Time Series Analysis by E. J. Hannan
1960

This book is a mathematically rigorous treatment of time series analysis, focusing on the statistical methods used to analyze data observed sequentially over time. It is one of the early foundational texts in the field, contributing to the development of modern statistical signal processing and econometrics.

Hannan begins by establishing the theoretical framework for stochastic processes, particularly stationary processes, which are central to time series modeling. The book emphasizes the use of probability theory and linear algebra to describe temporal dependence in data.

Key topics include:

Autocorrelation and covariance functions: measuring dependence between observations at different time lags
Spectral analysis: representing time series in the frequency domain to identify periodic components
Linear filtering: transforming time series to extract signals or reduce noise
Estimation techniques: methods for identifying model parameters from observed data

The text also explores the relationship between time-domain and frequency-domain approaches, providing a unified perspective on analysis methods.

Applications discussed are primarily theoretical, but the techniques are relevant to areas such as:

Economics and econometrics
Engineering and signal processing
Physical sciences involving temporal measurements