This book considers periodic time series models for seasonal data, characterized by parameters that differ across the seasons, and focuses on their usefulness for out-of-sample forecasting. Providing an up-to-date survey of the recent developments in periodic time series, the book presents a large number of empirical results. The first part of the book deals with model selection, diagnostic checking and forecasting of univariate periodic autoregressive models. Tests for periodic integration, are discussed, and an extensive discussion of the role of deterministic regressors in testing for periodic integration and in forecasting is provided. The second part discusses multivariate periodic autoregressive models. It provides an overview of periodic cointegration models, as these are the most relevant. This overview contains single-equation type tests and a full-system approach based on generalized method of moments. All methods are illustrated with extensive examples, and the book will be of interest to advanced graduate students and researchers in econometrics, as well as practitioners looking for an understanding of how to approach seasonal data.

In this insightful, modern study of the use of periodic models in the description and forecasting of economic data the authors investigate such areas as seasonal time series, periodic time series models, periodic integration and periodic cointegration.

"Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."

The paper provides a comparison of alternative univariate time series models that are advocated for the analysis of seasonal data. Consumption and income series from (West-) Germany, United Kingdom, Japan and Sweden are investigated. The performance of competing models in forecasting is used to assess the adequacy of a specific model. To account for nonstationarity first and annual differences of the series are investigated. In addition, time series models assuming periodic integration are evaluated. To describe the stationary dynamics (standard) time invariant parametrizations are compared with periodic time series models conditioning the data generating process on the season. Periodic models improve the in-sample fit considerably but in most cases under study this model class involves a loss in ex-ante forecasting relative to nonperiodic models. Inference on unit-roots indicates that the nonstationary characteristics of consumption and income data may differ. For German and Swedish data forecasting exercises yield a unique recommendation of unit roots in consumption and income data which is an important (initial) result for multivariate analysis. Time series models assuming periodic integration are parsimonious to specify but often involve correlated one-step-ahead forecast errors.

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.

This book provides a self-contained account of periodic models for seasonally observed economic time series with stochastic trends. Two key concepts are periodic integration and periodic cointegration. Periodic integration implies that a seasonally varying differencing filter is required to remove a stochastic trend. Periodic cointegration amounts to allowing cointegration paort-term adjustment parameters to vary with the season. The emphasis is on useful econrameters and shometric models that explicitly describe seasonal variation and can reasonably be interpreted in terms of economic behaviour. The analysis considers econometric theory, Monte Carlo simulation, and forecasting, and it is illustrated with numerous empirical time series. A key feature of the proposed models is that changing seasonal fluctuations depend on the trend and business cycle fluctuations. In the case of such dependence, it is shown that seasonal adjustment leads to inappropriate results.

This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.