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In what book can I learn the mathematical theory of times series?

I know times series is always taught in statistics courses, so a lot of other mathematical fields may omit this in their textbooks.

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At the introductory level, I recommend Introduction to Time Series and Forecasting by Peter J. Brockwell and Richard A. Davis. This book is used in the math dept in my university.

For the advanced level, Time Series Analysis by James Douglas Hamilton and Time Series: Theory and Methods by Peter J. Brockwell and Richard A. Davis are very demanding in your mathematical background.

Another is Econometrics by Fumio Hayashi. Although it is a book about econometrics, it contains very rigorous treatment on time series in the latter half of the book.