Book Recommendation on Time Series Statistics

Question

Professionally I am analysing high-frequency data coming from motion sensors and alike. I would like to "up my theoretical background game" in this area and am therefore looking for recommendations to books about (I guess) statistics and probability theory concerning time series pehomena.

Concerning my background: I hold a master's degree in theoretical mathematics (Did some Probability Theory, statistics und stochastical analysis, though it was not my focus)

Any hints would be greatly appreciated. Thanks in advance!

Answer 1

I think Ljung's System Identification: Theory for the user is the authoritative reference, although it was a bit difficult for me.

I have found there are several "schools of thought" in the field that pervade theory, notation, and approach to essentially the same methods: control (ODEs), statistics (ARIMA methods), signal theory (Kalman filters)...

You can also differentiate between continuous/discrete time approaches. As far as I recall, Ljung's book was mainly discrete.

Answer 2

These texts are popular in Economics/Finance.

1. Hamilton "Time Series" -Link It is a LONG book (816 pages) but actually does not cover THAT much material. However, instead it is very user-friendly which provides a lot of details for the material it covers. It is a standard reference in Economics PhD classes for Time Series (which are important topics for macroeconomists).

2. Tsay "Analysis of Financial Time Series" Link- More finance oriented text. I think this is a standard reference for Financial Time Series for Finance people. A bit expensive.

3. Brockwell "Time Series: Theory and Methods" Link - This used to be (still is?) the main reference for Time Series back in the day for those theoretically inclined. Heavy on mathematics, so only for people with strong mathematics/statistics background.