Time series modelling with unobserved components Pelagatti, Matteo M.

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.


(https://www.crcpress.com/Time-Series-Modelling-with-Unobserved-Components/Pelagatti/p/book/9781482225006)