Finishing Chapter 2

[stephaneguerrier]

Hi guys! As suggested by @coatless, it is better group all issues related to one chapter together to here is what is needed to finish the first chapter:

• [x] @coatless: Fixing AR(1) example, similarly to the MA(1) one.
• [ ] @coatless: Adding all material related bivariate stationarity + cross-cov and correlation, i.e.
  • [x] Joint Stationarity
  • [x] Examples (in class)
  • [x] Definitions of cross-cov and corr
  • [x] Estimator of these quantities
  • [ ] Maybe a simulated example
  • [ ] Maybe a real data example
• [x] @coatless: Fixing graph in section "Estimation of the Mean Function".
• [x] @robertomolinari: Adding discussion on robustness at the end of the chapter, i.e.
  • [x] Explain robustness paradigm (e.g. explain the contamination robust)
  • [x] Add an example with the hydro data to show the difference between the robust and classical ACF
• [ ] If possible, @coatless please address issue #18 to make the example described above pretty. This is of course not a priority!
• [x] @robertomolinari and @HaotianXu Could you please finish the proof of Theorem 1 in the Appendix. More details in my email. Thanks a lot!
• [ ] @robertomolinari: could you review this chapter and change anything you find relevant?
• [x] @HaotianXu: could you add a new section (i.e. 2.4) in this chapter about portemanteau tests. Does not have to be long just talk about the main tests (at most 3), maybe a small simulation and one real data example.

[stephaneguerrier]

Hi @HaotianXu Thanks a lot for the update on the proof. I made a few changes and added the content to the main document. Just one question: we mention the "bounded convergence theorem", why do you need that? Is it the make sure that $E[ sum X_i ] = sum E [X_i]? Could you also review my changes? Thanks again!

[HaotianXu]

Hi Stef, "bounded convergence theorem" is only needed for n goes to infinity, if we let n be finite, we do not need it.

[stephaneguerrier]

Sorry i meant: lim E[ sum X_i ] = lim sum E [X_i]

[HaotianXu]

Hi @stephaneguerrier , "bounded convergence theorem" is showing that lim E[ 1/n sum X_i ] = E [lim 1/n sum X_i] = E[ E[X_i] ] = E [X_i]

[stephaneguerrier]

@HaotianXu ok, makes sense! thanks

[stephaneguerrier]

@robertomolinari I made some changes in sec 2.3.3 (robust), could you review this section when you have the time? Thanks!

[stephaneguerrier]

@HaotianXu I have added something in the list related to issue (new section on white noise tests). Would you mind to address this? Not urgent of course! Merci!

[HaotianXu]

Hi @coatless, in the folder devel there is only "02-stationarity-old.Rmd". Can I edit it? I am not sure it is the right one?

[coatless]

@HaotianXu You can edit it. Just place the details at the end. @stephaneguerrier will then move over into the main.

[HaotianXu]

Hi @coatless , I want to add a simulation to the section 2.4 portemanteau tests and I attached the r code. Could you please help me to add it to the book? Thank you! portmanteau test.zip