7.10.1.16. statsmodels.stats.diagnostic.recursive_olsresiduals¶

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

calculate recursive ols with residuals and cusum test statistic

Parameters:

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

Returns:

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

Notes

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.

References

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.