Some Contrasting Examples of the Time and Frequency Domain Approaches to Time Series Analysis

Abstract Two distinct approaches to the analysis of time series data are in common use — the time side and the frequency side. The frequency approach involves essential use of sinusoids and bands of (angular) frequency, with Fourier transforms playing an important role. The time approach makes little use of these. Certain useful techniques are hybrids of these two approaches. This work proceeding via examples, compares and contrasts the two approaches with respect to modelling, statistical inference and researchers' aims.