statsmodels.stats.diagnostic.recursive_olsresiduals(olsresults, skip=None, lamda=0.0, alpha=0.95) [source]

calculate recursive ols with residuals and cusum test statistic

  • olsresults (instance of RegressionResults) – uses only endog and exog
  • skip (int or None) – number of observations to use for initial OLS, if None then skip is set equal to the number of regressors (columns in exog)
  • lamda (float) – weight for Ridge correction to initial (X’X)^{-1}
  • alpha ({0.95, 0.99}) – confidence level of test, currently only two values supported, used for confidence interval in cusum graph
  • rresid (array) – recursive ols residuals
  • rparams (array) – recursive ols parameter estimates
  • rypred (array) – recursive prediction of endogenous variable
  • rresid_standardized (array) – recursive residuals standardized so that N(0,sigma2) distributed, where sigma2 is the error variance
  • rresid_scaled (array) – recursive residuals normalize so that N(0,1) distributed
  • rcusum (array) – cumulative residuals for cusum test
  • rcusumci (array) – confidence interval for cusum test, currently hard coded for alpha=0.95


It produces same recursive residuals as other version. This version updates the inverse of the X’X matrix and does not require matrix inversion during updating. looks efficient but no timing

Confidence interval in Greene and Brown, Durbin and Evans is the same as in Ploberger after a little bit of algebra.


jplv to check formulas, follows Harvey BigJudge 5.5.2b for formula for inverse(X’X) updating Greene section 7.5.2

Brown, R. L., J. Durbin, and J. M. Evans. “Techniques for Testing the Constancy of Regression Relationships over Time.” Journal of the Royal Statistical Society. Series B (Methodological) 37, no. 2 (1975): 149-192.

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© 2006 Jonathan E. Taylor
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