class_docstr: Inherits time series methods from TSM class.
  
  **** BETA-t-EGARCH IN MEAN REGRESSION MODELS ****
  
  Parameters
  ----------
  data : pd.DataFrame
      Field to specify the time series data that will be used.
  
  p : int
      Field to specify how many GARCH terms the model will have.
  
  q : int
      Field to specify how many SCORE terms the model will have.
  
  formula : string
      patsy string describing the regression
class_docstr_tok: ["Inherits","time","series","methods","from","TSM","class",".","*","*","*","*","BETA-t-EGARCH","IN","MEAN","REGRESSION","MODELS","*","*","*","*","Parameters","--","--","--","--","--","data",":","pd.DataFrame","Field","to","specify","the","time","series","data","that","will","be","used",".","p",":","int","Field","to","specify","how","many","GARCH","terms","the","model","will","have",".","q",":","int","Field","to","specify","how","many","SCORE","terms","the","model","will","have",".","formula",":","string","patsy","string","describing","the","regression"]
docstr: 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
  
  X_oos : np.array
      Out of sample predictors
  
  Returns
  ----------
  h-length vector of mean predictions
docstr_tok: ["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","X_oos",":","np.array","Out","of","sample","predictors","Returns","--","--","--","--","--","h-length","vector","of","mean","predictions"]
code: def _mean_prediction(self, lmda, Y, scores, h, t_params, X_oos):
      """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
  
      X_oos : np.array
          Out of sample predictors
  
      Returns
      ----------
      h-length vector of mean predictions
      """
  
      # Create arrays to iteratre over
      lmda_exp = lmda.copy()
      scores_exp = scores.copy()
      Y_exp = Y.copy()
  
      # Loop over h time periods
      for t in range(0, h):
          new_lambda_value = 0
  
          if self.p != 0:
              for j in range(self.p):
                  new_lambda_value += t_params[j] * lmda_exp[-j - 1]
  
          if self.q != 0:
              for k in range(self.q):
                  new_lambda_value += (
                      t_params[k + self.p] * scores_exp[-k - 1]
                  )
  
          # No leverage term for mean (should be zero in expectation?)
  
          new_lambda_value += np.dot(
              X_oos[t],
              t_params[-len(self.X_names) * 2 : -len(self.X_names)],
          )
          new_theta_value = np.dot(
              X_oos[t], t_params[-len(self.X_names) :]
          ) + t_params[-(len(self.X_names) * 2) - 1] * np.exp(
              new_lambda_value / 2.0
          )
          lmda_exp = np.append(
              lmda_exp, [new_lambda_value]
          )  # For indexing consistency
          scores_exp = np.append(
              scores_exp, [0]
          )  # expectation of score is zero
          Y_exp = np.append(Y_exp, new_theta_value)
  
      return lmda_exp
  
imports: import sys
  import numpy
  import pandas
  import scipy.stats
  from patsy import dmatrices, dmatrix, demo_data
  from ..None import families
  from ..None import output
  from ..None import tests
  from ..None import tsm
  from ..None import gas
  from ..None import data_check
label_desc: Use image node_id 5 for calling the EGARCHMReg obj's underlying member method code with example usage: obj._mean_prediction(lmda, Y, scores, h, t_params, X_oos) and returns: lmda_exp