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Books for self-studying time series analysis?

I am new to time series modelling altogether. But I am aware about regression modelling and some data mining algorithms like decision trees.

I want to learn time series from scratch. My background is Mathematics. Please suggest me any good book/material/web resource for step by step learning with case studies.

Thanks

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    $\begingroup$ If you want the classical theory, it's hard to go wrong with Brockwell and Davis. $\endgroup$
    – cardinal
    Commented Apr 18, 2011 at 9:26
  • $\begingroup$ @mpiktas Let's keep it running here since the other question asked about applications with R. $\endgroup$
    – chl
    Commented Apr 18, 2011 at 9:39
  • $\begingroup$ @chl, ok, this is one of those good duplicates. No worries, I just wanted an additional moderated opinion :) $\endgroup$
    – mpiktas
    Commented Apr 18, 2011 at 9:46
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    $\begingroup$ stats.stackexchange.com/questions/24398/… is another "good duplicate" (online, rather than books). stats.stackexchange.com/questions/20514/… on the other hand is basically an exact duplicate, and should be merged. the three would then compliment each other nicely. $\endgroup$
    – naught101
    Commented May 9, 2012 at 23:14

2 Answers 2

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If you're coming from a mathematics background, and you want to learn time series, it's hard to go wrong with a combination of:

  1. The Analysis of Time Series (Chatfield): introduction at the undergraduate level
  2. Fourier Analysis of Time Series (Bloomfield): introduction to Fourier methods at the undergraduate level

and after you've gone through those two and learned the basics, proceed to:

  1. Time Series: Theory and Methods (Brockwell & Davis): excellent high-level undergraduate / starting graduate-level book
  2. Spectral Analysis and Time Series (Priestley): excellent graduate-level text

and if you become interested in spectrum estimation, the best book I'm aware of is:

  1. Spectral Analysis for Physical Applications (Percival and Walden): more of an engineering flavour, but lots of great examples and carefully written algorithms that you can turn into code.

When I want to look up something I've seen before in classical time series methods, I mostly use Priestley. It's not an easy read by any means, but it's very well written, and you can go back to it and learn new things every time. Since you're coming from a mathematics background, you shouldn't have too much issue with any of the probabilistic notation, especially if you've had some measure theory. If I'm reviewing an algorithm for spectral methods, I use Percival & Walden: it's the only good book I'm aware of that covers modern spectrum estimation techniques without diverging too strongly into wavelets or time-frequency methods.

I would encourage you to stay away from focused books on econometrics or any area of time series where the focus is on one particular area, as nonstandard notation and terminology tends to develop within these subfields. If it's your first approach to time series, start with a couple of good general undergraduate books (1 and 2 are decent, and have lots of examples that you can work through on your own with R). Only after you know the basics should you venture into the world of specific subfields and read books there.

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  • $\begingroup$ +1. Brockwell & Davis is a really strong text for general time series. $\endgroup$
    – Christopher Aden
    Commented Apr 19, 2011 at 16:14
  • $\begingroup$ +1, although I cannot understand disdain for econometrics. The OP mentions regression, for which I do not think spectral methods are useful. And I am curious about non-standard notation, could you elaborate more on that? $\endgroup$
    – mpiktas
    Commented Apr 19, 2011 at 20:25
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    $\begingroup$ I'm coming at time series from an applied perspective, so I started as an engineer, then moved into statistics. All the (and by no means has my exploration been comprehensive) books and papers I've read that came at time series from an econometrics point of view have been 'different'. I'm not sure I can describe it any better, but there's always subtle differences in notation or approaches that don't jive with mainstream statistical time series analysis. It's not that one is better than the other, but simply that for best overall coverage, general approaches win. $\endgroup$
    – Wesley Burr
    Commented Apr 19, 2011 at 22:26
  • $\begingroup$ This is an excellent answer. Thanks for the descriptions. I borrowed Chatfield from my library, and it's very readable. I'm going to get a copy of both it and Brockwell and Davis. $\endgroup$
    – naught101
    Commented May 9, 2012 at 23:18
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I have yet still not found the time series book which I like. Here is the list of books which I found very useful:

  1. Time Series Analysis by J. D. Hamilton. This is the book which contains practically everything.

  2. Applied econometric time series by W. Enders. Classical reference

  3. Introductory econometrics for finance by Ch. Brooks. I use this book for teaching time-series to students with little mathematical background. Nevertheless it is a good book for getting the ideas without too much mathematical detail.

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    $\begingroup$ These are classical / good references for econometric time series, but I wouldn't recommend them for a general approach or a first learner. I'm especially not a fan of the Hamilton book: I purchased it because it seemed comprehensive, but it's not particularly well written. $\endgroup$
    – Wesley Burr
    Commented Apr 19, 2011 at 15:58
  • $\begingroup$ @Wesley, note that I only claim that I found these books useful. Concerning Hamilton, it is a huge book, and probably some chapters are not good. On the other hand chapters on non-stationarity I found very good. In general I use this book as a reference, these type of books can be overwhelming at first, but in the end they are most useful, that is why I included it. $\endgroup$
    – mpiktas
    Commented Apr 19, 2011 at 18:28
  • $\begingroup$ @mpiktas: actually you claim that hamilton "contains practically everything" :P $\endgroup$
    – naught101
    Commented Apr 20, 2012 at 4:31
  • $\begingroup$ @naught101, well it does, doesn't it? The quality varies though, that was what I was trying to address with my comment. $\endgroup$
    – mpiktas
    Commented Apr 20, 2012 at 6:37

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