Book contents
- Frontmatter
- Contents
- List of figures
- Acknowledgement
- Preface
- Notation and conventions
- List of abbreviations
- 1 Introduction
- 2 Univariate time series models
- 3 State space models and the Kalman filter
- 4 Estimation, prediction and smoothing for univariate structural time series models
- 5 Testing and model selection
- 6 Extensions of the univariate model
- 7 Explanatory variables
- 8 Multivariate models
- 9 Continuous time
- Appendix 1 Principal structural time series components and models
- Appendix 2 Data sets
- Selected answers to exercises
- References
- Author, index
- Subject index
2 - Univariate time series models
Published online by Cambridge University Press: 05 July 2014
- Frontmatter
- Contents
- List of figures
- Acknowledgement
- Preface
- Notation and conventions
- List of abbreviations
- 1 Introduction
- 2 Univariate time series models
- 3 State space models and the Kalman filter
- 4 Estimation, prediction and smoothing for univariate structural time series models
- 5 Testing and model selection
- 6 Extensions of the univariate model
- 7 Explanatory variables
- 8 Multivariate models
- 9 Continuous time
- Appendix 1 Principal structural time series components and models
- Appendix 2 Data sets
- Selected answers to exercises
- References
- Author, index
- Subject index
Summary
A univariate time series consists of a set of observations on a single variable, y. If there are T observations, they may be denoted by yt, t = 1,…, T. A univariate time series model for yt is formulated in terms of past values of yt and/or its position with respect to time. Forecasts from such a model are therefore nothing more than extrapolations of the observed series made at time T. These forecasts may be denoted by ŷT+l|T, where l is a positive integer denoting the lead time.
No univariate statistical model can be taken seriously as a mechanism describing the way in which the observations are generated. If we are to start building workable models from first principles, therefore, it is necessary to begin by asking the question of what we expect our models to do. The ad hoc forecasting procedures described in section 2.2 provide the starting point. These procedures make forecasts by fitting functions of time to the observations but do so by placing relatively more weight on the more recent observations. This discounting of past observations is intuitively sensible but lacks any explicit statistical foundation. The first part of section 2.3 introduces the idea of a class of statistical models known as stochastic processes. Structural time series models are then built up by formulating stochastic components which, when combined, give forecasts of the required form. It turns out that these models provide a statistical rationale for the ad hoc procedures introduced earlier.
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- Publisher: Cambridge University PressPrint publication year: 1990
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