Cumulative sum of standardized recursive residuals statistics


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

Return type



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)



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.