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I bought the book "Introduction to Time Series and Forecasting" by Brockwell and Davis. The first chapter was ok, but in chapter 2 I am totally lost. I cannot figure out the main idea of the explanation, and I cannot figure out the intermediate steps in the author's results; so the math becomes useless. I have no background in stochastic processes.

Can someone recommend a book similar to Brockwell & Davis in contents, but where proofs are given without "It can be shown that..." (with intermediate steps), and which has more coherent explanations? I do not understand why the authors (Brockwell and Davis) are giving the details of all these propositions. I need the book for self-study.

utobi
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Artem Moskalev
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  • I have some slides from a course I taught that might go into more detail in certain places. I can send them to you if it helps – Taylor May 11 '18 at 13:36
  • @RichardHardy, that thread discusses Hamilton book alternatives, as well as general recommendations, while I am quite specific about the Brockwell and Davis book here. – Artem Moskalev May 11 '18 at 13:46
  • @Taylor, that would be super helpful. Do you have some web address for those? I need especially chapter 2. – Artem Moskalev May 11 '18 at 13:46
  • Why do you need proofs? – Aksakal May 11 '18 at 14:02
  • @SWIMS., I understand, but there are threads with numerous recommendations already, I think you will find some relevant material there. Besides, I am not sure how relevant this particular question would be to the general audience at Cross Validated; I think the broader threads are of greater interest. Of course, you may disagree. And if this does not get closed, perhaps it should be flagged and turned into Community Wiki? – Richard Hardy May 11 '18 at 14:11
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    @Aksakal, because I hate learning things by heart, and a proof is the simplest way to see why. Of course, unless the author says sth like "it is obvious..." or "The proof is left to the reader...". For me personally good intuition would also suffice, but usually in advanced math, the intuition is hard to develop unless at least some incomplete proof is given. – Artem Moskalev May 11 '18 at 14:15
  • Time series is not advanced math in these books. I wouldn't bother and move on to next chapters. You didn't even get to interesting stuff and are already stuck. Go through the whole book and later you'll see which proofs are important. Hint: almost none – Aksakal May 11 '18 at 14:19
  • @RichardHardy, maybe. I do not know the proper procedures. But I would say that this questions just seems specific, because Brockwell & Davis is quite a common book for the 1st course in TSA, and I have a feeling many people would want an alternative to exactly this book (like economist guys want an alternative to Hamilton - thus, the other question). – Artem Moskalev May 11 '18 at 14:21
  • @Aksakal, well, in my book (guy without formal math training, just CS) mean square convergence and omitted steps in almost all proofs that require maturity to fill in are "advanced math" :) Though i think that maybe your advice is correct and I should just skim through hard parts. – Artem Moskalev May 11 '18 at 14:25
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    Computer science analogy would be that when you're learning C, pretty much in the first hour of a class they'll give you printf function and ask you to import stdio, then somehow 'Hello World' shows up on screen. You wouldn't ask a professor to show you what's exactly in stdio and how exactly printf is implemented to see that it's doing it right. At some point later in OS class, they may show you bits and pieces of how device drivers work and how kernel interacts with them etc. When the right time comes :P – Aksakal May 11 '18 at 14:38
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    This is not a duplicate of the post that Richard Hardy suggested because it specifically asks about a book on the level of Brockwell and Davis that does not have so many gaps in proofs. Some of the referenced books in that post may be useful to the OP and include some that I referenced in my answer. – Michael R. Chernick May 11 '18 at 15:23
  • I voted to reopen because even though the claimed duplicate has numerous comments and answers about a wide variety of time series books to use for self study. The OP for this question was more specific asking for a book different from Brockwell and Davis but yet on the same level with more detail about the proofs. In my answer I recommended Shumway and Stoffer and Fuller as two books that might fill the OP's requirements. – Michael R. Chernick May 12 '18 at 23:42

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I like Brockwell and Davis. But if you want something at a similar level maybe Shumway and Stoffer would be good. I used Wayne Fuller's book when I taught a course in time series at the level of Brockwell and Davis. If you want a text that is intuitive and simple you can take a look at Christopher Chatfield's book. I assume you want a text that covers both the time and frequency domains. There are books that deal strictly with the frequency domain like Brillinger's book and also Priestley's text and Bloomfield (which is particularly readable). There are also some that deal solely with the time domain.

A great practical text concentrating on ARIMA modeling is the classic by Box and Jenkins. Lahiri has a text on using resampling methods for dependent data which includes a lot about bootstrap. Not many books on time series cover the use of bootstrapping.

utobi
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Michael R. Chernick
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    Thanks for suggestions. Yes, I would want something on Brockwell Davis level, but so that the authors explain things more (without omissions of steps since it is hard for me to fill in) and "why". – Artem Moskalev May 11 '18 at 14:33
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    Take a look at Wayne Fuller's "Introduction to Statistical Time Series" 2nd Edition (1995) Edited by Wiley. I taught out of the first edition. – Michael R. Chernick May 11 '18 at 15:16