Understanding Post ``Probabilistic CUSUM for change point detection''

[AndrewLawrence80]

The method in the post is a p-value hypothesis testing based on CLT assumption on the sum of time series observations. However I'm confused how it related with the CUSUM algorithm. In this article, The CUSUM algorithm a small review, the instantaneous log-likelihood ratio is defined as eq 1.19

$$s=\dfrac{\delta}{\sigma^2}(x_i-\mu-\dfrac{\delta}{2})$$

for single side CUSUM.

If you sum up the log-likelihood ratio, the result is still different from the CLT definition.

So how to understand the relation between CUSUM and the p-value hypothesis testing?

[SaremS]

Hi,

yes, you are likely right that CUSUM is a misnomer for my idea. When writing the article, I presumed that any CP algorithm based on cumulative sums is a CUSUM-algo but, apparently, it is specifically used for the likelihood-ratio test you linked.

Let me dig in a bit deeper to see if this is indeed the case. But if in doubt, the paper you linked is the preferable source.

[AndrewLawrence80]

Hi,

yes, you are likely right that CUSUM is a misnomer for my idea. When writing the article, I presumed that any CP algorithm based on cumulative sums is a CUSUM-algo but, apparently, it is specifically used for the likelihood-ratio test you linked.

Let me dig in a bit deeper to see if this is indeed the case. But if in doubt, the paper you linked is the preferable source.

Yes, I think the post is using the z-test algorithm. It really works well. And recently I'm working for time series mean change detection in my research paper. I think the t-test is a good alternative for small samples. Furthermore, I'm confused if one-sample hypothesis test strictly works for time series data, or we should resort to two-sample test according to wiki by assuming observations before and after change points are from different distributions.