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I have some decent knowledge of probability, stochastic processes and option theory, however I do not have a proper background in statistics.

Now I am working quite a lot with data, and trying methods from here and there such as linear/logistic regression, PCA etc. Yet, I would be comfortable if I had a couple of books that describe main idea, popular methods and their possible well-known and hidden drawbacks.

Ideally such a book would be written with financial applications in mind, preferrably with a good technical level. I've tried Mathematical Statistics with Applications by Wackerly et al. but that lacks focus on quantitative finance, and also seems to cover only very basic things.

I'm grateful for any advice on this topic.

Perhaps worth clarifying that if the book contains other methods of working with data, e.g. particle filters, neural networks etc. I'm even more interested in it.

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    $\begingroup$ I think this really depends on the type of data and purpose of your analysis. A good start for time-series is Handbook of Financial Timeseries, which also has a chapter about particle filters in the end. $\endgroup$ – J.R. Nov 24 '14 at 16:21
  • $\begingroup$ @J.R. judging by the TOC, it seems that it's a collection of papers - does it indeed provides a background in statistics, or it actually requires such a background and only provides advanced material? $\endgroup$ – Ulysses Nov 25 '14 at 10:07
  • $\begingroup$ I noticed that you have not accepted one single answer to all of your questions yet :-( I would very respectfully ask you to do that because members of this community generally put much effort into helping others (and in this case you). Thank you :-) $\endgroup$ – vonjd Nov 28 '14 at 10:49
  • $\begingroup$ @vonjd: I understand this, and I appreciate the help a lot, however before accepting an answer (which would also be the first the others users will see visiting this question) I wanted to make sure that it is indeed answers the best my original request. I have checked the Meucci's book, and found it useful, though not exactly what I need - I'm still trying to find some time to check out other suggestions. I certainly will come back with accepting one of the answers, although less than one week is barely a period to ask for accepting an answer :) $\endgroup$ – Ulysses Nov 28 '14 at 15:33
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I think a good book to start in your case is:

Attilio Meucci: Risk and Asset Allocation

I once had a seminar held by Attilio that was based on the book and it blew my mind. The book is very intuitive yet rigorous.

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    $\begingroup$ And his website has tons of support materials. $\endgroup$ – John Nov 24 '14 at 21:36
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    $\begingroup$ This book is awesome indeed, but the notation gets kind of crazy sometimes, as usual in Meucci's articles. $\endgroup$ – SRKX Nov 25 '14 at 1:59
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    $\begingroup$ Meucci, also gives source code in matlab on his website which is invaluable for understanding some of the tools/techniques, even though it's in matlab. $\endgroup$ – Kyle Balkissoon Dec 16 '14 at 22:07
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Elements of Statistical Learning by Hastie, Tibshirani and Friedman is one of the most-cited books for your purpose. Although it does not have any direct applications to Finance, this is definitely a good book to have in your professional library and can be used as a reference for most topics.

If you want to use a book with more financial applications, I would say that Statistics and Data Analysis for Financial Engineering by Ruppert is one of the best for you. It contains the necessary basics as well as more advanced topics for time series, regression techniques, copulas, and general multivariate statistical methods. I would suggest that you look through the table of contents to get a good overview. The book also contains R code, which might be useful to you, since it is one of the most used languages in statistical analysis.

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1) Analysis of Financial Time Series by Ruey Tsay

2) An Introduction to Bayesian Inference in Econometrics by Arnold Zellner

Not finance specific, but this is the best multivariate stats book I know of: 3) Applied Multivariate Statistical Analysis by Johnson and Wichern

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I would highly recommend this books: Mathematics and Statistics for Financial Risk Management: Book 1

The other one, is Chapter three from, Practical Methods of Financial Engineering and Risk Management: Tools for Modern Financial Professionals: Book 2

Hope it helps.

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