class_docstr: Model specification.
class_docstr_tok: ["Model","specification","."]
docstr: Generate sample data given the state model specification.
docstr_tok: ["Generate","sample","data","given","the","state","model","specification","."]
code: def generate_parametrized_sample_data(
      self, n, sigma_zeta=0.1, sigma_eta=0.1, sigma_epsilon=0.1
  ):
      """Generate sample data given the state model specification."""
      # Initialize variables
      y = np.zeros(n)
      mu = np.zeros(n)
      beta = np.zeros(n)
      epsilon = np.zeros(n)
      eta = np.zeros(n)
      zeta = np.zeros(n)
  
      # Sample from model parameters.
      for t in range(1, n):
          zeta[t] = self.params["zeta"] * np.random.normal(
              loc=0.0, scale=sigma_zeta
          )
          beta[t] = self.params["beta_1"] * beta[t - 1] + zeta[t]
  
          eta[t] = self.params["eta"] * np.random.normal(
              loc=0.0, scale=sigma_eta
          )
          mu[t] = (
              self.params["mu_1"] * mu[t - 1]
              + self.params["beta_1"] * beta[t - 1]
              + eta[t]
          )
  
          epsilon[t] = self.params["epsilon"] * np.random.normal(
              loc=0.0, scale=sigma_epsilon
          )
          y[t] = self.params["mu"] * mu[t] + epsilon[t]
  
      return y, mu, beta
  
imports: import numpy
  import pandas
  import pytest
  from pandas.testing import assert_series_equal
  from sktime.datasets import load_airline, load_longley
  from sktime.forecasting.model_evaluation import evaluate
  from sktime.forecasting.structural import UnobservedComponents
  from sktime.split import SlidingWindowSplitter
  from sktime.utils.validation._dependencies import _check_soft_dependencies
label_desc: Use image node_id 2 for calling the ModelSpec obj's underlying member method code with example usage: obj.generate_parametrized_sample_data(n, sigma_zeta, sigma_eta, sigma_epsilon) and returns: y,  mu,  beta