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Journal ArticleDOI

Chaotic dynamics: theory and applications to economics, by Alfredo Medio in collaboration with Giampaolo Gallo. Pp 344. £35. 1993. ISBN 0-521-39488-0; (Accompanying Disk ISBN 0-521-42107-1. £30 MSDOS or Apple Mac). (Cambridge University Press)

01 Mar 1995-The Mathematical Gazette (Cambridge University Press (CUP))-Vol. 79, Iss: 484, pp 235-236
TL;DR: This book introduces chaos and economics in a continuous-time model of inventory business cycles and applications to Economics, and discusses the role of software in this transformation.
Abstract: Preface Part I. Theory: 1. General introduction: chaos and economics 2. Basic mathematical concepts 3. A user's guide 4. Surfaces of sections and Poincare maps 5. Spectral analysis 6. Lyapunov characteristic exponents 7. Dimensions 8. Symbolic dynamics 9. Transition to chaos: theoretical predictive criteria 10. Analysis of experimental signals: some theoretical problems Part II. Applications to Economics: 11. Discrete and continuous chaos 12. Cycles and chaos in overlapping generations models with production 13. Chaos in a continuous-time model of inventory business cycles 14. Analysis of experimental signals Part III. Software: 15. DMC manual 16. MODEL 17. EVAL 18. PLOT 19. STAT 20. FILES 21. UTIL 22. OPTS 23. QUIT 24. Internal menu commands 25. DMC internal compiler.
Citations
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Journal ArticleDOI
TL;DR: A survey of dynamic heterogeneous agent models (HAMs) in economics and finance can be found in this article, where the authors focus on simple models that are tractable by analytic methods in combination with computational tools.
Abstract: This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

892 citations

Book ChapterDOI
TL;DR: A survey of dynamic heterogeneous agent models (HAMs) in economics and finance can be found in this paper, where the authors focus on simple models that are tractable by analytic methods in combination with computational tools.
Abstract: This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

332 citations

MonographDOI
01 Jan 2013
TL;DR: In this paper, the nonlinear cobweb model with heterogeneous expectations was proposed and empirically validated in a laboratory experiment, and an asset pricing model was proposed with heterogenous beliefs.
Abstract: 1. Introduction 2. Bifurcations and chaos in 1-D systems 3. Bifurcations and strange attractors in 2-D systems 4. The nonlinear cobweb model 5. The cobweb model with heterogeneous expectations 6. An asset pricing model with heterogeneous beliefs 7. Empirical validation 8. Laboratory experiments.

327 citations

Book
13 Aug 2009
TL;DR: This work Constructing time series in cyclostratigraphy with a focus on environmental cycles recorded stratigraphically and additional methods of time-series analysis.
Abstract: Increasingly environmental scientists, palaeoceanographers and geologists are collecting quantitative records of environmental changes (time-series) from sediments, ice cores, cave calcite, corals and trees. This book explains how to analyse these records, using straightforward explanations and diagrams rather than formal mathematical derivations. All the main cyclostratigraphic methods are covered including spectral analysis, cross-spectral analysis, filtering, complex demodulation, wavelet and singular spectrum analysis. Practical problems of time-series analysis, including those of distortions of environmental signals during stratigraphic encoding, are considered in detail. Recent research into various types of tidal and climatic cycles is summarised. The book ends with an extensive reference section, and an appendix listing sources of computer algorithms. This book provides the ideal reference for all those using time-series analysis to study the nature and history of climatic and tidal cycles. It is suitable for senior undergraduate and graduate courses in environmental science, palaeoceanography and geology.

223 citations

01 Jan 1998
TL;DR: In this article, simple geometrical methods were developed to study local indeterminacy, bifurcations and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models.
Abstract: We develop in this paper simple geometrical methods to study local indeterminacy, bifurcations and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models. We present stochastic sunspot equilibria, which allows a constructive description of local bifurcations. The latter analysis is relevant when some eigenvalues of the linearized dynamics, near the steady state, have a modulus close to one (“unit root(s)”), as taking into account small nonlinearities generates linear local approximation. These methods are applied to a simple aggregative model (Woodford (JET, 1986)), to study in particular the influence of capital-labor substitution and of the aggregate labor supply wage elasticiy, on the occurrence of competitive endogenous deterministic or stochastic fluctuations.

190 citations

References
More filters
Book ChapterDOI
TL;DR: A survey of dynamic heterogeneous agent models (HAMs) in economics and finance can be found in this paper, where the authors focus on simple models that are tractable by analytic methods in combination with computational tools.
Abstract: This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

332 citations

MonographDOI
01 Jan 2013
TL;DR: In this paper, the nonlinear cobweb model with heterogeneous expectations was proposed and empirically validated in a laboratory experiment, and an asset pricing model was proposed with heterogenous beliefs.
Abstract: 1. Introduction 2. Bifurcations and chaos in 1-D systems 3. Bifurcations and strange attractors in 2-D systems 4. The nonlinear cobweb model 5. The cobweb model with heterogeneous expectations 6. An asset pricing model with heterogeneous beliefs 7. Empirical validation 8. Laboratory experiments.

327 citations

Book
13 Aug 2009
TL;DR: This work Constructing time series in cyclostratigraphy with a focus on environmental cycles recorded stratigraphically and additional methods of time-series analysis.
Abstract: Increasingly environmental scientists, palaeoceanographers and geologists are collecting quantitative records of environmental changes (time-series) from sediments, ice cores, cave calcite, corals and trees. This book explains how to analyse these records, using straightforward explanations and diagrams rather than formal mathematical derivations. All the main cyclostratigraphic methods are covered including spectral analysis, cross-spectral analysis, filtering, complex demodulation, wavelet and singular spectrum analysis. Practical problems of time-series analysis, including those of distortions of environmental signals during stratigraphic encoding, are considered in detail. Recent research into various types of tidal and climatic cycles is summarised. The book ends with an extensive reference section, and an appendix listing sources of computer algorithms. This book provides the ideal reference for all those using time-series analysis to study the nature and history of climatic and tidal cycles. It is suitable for senior undergraduate and graduate courses in environmental science, palaeoceanography and geology.

223 citations

01 Jan 1998
TL;DR: In this article, simple geometrical methods were developed to study local indeterminacy, bifurcations and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models.
Abstract: We develop in this paper simple geometrical methods to study local indeterminacy, bifurcations and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models. We present stochastic sunspot equilibria, which allows a constructive description of local bifurcations. The latter analysis is relevant when some eigenvalues of the linearized dynamics, near the steady state, have a modulus close to one (“unit root(s)”), as taking into account small nonlinearities generates linear local approximation. These methods are applied to a simple aggregative model (Woodford (JET, 1986)), to study in particular the influence of capital-labor substitution and of the aggregate labor supply wage elasticiy, on the occurrence of competitive endogenous deterministic or stochastic fluctuations.

190 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a stochastic simulation model of a prototype financial market, which is populated by both noise traders and fundamentalist speculators, and explore the behavior of the model when testing for the presence of chaos or non-linearity in the simulated data.
Abstract: We present a stochastic simulation model of a prototype financial market. Our market is populated by both noise traders and fundamentalist speculators. The dynamics covers switches in the prevailing mood among noise traders (optimistic or pessimistic) as well as switches of agents between the noise trader and fundamentalist group in response to observed differences in profits. The particular behavioral variant adopted by an agent also determines his decision to enter on the long or short side of the market. Short-run imbalances between demand and supply lead to price adjustments by a market maker or auctioneer in the usual Walrasian manner. Our interest in this paper is in exploring the behavior of the model when testing for the presence of chaos or non-linearity in the simulated data. As it turns out, attempts to determine the fractal dimension of the underlying process give unsatisfactory results in that we experience a lack of convergence of the estimate. Explicit tests for non-linearity and dependence (the BDS and Kaplan tests) also give very unstable results in that both acceptance and strong rejection of IIDness can be found in different realizations of our model. All in all, this behavior is very similar to experience collected with empirical data and our results may point towards an explanation of why robustness of inference in this area is low. However, when testing for dependence in second moments and estimating GARCH models, the results appear much more robust and the chosen GARCH specification closely resembles the typical outcome of empirical studies.

120 citations