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I've been studying discrete time series models for a while. I'm familiar with the usual time series models (ARMA, ARIMA, GARCH, etc.), but I want to study their continuous counterparts (CAR and CARMA processes seem very interesting) in order to implement some models to unevely spaced time series.

Despite of the above, I've been trying to find some introductions to continuous time series theory and methods as good as Brockwell & Davis (1991) book, but I couldn't find any, just some reviews here and there (specially the ones by Brockwell).

Do you have any suggestions for a good book on this topic? Thanks in advance!

PS: Please take into consideration that my background doesn't have much measure theory, and in order to read the discrete Time Series literature I had to pretty much teach myself from lecture notes and reviews I found on the web (suggestions on this topic are also welcomed!).

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  • $\begingroup$ What about Shreve's Stochastic Calculus 1 and 2? $\endgroup$ – Jen Bohold Jan 29 '14 at 17:25
  • $\begingroup$ Hi @Jen, thanks for your response: did you mean Stochastic Calculus for Finance? I haven't read it; I'll give it a try! Please, can you post your comment as an answer and, if you read it, give a small abstract of the books (like what background is needed, oriented at which careers, etc.)! $\endgroup$ – Néstor Jan 29 '14 at 17:33
  • $\begingroup$ Yes. Well, I am not reading it.... I just know that these are standard books for Master/PhD students and I think an advanced level of mathematics is needed. Since I did not read it by myself, I will not post it as an answer, since I cannot evaluate if it has an value added for you or not. It just came up to my mind when I read your post and thought it might relate to you. $\endgroup$ – Jen Bohold Jan 30 '14 at 14:37
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    $\begingroup$ But the level of measure theory will not be so high. Since also finance students from non-math faculties read it. So it should be appropriate, if you teach yourself the necessary math. $\endgroup$ – Jen Bohold Jan 30 '14 at 14:38
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For the interested reader, I bought Introduction to Stochastic Processes, Second Edition by Gregory F. Lawler. I found it to be a very gentle introduction to time-continuous and discrete stochastic proccesess, open for a wide audience of graduate or advanced undergraduate students :-).

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