Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on 'local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional 'local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance.

This is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.

Contents:Heavy-Tailed and Nonlinear Continuous-Time ARMA Models for Financial Time Series (P J Brockwell)Nonlinear State Space Model Approach to Financial Time Series with Time-Varying Variance (G Kitagawa & S Sato)Nonparametric Estimation and Bootstrap for Financial Time Series (J-P Kreiβ)A Note on Kernel Estimation in Integrated Time Series (Y-C Xia et al.)Stylized Facts on the Temporal and Distributional Properties of Absolute Returns: An Update (C W J Granger et al.)Volatility Computed by Time Series Operators at High Frequency (U A Müller)Missing Values in ARFIMA Models (W Palma)Second Order Tail Effects (C G de Vries)Bayesian Estimation of Stochastic Volatility Model via Scale Mixtures Distributions (S T B Choy & C M Chan)On a Smooth Transition Double Threshold Model (Y N Lee & W K Li)Interval Prediction of Financial Time Series (B Cheng & H Tong)A Decision Theoretic Approach to Forecast Evaluation (C W J Granger & M H Pesaran)Portfolio Management and Market Risk Quantification Using Neural Networks (J Franke)Detecting Structural Changes Using Genetic Programming with an Application to the Greater-China Stock Markets (X B Zhang et al.)and other papers Readership: Researchers in finance, time series analysis, economics and actuarial science, as well as investment bankers, stock market analysts and risk managers. Keywords:Proceedings;Workshop;Statistics;Finance;Hongkong (China)

This is the first book-length treatment of statistical surveillance methods used in financial analysis. It contains carefully selected chapters written by specialists from both fields and strikes a balance between the financial and statistical worlds, enhancing future collaborations between the two areas, and enabling more successful prediction of financial market trends. The book discusses, in detail, schemes for different control charts and different linear and nonlinear time series models and applies methods to real data from worldwide markets, as well as including simulation studies.

Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.

This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology. Appropriate for graduate coursework or professional reference, the book requires a background in extreme value theory for i.i.d. data and basics of time series. Following a brief review of foundational concepts, it progresses linearly through topics in limit theorems and time series models while including historical insights at each chapter’s conclusion. Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.