Time series modelling with unobserved components
Pelagatti, Matteo M.
- Boca Raton CRC Press 2016
- xvii, 257 p.
Table of Contents:
I. STATISTICAL PREDICTION AND TIME
i. Statistical Prediction ii. Optimal predictor iii. Optimal linear predictor iv. Linear models and joint normality v. Time Series Concepts vi. Definitions vii. Stationary processes viii. Integrated processes ix. ARIMA models x. Multivariate extensions
II. UNOBSERVED COMPONENTS
i. Unobserved Components Model ii. The unobserved components model iii. Trend iv. Cycle v. Seasonality vi. Regressors and Interventions vii. Static regression viii. Regressors in components and dynamic regression ix. Regression with time-varying coefficients x. Estimation xi. The state space form xii. Models in state space form xiii. Inference for the unobserved components xiv. Inference for the unknown parameters xv. Modelling xvi. Transforms xvii. Choosing the components xviii. State space form and estimation xix. Diagnostics checks, outliers and structural breaks xx. Model selection xxi. Multivariate Models xxii. Trends xxiii. Cycles xxiv. Seasonalities xxv. State space form and parametrisation
III. APPLICATIONS
i. Business Cycle Analysis with UCM ii. Introduction to the spectral analysis of time series iii. Extracting the business cycle from one time series iv. Extracting the business cycle from a pool of time series v. Case Studies vi. Impact of the point system on road injuries in Italy vii. An example of benchmarking: Building monthly GDP data viii. Hourly electricity demand ix. Software for UCM x. Software with ready-to-use UCM procedures xi. Software for generic models in state space form
Despite the unobserved components model (UCM) having many advantages over more popular forecasting techniques based on regression analysis, exponential smoothing, and ARIMA, the UCM is not well known among practitioners outside the academic community. Time Series Modelling with Unobserved Components rectifies this deficiency by giving a practical overview of the UCM approach, covering some theoretical details, several applications, and the software for implementing UCMs.
The book’s first part discusses introductory time series and prediction theory. Unlike most other books on time series, this text includes a chapter on prediction at the beginning because the problem of predicting is not limited to the field of time series analysis.
The second part introduces the UCM, the state space form, and related algorithms. It also provides practical modeling strategies to build and select the UCM that best fits the needs of time series analysts.
The third part presents real-world applications, with a chapter focusing on business cycle analysis and the construction of band-pass filters using UCMs. The book also reviews software packages that offer ready-to-use procedures for UCMs as well as systems popular among statisticians and econometricians that allow general estimation of models in state space form.
This book demonstrates the numerous benefits of using UCMs to model time series data. UCMs are simple to specify, their results are easy to visualize and communicate to non-specialists, and their forecasting performance is competitive. Moreover, various types of outliers can easily be identified, missing values are effortlessly managed, and working contemporaneously with time series observed at different frequencies poses no problem.