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