Time Series Analysis

Hello All. I am a new member to this forum. I wish to understand a couple of papers


which basically involve a lot of statistical analysis. I have a PhD in EE but my major was circuit design. I have taken basic courses in Probability but never went beyond that. I wish to now learn the ways to analyse systems whose mode of operation is far from being linear. This involves time series analysis and maybe more.

I wish to know the succession of books that I might have to read in order to be able to understand papers that I have cited above. Also, I like books which are easier to understand.

I'll greatly appreciate if you can suggest me a good plan of action so that I can finally be able to read and understand papers of the above kind.
Thanks very much Richie. I greatly appreciate your help. I was actually thinking of reading "Introduction to Stochastic Modeling" by Samuel Kirlin. I really loved the book. It has quite some information on Markov processes. Also, if needed, I will read Time Series Analysis by Brillinger after I am done with the first one. The first book actually gives a bit of information on Markov Chains and Markov Processes. I hope that after reading it, I might be able to assimilate those papers.

I'd greatly appreciate it if you can just go through the contents of Kirlin's book which is given in here


and let me know if you think this will suffice.

Thanks once again!


Dark Knight
The first book(Kirlin) is not discussed much about Time Series. I just go through the table of contents.
Brillinger's is a nice book. I thought this would be slightly difficult for non-stats ( actually maths) people.
Thanks Richie! I think I will read Kirlin's book because it was a long time that I read the basics of Probability Theory. I will then try to read Brillinger's book but if I find it hard, I will read the one you referred me to. Brockwell's book seems to be easier to understand.

I have yet another question for you. People who get a master's degree in stats are made to read Measure theory. What is the real purpose of reading that? I tried to read K. L. Chung's book on Probability and found it hard to understand. Can you please give your viewpoint as to why people are made to go through measure theoretic approach to probability? Is it necessary to know it?


Dark Knight
Probability is a measure. Measure theory lays foundation of statistical inference. Convergence( in prob, in law, almost surely ... etc) and Asymptotic properties are plays big role in estimation and hypothesis testing. Once you know more about the subject you can appreciate the importance of measure theory.
I am a statistician. For empirical statistical analysis one may not necessary to know all measure theory concepts. In general, for applied research one only need to know the intuition( type of convergence, asymptotic results: not required to know the proofs) of measure theory.

These are ACF and PACF tests of a stationary test series. I have gone through lots of videos and posts about Box-Jenkins, but still can't apply it in this case. What all terms should be included for an ARIMA model for this series?
I tried applying AIC in R, but it takes only consecutive ar/ma terms.
Please help me with this by referring to a relevant pdf or just explain the case here itself.


Fortran must die
I work with ARIMA, regression with AR error, and Exponential Smoothing most often and have started to work with Vector Autoregressive models and Vector Error Correction models. These are common in economics or social sciences, but you may not be interested in them in engineering. It depends specifically what you want to do. GARCH/ARCH models are also popular in finance (again they meet specific needs you may not have).

If you want books in these areas I can recommend some. You might also look at the little R book for time series https://media.readthedocs.org/pdf/a...latest/a-little-book-of-r-for-time-series.pdf
and this beginners book on forecasting. https://www.otexts.org/fpp