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As a former mathematics student, when reading any math-related materials I tend to care about their mathematical rigour very much. Such high attention to mathematical details might be a good habitat or might be bad, but at this time it still sticks to me very hard, so for a textbook it will be easier for me if:

  1. It has a well founded and preferably self contained mathematical framework. I don't need it to present every proof perfectly or build everything from scratch. But certainly it should be rigourous and not overlook important nontrivial mathematical subtlety (such as not fiddling with infinite series without proper assumption or explanation)

  2. It should preferably have compact, easy to read mathematical notations. For example, use matrix notations instead of term by term notations for summations etc. if applicable.

Hamilton's classic is surely a good choice and I already have it. However there might be two drawbacks with it: 1) too long... and some of its notations looks cubersome; 2) might be a bit outdated. So I'd appreciate it if anyone can give other recommendations. Thanks!

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    $\begingroup$ Time Series Analysis and Its Applications by R.H. Shumway and D.S. Stoffer .website. They have lots of examples and exercises, probably paying more attention to code than other books, but they do not neglect the science behind time series. $\endgroup$ – V. Aslanyan Sep 21 '18 at 18:17
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I recommend Time Series: Theory and Methods by Brockwell & Davis. They have a strong focus on ARIMA models and related topics (stationarity, autocorrelation etc.), and they are as rigorous as you would expect from a book that appeared in the Springer Series in Statistics. They include exercises for - without solutions, though.

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I learned Time Series from Time Series Analysis and Its Applications by R.H. Shumway and D.S. Stoffer. The textbook has its own website, where you can also find accompanying R packages, and a stripped down version of the textbook and the actual, statistically and mathematically rigorous version. If you have access to Springer Link, you can download the Springer markup version for free. The author version is available for free on the textbook website. It also has some exercises in the end of each chapter but with no solution guide. Some answers and solutions can be found on google or you can ask them here :)

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