Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

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

Another look at measures of forecast accuracy

Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package.

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Automatic Time Series Forecasting: The forecast Package for R

I. Introduction: Basic concepts.- Getting started. II. Essentials: Linear innovations state space models.- Non-linear and heteroscedastic innovations state space models.- Estimation of innovations state space models.- Prediction distributions and intervals.- Selection of models. III. Further topics: Normalizing seasonal components.- Models with regressor variables.- Some properties of linear models.- Reduced forms and relationships with ARIMA models.- Linear innovations state space models with random seed states.- Conventional state space models.- Time series with multiple seasonal patterns.- Non-linear models for positive data.- Models for count data.- Vector exponential smoothing. IV. Applications: Inventory control application.- Conditional heteroscedasticity and finance applications.- Economic applications: the Beveridge-Nelson decomposition.

Forecasting with Exponential Smoothing: The State Space Approach

A state space framework for automatic forecasting using exponential smoothing methods

Forecasting with Exponential Smoothing

Part I: INTRODUCTION AND REVIEW OF BASIC STATISTICS. 1. An Introduction to Forecasting. Forecasting and Data. Forecasting Methods. Errors in Forecasting. Choosing a Forescasting Technique. An Overview of Quantitative Forecasting Techniques. 2. Basic Statistical Concepts. Populations. Probability. Random Samples and Sample Statistics. Continuous Probability Distributions. The Normal Probability Distribution. The t-Distribution, the F-Distribution, the Chi-Square Distribution. Confidence Intervals for a Population Mean. Hypothesis Testing for a Population Mean. Exercises. Part II: REGRESSION ANALYSIS. 3. Simple Linear Regression. The Simple Linear Regression Model. The Least Squares Point Estimates. Point Estimates and Point Predictions. Model Assumptions and the Standard Error. Testing the Significance of the Slope and y Intercept. Confidence and Prediction Intervals. Simple Coefficients of Determination and Correlation. An F Test for the Model. Exercises. 4. Multiple Linear Regression. The Linear Regression Model. The Least Squares Estimates, and Point Estimation and Prediction. The Mean Square Error and the Standard Error. Model Utility: R2, Adjusted R2, and the Overall F Test. Testing the Significance of an Independent Variable. Confidence and Prediction Intervals. The Quadratic Regression Model. Interaction. Using Dummy Variables to Model Qualitative Independent Variables. The Partial F Test: Testing the Significance of a Portion of a Regression Model. Exercises. 5. Model Building and Residual Analysis. Model Building and the Effects of Multicollinearity. Residual Analysis in Simple Regression. Residual Analysis in Multiple Regression. Diagnostics for Detecting Outlying and Influential Observations. Exercises. Part III: TIME SERIES REGRESSION, DECOMPOSITION METHODS, AND EXPONENTIAL SMOOTHING. 6. Time Series Regression. Modeling Trend by Using Polynomial Functions. Detecting Autocorrelation. Types of Seasonal Variation. Modeling Seasonal Variation by Using Dummy Variables and Trigonometric Functions. Growth Curves. Handling First-Order Autocorrelation. Exercises. 7. Decomposition Methods. Multiplicative Decomposition. Additive Decomposition. The X-12-ARIMA Seasonal Adjustment Method. Exercises. 8. Exponential Smoothing. Simple Exponential Smoothing. Tracking Signals. Holts Trend Corrected Exponential Smoothing. Holt-Winters Methods. Damped Trends and Other Exponential Smoothing Methods. Models for Exponential Smoothing and Prediction Intervals. Exercises. Part IV: THE BOX-JENKINS METHODOLOGY. 9. Nonseasonal Box-Jenkins Modeling and Their Tentative Identification. Stationary and Nonstationary Time Series. The Sample Autocorrelation and Partial Autocorrelation Functions: The SAC and SPAC. An Introduction to Nonseasonal Modeling and Forecasting. Tentative Identification of Nonseasonal Box-Jenkins Models. Exercises. 10. Estimation, Diagnostic Checking, and Forecasting for Nonseasonal Box-Jenkins Models. Estimation. Diagnostic Checking. Forecasting. A Case Study. Box-Jenkins Implementation of Exponential Smoothing. Exercises. 11. Box-Jenkins Seasonal Modeling. Transforming a Seasonal Time Series into a Stationary Time Series. Three Examples of Seasonal Modeling and Forecasting. Box-Jenkins Error Term Models in Time Series Regression. Exercises. 12. Advanced Box-Jenkins Modeling. The General Seasonal Model and Guidelines for Tentative Identificatino. Intervention Models. A Procedure for Building a Transfer Function Model. Exercises. Appendix A: Statistical Tables Appendix B: Matrix Algebra for Regression Calculations. Matrices and Vectors. The Transpose of a Matrix. Sums and Differences of Matrices. Matrix Multiplication. The Identity Matrix. Linear Dependence and Linear Independence. The Inverse of a Matrix. The Least Squares Point Esimates. The Unexplained Variation and Explained Variation. The Standard Error of the Estimate b. The Distance Value. Using Squared Terms. Using Interaction Terms. Using Dummy Variable. The Standard Error of the Estimate of a Linear Combination of Regression Parameters. Exercises. Appendix C: References.

Anne B. Koehler

Papers

Another look at measures of forecast accuracy

Forecasting with Exponential Smoothing: The State Space Approach

A state space framework for automatic forecasting using exponential smoothing methods

Forecasting with Exponential Smoothing

Forecasting, time series, and regression : an applied approach