
  data : pd.DataFrame or np.ndarray
      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.
  
  ma : int
      Field to specify how many MA lags the model will have.
  
  integ : int (default : 0)
      Specifies how many times to difference the time series.
  
  target : str (if data is a pd.DataFrame) or int (if data is a np.ndarray)
      Specifies which column name or array index to use. By default, first
      column/array index will be selected as the dependent variable.
  
  family : family object
      E.g pf.Normal(), pf.t(), pf.Laplace()...
docstr: Creates a h-step ahead mean prediction
  
  This function is used for predict(). We have to iterate over the number
  of timepoints (h) that the user wants to predict, using as inputs the ARIMA
  parameters, past datapoints, and past predicted datapoints.
  
  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 np.array of mean predictions
docstr_tok: ["Creates","a","h-step","ahead","mean","prediction","This","function","is","used","for","predict","(",")",".","We","have","to","iterate","over","the","number","of","timepoints","(","h",")","that","the","user","wants","to","predict",",","using","as","inputs","the","ARIMA","parameters",",","past","datapoints",",","and","past","predicted","datapoints",".","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","np.array","of","mean","predictions"]
code: def _mean_prediction(self, mu, Y, h, t_z):
      """Creates a h-step ahead mean prediction
  
      This function is used for predict(). We have to iterate over the number
      of timepoints (h) that the user wants to predict, using as inputs the ARIMA
      parameters, past datapoints, and past predicted datapoints.
  
      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 np.array of mean predictions
      """
  
      # Create arrays to iteratre over
      Y_exp = Y.copy()
      mu_exp = mu.copy()
  
      # Loop over h time periods
      for t in range(0, h):
          new_value = t_z[0]
  
          if self.ar != 0:
              for j in range(1, self.ar + 1):
                  new_value += t_z[j] * Y_exp[-j]
  
          if self.ma != 0:
              for k in range(1, self.ma + 1):
                  if (k - 1) >= t:
                      new_value += t_z[k + self.ar] * (
                          Y_exp[-k] - self.link(mu_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)])
  
          mu_exp = np.append(mu_exp, [0])  # For indexing consistency
      del mu_exp
      return Y_exp
  
imports: import sys
  import numpy
  import pandas
  import scipy.stats
  import scipy.special
  from ..None import families
  from ..None import output
  from ..None import tests
  from ..None import tsm
  from ..None import data_check
  from .arma_recursions import arima_recursion, arima_recursion_normal, arima_recursion_poisson
label_desc: Use image node_id 12 for calling the ARIMA obj's underlying member method code with example usage: obj._mean_prediction(mu, Y, h, t_z) and returns: Y_exp