In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

/pdf/an-introduction-to-mcmc-for-machine-learning-22slt5b6x5.pdf

An introduction to MCMC for machine learning

In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops simulation-based methods for filtering, likelihood evaluation and model failure diagnostics. The issue of model choice using non-nested likelihood ratios and Bayes factors is also investigated. These methods are used to compare the fit of stochastic volatility and GARCH models. All the procedures are illustrated in detail.

/pdf/stochastic-volatility-likelihood-inference-and-comparison-5guxxaxw3x.pdf

Stochastic volatility : likelihood inference and comparison with arch models

Generalized Linear Models (2nd ed.)

This paper briefly reviews the analytic hierarchy process (AHP) and its applications in diverse decision problems. It addresses some of the major extensions and criticisms of the method, as well.

The Analytic Hierarchy Process—A Survey of the Method and its Applications

SUMMARY Recently suggested procedures for simulating from the posterior density of states given a Gaussian state space time series are refined and extended. We introduce and study the simulation smoother, which draws from the multivariate posterior distribution of the disturbances of the model, so avoiding the degeneracies inherent in state samplers. The technique is important in Gibbs sampling with non-Gaussian time series models, and for performing Bayesian analysis of Gaussian time series.

/pdf/the-simulation-smoother-for-time-series-models-4lrnucz569.pdf

The simulation smoother for time series models

Preface 1. Insurance data 2. Response distributions 3. Exponential family responses and estimation 4. Linear modeling 5. Generalized linear models 6. Models for count data 7. Categorical responses 8. Continuous responses 9. Correlated data 10. Extensions to the Generalized linear model Appendix 1. Computer code and output Bibliography Index.

/pdf/generalized-linear-models-for-insurance-data-1yui6bdpeh.pdf

Generalized Linear Models for Insurance Data

The Kalman recursion for state space models is extended to allow for likelihood evaluation and minimum mean square estimation given states with an arbitrarily large covariance matrix. The extension is computationally minor. Application is made to likelihood evaluation, state estimation, prediction and smoothing.

/pdf/the-diffuse-kalman-filter-19fuhqi9ty.pdf

The Diffuse Kalman Filter

A new result dealing with smoothing and interpolation in the state-space model is developed and explored. The result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages. The connection to signal extraction and interpolation is explored, and diffuse specifications are considered.

Smoothing and Interpolation with the State-Space Model

We compare the short- to medium- term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ullah and De Jong-Tickle extensions. These methods are compared by applying them to sex-specific populations of 10 developed countries using data for 1986–2000 for evaluation. All variants and extensions are more accurate than the original Lee-Carter method for forecasting log death rates, by up to 61%. However, accuracy in log death rates does not necessarily translate into accuracy in life expectancy. There are no significant differences among the five methods in forecast accuracy for life expectancy.

/pdf/lee-carter-mortality-forecasting-a-multi-country-comparison-1iayay4rdq.pdf

Piet de Jong

Papers

The simulation smoother for time series models

Generalized Linear Models for Insurance Data

The Diffuse Kalman Filter

Smoothing and Interpolation with the State-Space Model

Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions