TIME SERIES ANALY BY STATE SPACE METHODS:SECOND EDITION OSSS (Oxford Statistical Science Series)
This is a comprehensive treatment of the state space approach to time series analysis. A distinguishing feature of state space time series models is that observations are regarded as made up of distinct components, which are each modelled separately.
Why Read This Book
You will gain a rigorous, component-based framework for modeling, estimating, and forecasting time series using state‑space methods that map directly to signal processing problems (Kalman filtering, smoothing, and likelihood‑based estimation). The book gives the mathematical tools and algorithms you need to convert ARMA/structural models into state‑space form so you can tackle spectral analysis, missing data, time‑varying systems and practical DSP tasks in audio, radar and communications.
Who Will Benefit
Engineers and quantitative practitioners with an intermediate-to-advanced background in statistics or signal processing who need principled state‑space and Kalman‑filter solutions for estimation, spectral analysis, and forecasting.
Level: Advanced — Prerequisites: Undergraduate multivariable calculus and linear algebra, probability and basic statistical inference, familiarity with ARMA/ARIMA concepts (or equivalent exposure to classical time series). Some programming experience (R/MATLAB/Python) is helpful for implementing algorithms.
Key Takeaways
- Implement the Kalman filter and smoother for state‑space models and use them for online estimation and offline smoothing.
- Represent ARMA, ARIMA and structural (unobserved component) models in state‑space form and translate between representations.
- Estimate model parameters by maximum likelihood (including diffuse priors) and apply model diagnostics for time series.
- Perform spectral analysis and compute time‑varying spectra via state‑space techniques for signals such as audio, speech, radar and communications.
- Handle missing data, irregular sampling, intervention/outlier detection, and forecasting within a unified filtering/smoothing framework.
- Formulate and apply simulation smoothing and Monte Carlo methods for uncertainty quantification and nonlinear/non‑Gaussian extensions.
Topics Covered
- Introduction and overview of state‑space approach
- Linear Gaussian state‑space models: definitions and notation
- The Kalman filter: recursion, stability and implementation
- Smoothing algorithms and simulation smoothing
- Likelihood evaluation, estimation and diffuse initialization
- State‑space representations of ARMA/ARIMA and structural models
- Unobserved components, trend/seasonality and intervention models
- Multivariate state‑space models and system identification
- Forecasting, missing data and model diagnostics
- Spectral analysis and frequency‑domain interpretation via state‑space
- Time‑varying parameters, adaptive filtering and time‑series control
- Nonlinear and non‑Gaussian state‑space models (extensions)
- Applications and worked examples (signal estimation, audio/speech, radar, communications)
Languages, Platforms & Tools
How It Compares
More mathematically detailed and algorithmically focused on state‑space techniques than Harvey's 'Forecasting, Structural Time Series Models and the Kalman Filter', and more concentrated on state‑space methods than Shumway & Stoffer's broader 'Time Series Analysis and Its Applications.'
