Analysis of Financial Time Series, Third Edition

Chapter 11

State-Space Models and Kalman Filter

The state-space model provides a flexible approach to time series analysis, especially for simplifying maximum-likelihood estimation and handling missing values. In this chapter, we discuss the relationship between the state-space model and the ARIMA model, the Kalman filter algorithm, various smoothing methods, and some applications. We begin with a simple model that shows the basic ideas of the state-space approach to time series analysis before introducing the general state-space model. For demonstrations, we use the model to analyze realized volatility series of asset returns, the time-varying coefficient market models, and the quarterly earnings per share of a company.

There are many books on statistical analysis using the state-space model. Durbin and Koopman (2001) provide a recent treatment of the approach, Kim and Nelson (1999) focus on economic applications and regime switching, and Anderson and Moore (1979) give a nice summary of theory and applications of the approach for engineering and optimal control. Many time series textbooks include the Kalman filter and state-space model. For example, Chan (2002), Shumway and Stoffer (2000), Hamilton (1994), and Harvey (1993) all have chapters on the topic. West and Harrison (1997) provide a Bayesian treatment with emphasis on forecasting, and Kitagawa and Gersch (1996) use a smoothing prior approach.

The derivation of Kalman filter and smoothing algorithms necessarily involves ...