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The Akaike information criterion (AIC) derived as an estimator of the Kullback-Leibler information discrepancy provides a useful tool for evaluating statistical models, and numerous successful applications of the AIC have been reported in various fields of natural sciences, social sciences and engineering.

One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and...

Due to the introduction of the information criterion AIC and development of prac- tical use of Bayesian modeling, the method of time analysis is now showing remarkable progress. In attempting the study of a new field the actual phenomenon is rarely so simple as to allow direct applications of existing methods of analysis or models. The real thrill of the statistical analysis lies in the process of developing a new model depending on the purpose and the characteristics of the object of the research. The purpose of this book ist.o introduce the readers to successful applications of the meth-...

​This book presents a new statistical method of constructing a price index of a financial asset where the price distributions are skewed and heavy-tailed and investigates the effectiveness of the method. In order to fully reflect the movements of prices or returns on a financial asset, the index should reflect their distributions. However, they are often heavy-tailed and possibly skewed, and identifying them directly is not easy. This book first develops an index construction method depending on the price distributions, by using nonstationary time series analysis. Firstly, the long-term...

The Akaike information criterion (AIC) derived as an estimator of the Kullback-Leibler information discrepancy provides a useful tool for evaluating statistical models, and numerous successful applications of the AIC have been reported in various fields of natural sciences, social sciences and engineering.

One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and...

Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian...

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...