Description

Chapter 7

These slides accompany Chapter 7 (“Filtering”) of the book

Yongmiao Hong, Oliver Linton, Jiajing Sun
Econometrics and Time Series Methods: Theory, Applications, and R Implementation.

The slides provide a structured introduction to filtering methods for time series, with a focus on extracting latent signals from noisy observations. They develop the state–space representation of dynamic models and show how many familiar time series models can be cast in this framework. Core topics typically include the formulation of state and observation equations, the Kalman filter for optimal linear prediction, updating and forecasting recursions, and the concepts of filtering, smoothing, and prediction. The slides also discuss initialization issues, handling missing data, and interpreting filtered and smoothed states in empirical applications.

In line with the book’s integration of theory, applications, and computation, the slides connect the underlying state–space and filtering theory with practical implementation in R. They illustrate how to specify state–space models, run filtering and smoothing algorithms, obtain estimates of unobserved components, and use them for forecasting and structural analysis. The material is suitable for advanced undergraduate and graduate teaching and can be directly used or adapted by instructors.

Unless otherwise indicated, the slides are shared under the Creative Commons Attribution–NonCommercial 4.0 International License (CC BY-NC 4.0). Readers and instructors who wish to request the LaTeX source files or provide feedback are welcome to contact us at jiajing.sun@gmail.com.