Masanobu Taniguchi - Böcker

There has been much demand for the statistical analysis of dependent ob­ servations in many fields, for example, economics, engineering and the nat­ ural sciences. A model that describes the probability structure of a se­ ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process­ es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d­ ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal­ ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo­ metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.

The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul­ tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.

The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered.This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.

There has been much demand for the statistical analysis of dependent ob­ servations in many fields, for example, economics, engineering and the nat­ ural sciences. A model that describes the probability structure of a se­ ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process­ es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d­ ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal­ ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo­ metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.

The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered.This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.

Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively describe actual financial data and illustrates how to properly estimate the proposed models.After explaining the elements of probability and statistical inference for independent observations, the book discusses the testing hypothesis and discriminant analysis for independent observations. It then explores stochastic processes, many famous time series models, their asymptotically optimal inference, and the problem of prediction, followed by a chapter on statistical financial engineering that addresses option pricing theory, the statistical estimation for portfolio coefficients, and value-at-risk (VaR) problems via residual empirical return processes. The final chapters present some models for interest rates and discount bonds, discuss their no-arbitrage pricing theory, investigate problems of credit rating, and illustrate the clustering of stock returns in both the New York and Tokyo Stock Exchanges.Basing results on a modern, unified optimal inference approach for various time series models, this reference underlines the importance of stochastic models in the area of financial engineering.

​This monograph provides the fundamentals of statistical inference for financial engineering and covers some selected methods suitable for analyzing financial time series data. In order to describe the actual financial data, various stochastic processes, e.g. non-Gaussian linear processes, non-linear processes, long-memory processes, locally stationary processes etc. are introduced and their optimal estimation is considered as well. This book also includes several statistical approaches, e.g., discriminant analysis, the empirical likelihood method, control variate method, quantile regression, realized volatility etc., which have been recently developed and are considered to be powerful tools for analyzing the financial data, establishing a new bridge between time series and financial engineering.This book is well suited as a professional reference book on finance, statistics and statistical financial engineering. Readers are expected to have an undergraduate-level knowledge of statistics.

This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error.

This book contains new aspects of model diagnostics in time series analysis, including variable selection problems and higher-order asymptotics of tests. The book begins by introducing a unified view of a portmanteau-type test based on a likelihood ratio test, useful to test general parametric hypotheses inherent in statistical models.