How to make forecasts that (1) satisfy constraints, like accounting identities, and (2) are smooth over time? Solving this common forecasting problem manually is resource-intensive, but the existing literature provides little guidance on how to achieve both objectives. This paper proposes a new method to smooth mixed-frequency multivariate time series subject to constraints by integrating the minimum-trace reconciliation and Hodrick-Prescott filter. With linear constraints, the method has a closed-form solution, convenient for a high-dimensional environment. Three examples show that the proposed method can reproduce the smoothness of professional forecasts subject to various constraints and slightly improve forecast performance.
Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.
To use statistical methods and SAS applications to forecast the future values of data taken over time, you need only follow this thoroughly updated classic on the subject. With this third edition of SAS for Forecasting Time Series, intermediate-to-advanced SAS users—such as statisticians, economists, and data scientists—can now match the most sophisticated forecasting methods to the most current SAS applications. Starting with fundamentals, this new edition presents methods for modeling both univariate and multivariate data taken over time. From the well-known ARIMA models to unobserved components, methods that span the range from simple to complex are discussed and illustrated. Many of the newer methods are variations on the basic ARIMA structures. Completely updated, this new edition includes fresh, interesting business situations and data sets, and new sections on these up-to-date statistical methods: ARIMA models Vector autoregressive models Exponential smoothing models Unobserved component and state-space models Seasonal adjustment Spectral analysis Focusing on application, this guide teaches a wide range of forecasting techniques by example. The examples provide the statistical underpinnings necessary to put the methods into practice. The following up-to-date SAS applications are covered in this edition: The ARIMA procedure The AUTOREG procedure The VARMAX procedure The ESM procedure The UCM and SSM procedures The X13 procedure The SPECTRA procedure SAS Forecast Studio Each SAS application is presented with explanation of its strengths, weaknesses, and best uses. Even users of automated forecasting systems will benefit from this knowledge of what is done and why. Moreover, the accompanying examples can serve as templates that you easily adjust to fit your specific forecasting needs. This book is part of the SAS Press program.
Exponential smoothing methods have been around since the 1950s, and are still the most popular forecasting methods used in business and industry. However, a modeling framework incorporating stochastic models, likelihood calculation, prediction intervals and procedures for model selection, was not developed until recently. This book brings together all of the important new results on the state space framework for exponential smoothing. It will be of interest to people wanting to apply the methods in their own area of interest as well as for researchers wanting to take the ideas in new directions. Part 1 provides an introduction to exponential smoothing and the underlying models. The essential details are given in Part 2, which also provide links to the most important papers in the literature. More advanced topics are covered in Part 3, including the mathematical properties of the models and extensions of the models for specific problems. Applications to particular domains are discussed in Part 4.
INTERMITTENT DEMAND FORECASTING The first text to focus on the methods and approaches of intermittent, rather than fast, demand forecasting Intermittent Demand Forecasting is for anyone who is interested in improving forecasts of intermittent demand products, and enhancing the management of inventories. Whether you are a practitioner, at the sharp end of demand planning, a software designer, a student, an academic teaching operational research or operations management courses, or a researcher in this field, we hope that the book will inspire you to rethink demand forecasting. If you do so, then you can contribute towards significant economic and environmental benefits. No prior knowledge of intermittent demand forecasting or inventory management is assumed in this book. The key formulae are accompanied by worked examples to show how they can be implemented in practice. For those wishing to understand the theory in more depth, technical notes are provided at the end of each chapter, as well as an extensive and up-to-date collection of references for further study. Software developments are reviewed, to give an appreciation of the current state of the art in commercial and open source software. “Intermittent demand forecasting may seem like a specialized area but actually is at the center of sustainability efforts to consume less and to waste less. Boylan and Syntetos have done a superb job in showing how improvements in inventory management are pivotal in achieving this. Their book covers both the theory and practice of intermittent demand forecasting and my prediction is that it will fast become the bible of the field.” —Spyros Makridakis, Professor, University of Nicosia, and Director, Institute for the Future and the Makridakis Open Forecasting Center (MOFC). “We have been able to support our clients by adopting many of the ideas discussed in this excellent book, and implementing them in our software. I am sure that these ideas will be equally helpful for other supply chain software vendors and for companies wanting to update and upgrade their capabilities in forecasting and inventory management.” —Suresh Acharya, VP, Research and Development, Blue Yonder. “As product variants proliferate and the pace of business quickens, more and more items have intermittent demand. Boylan and Syntetos have long been leaders in extending forecasting and inventory methods to accommodate this new reality. Their book gathers and clarifies decades of research in this area, and explains how practitioners can exploit this knowledge to make their operations more efficient and effective.” —Thomas R. Willemain, Professor Emeritus, Rensselaer Polytechnic Institute.
This book surveys big data tools used in macroeconomic forecasting and addresses related econometric issues, including how to capture dynamic relationships among variables; how to select parsimonious models; how to deal with model uncertainty, instability, non-stationarity, and mixed frequency data; and how to evaluate forecasts, among others. Each chapter is self-contained with references, and provides solid background information, while also reviewing the latest advances in the field. Accordingly, the book offers a valuable resource for researchers, professional forecasters, and students of quantitative economics.
The pioneering research of Hirotugu Akaike has an international reputation for profoundly affecting how data and time series are analyzed and modelled and is highly regarded by the statistical and technological communities of Japan and the world. His 1974 paper "A new look at the statistical model identification" (IEEE Trans Automatic Control, AC-19, 716-723) is one of the most frequently cited papers in the area of engineering, technology, and applied sciences (according to a 1981 Citation Classic of the Institute of Scientific Information). It introduced the broad scientific community to model identification using the methods of Akaike's criterion AIC. The AIC method is cited and applied in almost every area of physical and social science. The best way to learn about the seminal ideas of pioneering researchers is to read their original papers. This book reprints 29 papers of Akaike's more than 140 papers. This book of papers by Akaike is a tribute to his outstanding career and a service to provide students and researchers with access to Akaike's innovative and influential ideas and applications. To provide a commentary on the career of Akaike, the motivations of his ideas, and his many remarkable honors and prizes, this book reprints "A Conversation with Hirotugu Akaike" by David F. Findley and Emanuel Parzen, published in 1995 in the journal Statistical Science. This survey of Akaike's career provides each of us with a role model for how to have an impact on society by stimulating applied researchers to implement new statistical methods.
Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.
Applied Data Mining for Forecasting Using SAS, by Tim Rey, Arthur Kordon, and Chip Wells, introduces and describes approaches for mining large time series data sets. Written for forecasting practitioners, engineers, statisticians, and economists, the book details how to select useful candidate input variables for time series regression models in environments when the number of candidates is large, and identifies the correlation structure between selected candidate inputs and the forecast variable. This book is essential for forecasting practitioners who need to understand the practical issues involved in applied forecasting in a business setting. Through numerous real-world examples, the authors demonstrate how to effectively use SAS software to meet their industrial forecasting needs. This book is part of the SAS Press program.
