I'd like to ask you if there are any formal, proof-based and mainly theoretical books on time series and panel data. When searching for books on time series and panel data I got really good recommendations but all the books were more leaning towards the applied aspect. Either the books focused more on the computer science aspect (how to plot time series, how to execute Dickey-Fuller test, how to run regressions on panel data) accompanied with intuition but there are no proofs. Sometimes basic stuff is proven (like AR(1) is stationary if and only if the coefficient next to the laggued variable is between -1 and 1).
But, I've already seen a similar question asked here and the only recommended book that meets my needs is this one : Time Series Theory and Methods by Peter J. Brockwell, Richard A. Davis. The one that suggested this book said, I quote, "This used to be (still is?) the main reference for Time Series back in the day for those theoretically inclined." And so I'd like to know if there are any other books of the sort that are more recent or, even if they're old but were heavily used back in the days.
Thank you in advance.
I am not really in a position to answer this question, since I was about to ask something similar when I stumbled upon it...
Also, I am not entirely clear on what you are looking for exactly...
And not knowing the subject very well, I do not know what I am looking for exactly either...
Having said that, let's say we are interested in mathematical treatments of stochastic processes indexed by $\mathbb{Z}$ which are stationary in the $L^2$ sense (i.e. covariance stationary or wide-sense stationary).
Then I have selected these three books
There are really a lot of books trating these topics from the point of view of a statistician, engineer, economist and so on. But I find them so (mathematically) sloppy that I basically cannot read them.
I will try to build-up some knowledge on the subject and hopefully add suggestions in the future.
In the meantime I hope this helps. Let me know.