This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical method for IID data proposed by R.A. Fisher to investigate factors and interactions of phenomena. In contrast, the methods developed in this book apply to time series data. Testing theory of the homogeneity of groups is presented under a wide variety of situations including uncorrelated and correlated groups, fixed and random effects, multi- and high-dimension, parametric and nonparametric spectral densities. These methods have applications in several scientific fields. A test for the existence of interactions is also proposed. The book deals with asymptotics when the number of groups is fixed and sample size diverges. This framework distinguishes the approach of the book from panel data and longitudinal analyses, which mostly deal with cases in which the number of groups is large. The usefulness of the theory in this book is illustrated by numerical simulation and real data analysis. This book is suitable for theoretical statisticians and economists as well as psychologists and data analysts.

Autorentext

Yuichi Goto is an assistant professor in Department of Mathematical Sciences, Faculty of Mathematics at Kyushu University. He earned his Ph.D. from Waseda University in 2021 and he was an assistant professor in Waseda University for one year. He completed a master's course in one year (one year early) and a doctor's course in two years (one year early). His research interests include time series analysis, especially frequency domain analysis, integer-valued time series, and analysis of variance. He received the Azusa Ono Memorial Award in 2021 and IMS New Researcher Travel Awards in 2023.

Hideaki Nagahata is a project assistant professor in Risk Analysis Research Center at the Institute of Statistical Mathematics. His research interests include multivariate time series analysis and quantitative aspects of risk modelling. He has worked on the estimation of loss given default (LGD) with local banks and quantifying the risk of compensation triggered on the CompoundLivestock Feed Supply Stabilization System with the Ministry of Agriculture, Forestry, and Fisheries.

Masanobu Taniguchi is an Emeritus professor at Waseda University. His research interests include time series analysis, mathematical statistics, multivariate analysis, information geometry, signal processing, econometric theory, and financial engineering. His main contributions in time series analysis are collected in his book: "Asymptotic Theory of Statistical Inference for Time Series" (New York : Springer-Verlag, 2000). He received the Ogawa Prize (Japan) in 1989, the Econometric Theory Award (USA) in 2000, the Japan Statistical Society Prize in 2004, Analysis Award in 2013 (Mathematical Society of Japan), Award of Japanese Minister of Education, Culture, Sports, Science & Technology in 2022, and the Distinguished Author Award in 2020 (Journal of Time Series Analysis, UK). He is a fellow of the Institute of Mathematical Statistics (USA, 1987 - ).

Anna Clara Monti is a professor in the Department of Law, Economics, Management, and Quantitative Methods at University of Sannio. She acted as dean of the Faculty of Economics and the Faculty of Law. Her research interests concern statistical inference, robustness, ordinal response models, and time series. She has published several papers in international journals of statistics, e.g. Biometrika, JRSS(B), JASA, etc.

Xiaofei Xu is an assistant professor in School of Mathematics and Statistics at Wuhan University. Before joining Wuhan University, she worked as an assistant professor in Waseda Unversity. She got Ph.D. degree in statistics in 2020. Her research interests include functional data analysis, count time series analysis, non-stationarity and high dimensionality, and energy forecasting. Xiaofei has published several papers in famous international journals including Annals of Applied Statistics and Journal of Business and Economic Statistics.