class_docstr: Results class from estimated Theta Models.
  
  Parameters
  ----------
  b0 : float
      The estimated trend slope.
  alpha : float
      The estimated SES parameter.
  sigma2 : float
      The estimated residual variance from the SES/IMA model.
  one_step : float
      The one-step forecast from the SES.
  seasonal : ndarray
      An array of estimated seasonal terms.
  use_mle : bool
      A flag indicating that the parameters were estimated using MLE.
  model : ThetaModel
      The model used to produce the results.
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docstr: Parameters
  ----------
  steps : int, default 1
      The number of steps ahead to compute the forecast components.
  theta : float, default 2
      The theta value to use when computing the weight to combine
      the trend and the SES forecasts.
  alpha : float, default 0.05
      Significance level for the confidence intervals.
  
  Returns
  -------
  DataFrame
      DataFrame with columns lower and upper
  
  Notes
  -----
  The variance of the h-step forecast is assumed to follow from the
  integrated Moving Average structure of the Theta model, and so is
  :math:`\sigma^2(1 + (h-1)(1 + (\alpha-1)^2)`. The prediction interval
  assumes that innovations are normally distributed.
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code: def prediction_intervals(
      self, steps: int = 1, theta: float = 2, alpha: float = 0.05
  ) -> pd.DataFrame:
      r"""
      Parameters
      ----------
      steps : int, default 1
          The number of steps ahead to compute the forecast components.
      theta : float, default 2
          The theta value to use when computing the weight to combine
          the trend and the SES forecasts.
      alpha : float, default 0.05
          Significance level for the confidence intervals.
  
      Returns
      -------
      DataFrame
          DataFrame with columns lower and upper
  
      Notes
      -----
      The variance of the h-step forecast is assumed to follow from the
      integrated Moving Average structure of the Theta model, and so is
      :math:`\sigma^2(1 + (h-1)(1 + (\alpha-1)^2)`. The prediction interval
      assumes that innovations are normally distributed.
      """
      model_alpha = self.params.iloc[1]
      sigma2_h = (
          1 + np.arange(steps) * (1 + (model_alpha - 1) ** 2)
      ) * self.sigma2
      sigma_h = np.sqrt(sigma2_h)
      quantile = stats.norm.ppf(alpha / 2)
      predictions = self.forecast(steps, theta)
      return pd.DataFrame(
          {
              "lower": predictions + sigma_h * quantile,
              "upper": predictions + sigma_h * -quantile,
          }
      )
  
imports: from typing import TYPE_CHECKING, Optional
  import numpy
  import pandas
  from scipy import stats
  from statsmodels.iolib.summary import Summary
  from statsmodels.iolib.table import SimpleTable
  from statsmodels.tools.validation import array_like, bool_like, float_like, int_like, string_like
  from statsmodels.tsa.deterministic import DeterministicTerm
  from statsmodels.tsa.seasonal import seasonal_decompose
  from statsmodels.tsa.statespace.exponential_smoothing import ExponentialSmoothing
  from statsmodels.tsa.statespace.sarimax import SARIMAX
  from statsmodels.tsa.stattools import acf
  from statsmodels.tsa.tsatools import add_trend, freq_to_period
label_desc: Use image node_id 8 for calling the ThetaModelResults obj's underlying member method code with example usage: obj.prediction_intervals(steps, theta, alpha) and returns: pd