class_docstr: AR(1) model for monthly growth rates aggregated to quarterly frequency
  
  Parameters
  ----------
  endog : array_like
      The observed time-series process :math:`y`
  
  Notes
  -----
  This model is internal, used to estimate starting parameters for the
  DynamicFactorMQ class. The model is:
  
  .. math::
  
      y_t & = \begin{bmatrix} 1 & 2 & 3 & 2 & 1 \end{bmatrix} \alpha_t \\
      \alpha_t & = \begin{bmatrix}
          \phi & 0 & 0 & 0 & 0 \\
             1 & 0 & 0 & 0 & 0 \\
             0 & 1 & 0 & 0 & 0 \\
             0 & 0 & 1 & 0 & 0 \\
             0 & 0 & 0 & 1 & 0 \\
      \end{bmatrix} +
      \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix} \varepsilon_t
  
  The two parameters to be estimated are :math:`\phi` and :math:`\sigma^2`.
  
  It supports fitting via the usual quasi-Newton methods, as well as using
  the EM algorithm.
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code: def __init__(self, endog):
      super().__init__(
          endog, k_states=5, k_posdef=1, initialization="stationary"
      )
      self["design"] = [1, 2, 3, 2, 1]
      self["transition", 1:, :-1] = np.eye(4)
      self["selection", 0, 0] = 1.0
  
file_path: statsmodels/statsmodels/tsa/statespace/_quarterly_ar1.py
imports: import warnings
  import numpy
  from statsmodels.tools.tools import Bunch
  from statsmodels.tsa.statespace import mlemodel, initialization
  from statsmodels.tsa.statespace.kalman_smoother import SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_STATE_AUTOCOV
  from statsmodels.tsa.statespace.tools import constrain_stationary_univariate, unconstrain_stationary_univariate
label_desc: Use image node_id 1 to create a new QuarterlyAR1 object from inherited base classes: mlemodel with example: obj = QuarterlyAR1(endog)