RecursiveLSResults.cusum() [source]

Cumulative sum of standardized recursive residuals statistics

Returns: cusum – An array of length nobs - k_exog holding the CUSUM statistics.
Return type: array_like


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.

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