Time series: state space models and Kalman filter · Introduction

Introduction

What this guide covers

Rigorous theoretical foundations, detailed algebraic derivations of prediction, updating and smoothing algorithms, structural component modeling and non-linear methodologies.

Overview

Topics covered

Introduction
State Space Models and the Kalman Filter
Philosophical and Methodological Transition: From the Classical Approach to the Space of States
General Mathematical Formulation of Linear State Space Models
Structural Assumptions about Stochastic Processes
Representation of Classical Time Series Models in State Space

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

y_t = Z_t \alpha_t + d_t + \varepsilon_t, \quad \varepsilon_t \sim \mathcal{N}(0, H_t) \quad \text{[Measurement Equation]}

View LaTeX source

y_t = Z_t \alpha_t + d_t + \varepsilon_t, \quad \varepsilon_t \sim \mathcal{N}(0, H_t) \quad \text{[Measurement Equation]}