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text 2017-11-20 18:45
Reading progress update: I've read 129 out of 320 pages.
Nonlinear Time Series Analysis - Thomas Schreiber,Holger Kantz

I while back I arrived at the "advanced topics" and sure enough things got a lot harder. There was one hilarious bit where the author spouts a horrendous mess of incomprehensible point-set topological jargon and then announces that was the version accessible to physicists, avoiding mathematical technicalities...

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text 2017-11-09 19:18
Reading progress update: I've read 85 out of 320 pages.
Nonlinear Time Series Analysis - Thomas Schreiber,Holger Kantz

This is proving to an excellent introduction to a fascinating but notoriously treacherous subject. I wish I had started reading it much earlier.

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text 2017-10-18 09:42
Reading progress update: I've read 29 out of 320 pages.
Nonlinear Time Series Analysis - Thomas Schreiber,Holger Kantz

If I've understood this properly, linear filtering will not remove dynamical noise from a non-linear time series but can remove narrow-spectrum error noise.

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text 2017-10-17 08:53
Reading progress update: I've read 13 out of 320 pages.
Nonlinear Time Series Analysis - Thomas Schreiber,Holger Kantz

Second hand copy: some unmentionable has annotated the text in ink!
Arrrrrrrrrrrghhh!

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review 2017-06-08 09:12
Time Series Analysis and its Applications, Shumway and Stoffer
Time Series Analysis and Its Applications: With R Examples (Springer Texts in Statistics) - David S. Stoffer,Robert H. Shumway

I read the first ~100p of this book. I stopped because the subject matter had diverged too far from my area of immediate interest (which was covered in the first chapter) rather than because the book is bad. In fact I think it is a good introduction to the topic for those with an interest and a background covering "normal" statistics to a level most STEM undergrads would have. Perhaps one thing that became obvious to me by inference should have been made explicit at the outset, which is that the fundamental general approach is as follows:

 

1. Get time series and plot it.
2. Guess any trends and/or periodicities in the data (various methods)
3. Subtract them (various methods)
4. Examine what's left ("residuals") to see if it behaves like noise (i.e. has some known type of random distribution) (various methods)
5. If it does, YAY! You have a usable model of the time series
6. If it does not, either make further guesses about trends/periodicities in the residuals and repeat from step 2 OR
7. Go back to the original time series and start from step 2 with different guesses about the nature of trends/periodicities

 

A flow chart of this at the beginning of the book would make what the book is actually about crystal clear.

 

As mentioned in a status update, the book does not assume the reader is scientifically motivated and does not discuss the meaning or validity of any trends, correlations or periodicities discovered. There are applications where this is entirely legitimate, probably the biggest and most utilised being analysis of financial/economic data for purposes of investment or trading: One only needs a model that works and not an explanation of why it works in order to make practical decisions. I would advise budding scientists to approach with caution, however; this form of analysis can only generate empirical models and hypotheses about why they are true are a separate but essential part of the scientific process. So, for example, if one discovers a model of the form, seasonal oscillation + white noise, describing your time series, one can make predictions about the future but there is no explanation of why the seasonal variation occurs. You are only part way there, scientifically.

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