Cumulative sum of standardized recursive residuals statistics


cusum : array_like

An array of length nobs - k_exog holding the CUSUM statistics.


The CUSUM statistic takes the form:

W_t = \frac{1}{\hat \sigma} \sum_{j=k+1}^t w_j

where w_j is the recursive residual at time j and \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 \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)


[R43]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.