Fourier Analysis of Time Series : An Introduction (Wiley Series in Probability and Statistics)

Rating:
Summary: nice beginning treatment of frequency domain time series
Review: As a time series analyst who studied time series in graduate school when the first edition of Bloomfield's book came out, I really appreciated it. The frequency approach to time series is not natural because we tend to look at the series to see how it changes (fluctuates) over time. This makes the time domain approach very natural. It is only when one sees periodicity in the series and can relate the series to a summation of sine and cosine waves that the frequency domain ideas get appreciated.

Bloomfield introduces Fourier series in a gentle way, making it clear. Concepts are introduced as needed to deal with specific aspects of real time series data. I particularly liked his treatment of complex demodulation, which could be a very difficult concept to grasp if not presented carefully. But Bloomfield explains it well and provides another way to look at the famous Wolfer sunspot data using an approach based on complex demodulation (assuming a slowly changing period for the series).