Long-rangedependent, or long-memory,time seriesarestationarytime series displaying a statistically signi?cant dependence between very distant obs- vations. We formalize this dependence by assuming that the autocorrelation function of these stationary series decays very slowly, hyperbolically, as a function of the time lag. Many economic series display these empirical features: volatility of asset prices returns, future interest rates, etc. There is a huge statistical literature on long-memory processes, some of this research is highly technical, so that it is cited, but often misused in the applied econometrics and empirical e- nomics literature. The ?rst purpose of this book is to present in a formal and pedagogical way some statistical methods for studying long-range dependent processes. Furthermore, the occurrence of long-memory in economic time series might be a statistical artefact as the hyperbolic decay of the sample autoc- relation function does not necessarily derive from long-range dependent p- cesses. Indeed, the realizations of non-homogeneous processes, e.g., switching regime and change-point processes, display the same empirical features. We thus also present in this book recent statistical methods able to discriminate between the long-memory and change-point alternatives. Going beyond the purely statistical analysis of economic series, it is of interest to determine which economic mechanisms are generating the strong dependence properties of economic series, whether they are genuine, or spu- ous. The regularities of the long-memory and change-point properties across economic time series, e.g., common degree of long-range dependence and/or common change-points, suggest the existence of a common economic cause.

"In some ways, the e?ect of achieving understanding is to reverse completely our initial attitude of mind. For everyone starts (as we have said) by being perplexed by some fact or other: for instance... the fact that the diagonal of a square is incommensurable with the side. Anyone who has not yet seen why the side and the diagonal have no common unit regards this as quite extra- dinary. But one ends up in the opposite frame of mind... for nothing would so much ?abbergast a mathematician as if the diagonal and side of a square were to become commensurable". [Aristotele] This is the ?rst volume of a new series entitled "New Economic Windows". Each volume in the series will, we hope, provide pointers towards a better understanding of the nature of economic phenomena and help to "reverse our initial state of mind" as economists. As H. Simon observed, Economics must be considered a "hard", (in the sense of di?cult rather than precise), science. As he cogently argued, the problems dealt with are so complex they "cannot simply be reduced to analytically solvable models or decomposed into sepa- 1 rate sub processes". In this he was following on from Einstein who, many years earlier, when asked why he had not turned his attention to economics said that he found it too di?cult a subject to handle scienti?cally.

"In some ways, the e?ect of achieving understanding is to reverse completely our initial attitude of mind. For everyone starts (as we have said) by being perplexed by some fact or other: for instance... the fact that the diagonal of a square is incommensurable with the side. Anyone who has not yet seen why the side and the diagonal have no common unit regards this as quite extra- dinary. But one ends up in the opposite frame of mind... for nothing would so much ?abbergast a mathematician as if the diagonal and side of a square were to become commensurable". [Aristotele] This is the ?rst volume of a new series entitled "New Economic Windows". Each volume in the series will, we hope, provide pointers towards a better understanding of the nature of economic phenomena and help to "reverse our initial state of mind" as economists. As H. Simon observed, Economics must be considered a "hard", (in the sense of di?cult rather than precise), science. As he cogently argued, the problems dealt with are so complex they "cannot simply be reduced to analytically solvable models or decomposed into sepa- 1 rate sub processes". In this he was following on from Einstein who, many years earlier, when asked why he had not turned his attention to economics said that he found it too di?cult a subject to handle scienti?cally.

Long-rangedependent, or long-memory, time seriesarestationarytime series displaying a statistically signi?cant dependence between very distant obs- vations. We formalize this dependence by assuming that the autocorrelation function of these stationary series decays very slowly, hyperbolically, as a function of the time lag. Many economic series display these empirical features: volatility of asset prices returns, future interest rates, etc. There is a huge statistical literature on long-memory processes, some of this research is highly technical, so that it is cited, but often misused in the applied econometrics and empirical e- nomics literature. The ?rst purpose of this book is to present in a formal and pedagogical way some statistical methods for studying long-range dependent processes. Furthermore, the occurrence of long-memory in economic time series might be a statistical artefact as the hyperbolic decay of the sample autoc- relation function does not necessarily derive from long-range dependent p- cesses. Indeed, the realizations of non-homogeneous processes, e.g., switching regime and change-point processes, display the same empirical features. We thus also present in this book recent statistical methods able to discriminate between the long-memory and change-point alternatives. Going beyond the purely statistical analysis of economic series, it is of interest to determine which economic mechanisms are generating the strong dependence properties of economic series, whether they are genuine, or spu- ous. The regularities of the long-memory and change-point properties across economic time series, e.g., common degree of long-range dependence and/or common change-points, suggest the existence of a common economic cause

The economy is examined by the authors as a complex interactive system. The emphasis is on the direct interaction between agents rather than on the indirect and autonomous interaction through the market mechanism. Contributions from economists and physicists emphasise the consequences for aggregate behaviour of the interaction between agents with limited rationality. Models of financial markets which exhibit many of the stylised facts of empirical markets such as bubbles, herd behaviour and long memory are presented. This includes contributions on bargaining, buyer-seller relations, the evolution of economic networks and several aspects of macro-economic behaviour. This book will be of interest to all those interested in the foundations of collective social and economic behaviour and in particular, to those concerned with the dynamics of market behaviour and recent applications of physics to economics.

3 Domenico Delli Gatti!, Mauro GallegatF, Alan P. Kirman ! ITEMQ, Catholic University, Milan, Italy 2 MET, University of Teramo, Italy 3 GREQAM, Universite d'Aix-Marseille, Ecole des Hautes Etudes en Sciences Sociales, and Institut Universitaire de France The economics of heterogeneity This volume contains a set of papers which pursue the aim of examining how the properties of aggregate economic variables are influenced by the actions and interactions of individuals. This has been the central theme of a series of workshops held at the University of Ancona, Italy, since 1996, whose general title is Workshops on Economics with Heterogeneous Interactive Agents (WEHIA for short). ! Considering the economy as a complex evolving system of interacting agents, one has to take seriously three fundamental issues: * the heterogeneity of the agents in the economy, * the ways in which agents interact, * the dynamic process which governs the evolution of the individual and the aggregate variables. The third issue concerns especially the idea that agents learn and adapt rather than calculate optimally (Anderson et aI. , 1988; Arthur et aI. , 1997; Allen, 1988. ) As to the first issue, general equilibrium theory allows, of course, agents to be as heterogeneous as one wants but as the Sonnenschein-Mantel-Debreu results have I The papers published in this book are a selected sample of the papers presented at the 3rd WEHIA workshop held at the University of Ancona on May 29-30,1998.

Nonlinear Dynamics and Economics, first published in 1997, presents developments in nonlinear economic dynamics along with related research from associated fields, including mathematics, statistics, biology, and physics. Specific areas covered include instability in economic theory, nonlinearity in financial markets, tests for nonlinearity and chaos, frequency domain methods, nonlinear business cycles, and nonlinear prediction and forecasting. This volume comprises the tenth in the International Symposia in Economic Theory and Econometrics series under the general editorship of William Barnett. This proceedings volume includes revisions of the most important papers presented at a conference held at the European University Institute in Florence on July 6-17, 1992, along with revisions of the related, invited papers presented at the annual meetings of the American Statistical Association held in San Francisco on August 8-12, 1993.

Economics: Beyond the Millennium contains articles by leading authorities in various fields of economic theory and econometrics. Each contributor gives an account of the current state of the art in their own field and indicates the direction that they think it will take in the next ten years. The book is split into three sections: the microfoundations of macroeconomics, markets and organization, and econometrics, with highlights including Malinvaud on resource allocation, Van Damme on game theory, and Gourieroux on econometric modelling.