Ljung-Box and Box-Pierce tests for autocorrelation

[rmehta004]

• Implement a version of the Ljung-Box and Box-Pierce test for autocorrelation of time series, that works for testing cross correlation in time series. This probably amounts to just replace the autocorrelation with cross correlation in the following formula. https://en.wikipedia.org/wiki/Ljung%E2%80%93Box_test but if it is any more problematic, let me know.
• These can be in a file acorr.py in the mgcpy\independence_tests module, or in separate files. Can also be the same test with a flag for the two tests.
• As a methodological test, be convinced that it is asymptotically valid (use IndependentAR1 simulation), and that it is consistent for linear processes (use CorrelatedAR1 simulation).
• Unit tests can just be a copy of those that exist for other time series, in mgcpy\independence_test\unit_tests. PR to time-series branch of https://github.com/neurodata/mgcpy.

[j1c]

Def not asymptotically valid?

[rmehta004]

Thanks! If block permutation does not work as well, then we can take it as is, and say that to our knowledge there are no classical tests of cross correlation.

[j1c]

Block permutation!