Time series analysis in the frequency domain: rigorous approach · Introduction

Introduction

What this guide covers

An exhaustive mathematical decomposition of stationary processes into their cyclic harmonic components through Fourier analysis and Cramér's spectral theory.

Overview

Topics covered

Introduction
The Frequency Domain in Time Series
Introduction and Fundamentals of the Frequency Domain
1.1 Temporal-Frequency Duality
1.2 Determined Harmonic Analysis
The Spectral Representation Theorem

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

X_t = A \cos(2\pi \nu t + \phi) = U_1 \cos(2\pi \nu t) + U_2 \sin(2\pi \nu t)

View LaTeX source

X_t = A \cos(2\pi \nu t + \phi) = U_1 \cos(2\pi \nu t) + U_2 \sin(2\pi \nu t)