class_docstr: Class to hold results from fitting a recursive least squares model.
  
  Parameters
  ----------
  model : RecursiveLS instance
      The fitted model instance
  
  Attributes
  ----------
  specification : dictionary
      Dictionary including all attributes from the recursive least squares
      model instance.
  
  See Also
  --------
  statsmodels.tsa.statespace.kalman_filter.FilterResults
  statsmodels.tsa.statespace.mlemodel.MLEResults
class_docstr_tok: ["Class","to","hold","results","from","fitting","a","recursive","least","squares","model",".","Parameters","--","--","--","--","--","model",":","RecursiveLS","instance","The","fitted","model","instance","Attributes","--","--","--","--","--","specification",":","dictionary","Dictionary","including","all","attributes","from","the","recursive","least","squares","model","instance",".","See","Also","--","--","--","--","statsmodels.tsa.statespace.kalman_filter.FilterResults","statsmodels.tsa.statespace.mlemodel.MLEResults"]
docstr: Cumulative sum of standardized recursive residuals statistics
  
  Returns
  -------
  cusum : array_like
      An array of length `nobs - k_exog` holding the
      CUSUM statistics.
  
  Notes
  -----
  The CUSUM statistic takes the form:
  
  .. math::
  
      W_t = \frac{1}{\hat \sigma} \sum_{j=k+1}^t w_j
  
  where :math:`w_j` is the recursive residual at time :math:`j` and
  :math:`\hat \sigma` is the estimate of the standard deviation
  from the full sample.
  
  Excludes the first `k_exog` datapoints.
  
  Due to differences in the way :math:`\hat \sigma` is calculated, the
  output of this function differs slightly from the output in the
  R package strucchange and the Stata contributed .ado file cusum6. The
  calculation in this package is consistent with the description of
  Brown et al. (1975)
  
  References
  ----------
  .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975.
     "Techniques for Testing the Constancy of
     Regression Relationships over Time."
     Journal of the Royal Statistical Society.
     Series B (Methodological) 37 (2): 149-92.
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code: def cusum(self):
      r"""
      Cumulative sum of standardized recursive residuals statistics
  
      Returns
      -------
      cusum : array_like
          An array of length `nobs - k_exog` holding the
          CUSUM statistics.
  
      Notes
      -----
      The CUSUM statistic takes the form:
  
      .. math::
  
          W_t = \frac{1}{\hat \sigma} \sum_{j=k+1}^t w_j
  
      where :math:`w_j` is the recursive residual at time :math:`j` and
      :math:`\hat \sigma` is the estimate of the standard deviation
      from the full sample.
  
      Excludes the first `k_exog` datapoints.
  
      Due to differences in the way :math:`\hat \sigma` is calculated, the
      output of this function differs slightly from the output in the
      R package strucchange and the Stata contributed .ado file cusum6. The
      calculation in this package is consistent with the description of
      Brown et al. (1975)
  
      References
      ----------
      .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975.
         "Techniques for Testing the Constancy of
         Regression Relationships over Time."
         Journal of the Royal Statistical Society.
         Series B (Methodological) 37 (2): 149-92.
      """
      d = max(self.nobs_diffuse, self.loglikelihood_burn)
      return np.cumsum(self.resid_recursive[d:]) / np.std(
          self.resid_recursive[d:], ddof=1
      )
  
imports: import numpy
  import pandas
  from statsmodels.compat.pandas import Appender
  from statsmodels.tools.data import _is_using_pandas
  from statsmodels.tsa.statespace.mlemodel import MLEModel, MLEResults, MLEResultsWrapper, PredictionResults, PredictionResultsWrapper
  from statsmodels.tsa.statespace.tools import concat
  from statsmodels.tools.tools import Bunch
  from statsmodels.tools.decorators import cache_readonly
  import statsmodels.base.wrapper
label_desc: Use image node_id 4 for calling the RecursiveLSResults obj's underlying member method code with example usage: obj.cusum() and returns: unknown