Name: Time Series Analysis
ISBN: 9780816211043

Time Series Analysis

Bridging classical models and modern topics, the _Fifth Edition_ of _Time Series Analysis: Forecasting and Control_ maintains a balanced presentation of the tools for modeling and analyzing time series. Also describing the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering, the _Fifth Edition_ continues to serve as one of the most influential and prominent works on the subject. _Time Series Analysis: Forecasting and Control_, _Fifth Edition_ provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series and describes their use in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes.

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graycatNov 2019

Here are some old references for the problem of the OP:

David R. Brillinger, Time Series Analysis: Data Analysis and Theory, Expanded Edition, ISBN 0-8162-1150-7, Holden-Day, San Francisco, 1981.

George E. P. Box and Gwilym M. Jenkins, Time Series Analysis --- Forecasting and Control: Revised Edition, ISBN 0-8162-1104-3, Holden-Day, San Francisco, 1976.

Brillinger was a John Tukey student at Princeton and long at Berkeley.

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helwrSep 2010

Well, there are some related topics on Quora: http://www.quora.com/Randomness?q=random and http://www.quora.com/What-are-some-good-books-on-random-proc...

You can actually ask your question there as well in case this question gets unnoticed on HN; Quora people are very smart and pretty responsive

see http://en.wikipedia.org/wiki/Stochastic_process, http://en.wikipedia.org/wiki/Random_walk and do a search for Random Processes or Stochastic Processes on Amazon bookstore

Read about Entropy: http://en.wikipedia.org/wiki/Entropy A good book on Information theory can help you put it in context: http://www.amazon.com/s/ref=nb_sb_ss_c_1_18?url=search-alias...

Check out GMP http://gmplib.org/

If you're philosophically inclined read some existentialists, they deal a lot with irrationality and chaos: http://en.wikipedia.org/wiki/Existentialism

If you're financially inclined read Random Walk Down Wall Street: http://www.amazon.com/Random-Walk-Down-Wall-Street/dp/039331 and the Black Swan: http://www.amazon.com/Black-Swan-Impact-Highly-Improbable/dp... you may want to check out his other book as well, it is rather non-technical: http://www.amazon.com/Fooled-Randomness-Hidden-Chance-Market...

To learn more on how Wall Street deals with the stock market randomness read some books on Time Series analysis and forecasting, e.g the classic http://www.amazon.com/Time-Analysis-Forecasting-Probability-...

If you are a data scientist in heart read this great Q&A thread: http://www.quora.com/How-do-I-become-a-data-scientist

I wish I could help you with a link to a clear non-technical introductory article but this is all I've got. As random as it gets:)

Probably some good introductory book on science will fit the bill, science after all deals primarily with randomness. You may want to check out http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

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graycatJun 2017

I agree with a lot of that.

But hypothesis testing remains important because in some contexts with too little data that's about the best can do. For parametric tests, there are some cases when that's okay.

The asymptotic stuff is mostly okay: Can't figure out precisely what the darned thing will do for case n so let n go to infinity and maybe can see what happens. Then say, "for large n, this is about what happens" -- crude but better than nothing.

The central limit theorem and more says that the Gaussian is really important. Okay. Done. We know that. But, right, for too long too much of statistics made nearly a religion out of the Gaussian. Bummer.

Today happened to see the discussion panel at Stanford at

https://www.youtube.com/watch?v=hxXIJnjC_HI

It's fun stuff, with some big names.

They are laughing at ML: ML discovered statistics like Columbus discovered America. Columbus didn't discover America since when he landed millions of people were already living there. And when CS AL/ML discovered statistics, there was already a huge field there.

Moreover, the situation is reversed: Columbus brought better ship, etc. technology to the Americas than the Americas had, but CS AL/ML are bringing nearly all highly inferior technology to statistics, pure/applied math, etc.

CS AI/ML is nearly all new labels for adulterated old wine.

So, take some data on two variables, plot on an X-Y graph, fit a straight line, get the coefficients of the line as in first year algebra, and, presto, bingo, "The AI revolution is here!!!!", CS had had a machine "learn" the coefficients and they started with "training" data, that is trained the machine!!!!!! Where can I get one of those airline seat barf bags? Upchuck time!

Uh, I have a pretty good professional library; much of my house is lined with -bookshelves. The main topics are pure/applied math. Some of the books relevant to statistics include (with TeX markup)

Alexander M.\ Mood, Franklin A.\ Graybill, and Duane C.\ Boas, {\it Introduction to the Theory of Statistics, Third Edition,\/} McGraw-Hill, New York, 1974.\ \

N.\ R.\ Draper and H.\ Smith, {\it Applied Regression Analysis,\/} John Wiley and Sons, New York, 1968.\ \

C.\ Radhakrishna Rao, {\it Linear Statistical Inference and Its Applications:\ \ Second Edition,\/} ISBN 0-471-70823-2, John Wiley and Sons, New York, 1967.\ \

Henry Scheff\'e, {\it Analysis of Variance,\/} John Wiley and Sons, New York, 1967.\ \

Yvonne M.\ M.\ Bishop, Stephen E.\ Fienberg, Paul W.\ Holland, {\it Discrete Multivariate Analysis:\ \ Theory and Practice,\/} ISBN 0-262-52040-0, MIT Press, Cambridge, Massachusetts, 1979.\ \

Stephen E.\ Fienberg, {\it The Analysis of Cross-Classified Data,\/} ISBN 0-262-06063-9, MIT Press, Cambridge, Massachusetts, 1979.\ \

Leo Breiman, Jerome H.\ Friedman, Richard A.\ Olshen, Charles J.\ Stone, {\it Classification and Regression Trees,\/} ISBN 0-534-98054-6, Wadsworth \& Brooks/Cole, Pacific Grove, California, 1984.\ \

R.\ B.\ Blackman and J.\ W.\ Tukey, {\it The Measurement of Power Spectra:\ \ From the Point of View of Communications Engineering,\/} Dover, New York, 1959.\ \

William W.\ Cooley and Paul R.\ Lohnes, {\it Multivariate Data Analysis,\/} John Wiley and Sons, New York, 1971.\ \

Maurice M.\ Tatsuoka, {\it Multivariate Analysis: Techniques for Educational and Psychological Research,\/} John Wiley and Sons, 1971.\ \

E.\ L.\ Lehmann, {\it Testing Statistical Hypotheses,\/} John Wiley, New York, 1959.\ \

E.\ L.\ Lehmann, {\it Nonparametrics: Statistical Methods Based on Ranks,\/} ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975.\ \

Jaroslav H\'ajek and Zbyn\v ek \v Sid\'ak, {\it Theory of Rank Tests,\/} Academia, Prague, 1967.\ \

Sidney Siegel, {\it Nonparametric Statistics for the Behavioral Sciences,\/} McGraw-Hill, New York, 1956.\ \

Donald F.\ Morrison, {\it Multivariate Statistical Methods: Second Edition,\/} ISBN 0-07-043186-8, McGraw-Hill, New York, 1976.\ \

Harry H.\ Harman, {\it Modern Factor Analysis: Second Edition, Revised,\/} The University of Chicago Press, Chicago, 1967.\ \

George E.\ P.\ Box and Gwilym M.\ Jenkins, {\it Time Series Analysis --- Forecasting and Control: Revised Edition,\/} ISBN 0-8162-1104-3, Holden-Day, San Francisco, 1976.\ \

Jean-Ren\'e Barra, {\it Mathematical Basis of Statistics}, ISBN 0-12-079240-0, Academic Press, New York, 1981.\ \

So, what is really significant recent ML is adding to this quite old material? How much of the good stuff in that material has CS AI/ML even read and understood so far? Uh, what am I missing? I can think of a little but not much.

CS AI/ML going for applications of statistics is a lot like Stanley Tools, long in the hammer, screwdriver, saw, drill, and nail gun business, going into the residential construction business building, selling new houses and claiming that they have something new! That is, because they make good nail guns they conclude that they are the best at building houses. They know nothing of excavation, masonry, framing carpentry, windows, doors, roofing, plumbing, electrical, HVAC, dry wall, painting, circular stairs, walnut paneling, landscaping, or even the building codes, but they've got some good nail guns!

The math I derived and published in multi-dimensional, distribution-free anomaly detection has next to nothing to do with any of those books above; instead, I did original work and drew from ergodic theory, abstract algebra, and a classic result of Ulam. For the math for my startup, it's also original and even farther from those books above. In both cases, the core results are presented as theorems with proofs. Such math is mostly not what I'm seeing in CS AI/ML.

I DID see some cute, recent work in analysis, maybe from ML, of the over fitting problem; I don't need that work for my startup, but I do intend to go back and read that work.

My main points are:

(1) If AI/ML have some applied math tools that are solid, good, and new, terrific. Then those cases will add to the many thousands of such tools already on the shelves of the research libraries.

(2) The most important paradigm for a solid future for such tools is new, solid, correct, and powerful theorems and proofs building on solid material in math. That is, we want better stuff than is already in the libraries.

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