I have a time series $(x_i)_{i=0}^n$ and want to know if a positive (resp. negative) increment is more likely to be followed by another positive (resp. negative) increment or not.

The naïve statistic to use is $$S=\frac{\sum_{i=1}^{n-1}\mathrm{sign}(x_{i+1}-x_i)\cdot\mathrm{sign}(x_i-x_{i-1})}{n-1}.$$

Is this a known statistic? Is its distribution known?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.