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62
Nonlinear Dynamic Structures
 Econometrica
, 1993
"... We describe three methods for analyzing the dynamics of a nonlinear time series that is represented by a nonparametric estimate of its onestep ahead conditional density. These strategies are based on examination of conditional moment profiles corresponding to certain shocks; a conditional moment pr ..."
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Cited by 122 (10 self)
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We describe three methods for analyzing the dynamics of a nonlinear time series that is represented by a nonparametric estimate of its onestep ahead conditional density. These strategies are based on examination of conditional moment profiles corresponding to certain shocks; a conditional moment profile is the conditional expectation evaluated at time t of a time invariant function evaluated at time t + j regarded as a function of j. The first method, which compares conditional moment profiles to baseline profiles, is the nonlinear analog of conventional impulseresponse analysis. The second assesses the significance of a profile by comparing its supnorm confidence band to a null profile. The third examines profile bundles for evidence of damping or persistence. Experimental designs for choosing an appropriate set of shocks are discussed. These methods are applied to a bivariate series comprised of daily changes in the Standard and Poor's composite price index and daily NYSE transactions volume from 1928 to 1987. The findings from these data are: (i) The multistep ahead conditional volatility profile exhibits a symmetric response to both positive and negative price shocks. In contrast, the conditional volatility profile of the univariate price change process exhibits an asymmetric response. (ii) The onestep ahead response of volume to price shocks is different than the multistep ahead response. Price shocks produce an increase in volume onestep ahead but decrease it in subsequent steps. (iii) There is little evidence for longterm persistence in either the conditional mean or volatility of the bivariate process. o 1
A SingleBlind Controlled Competition Among Tests for Nonlinearity and Chaos
 Journal of Econometrics
, 1997
"... Abstract: Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a singleblind controlled competition among five highly regard ..."
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Cited by 54 (9 self)
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Abstract: Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a singleblind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by email, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos.
Scale Invariance in Biology: Coincidence Or Footprint of a Universal Mechanism?
, 2001
"... In this article, we present a selfcontained review of recent work on complex biological systems which exhibit no characteristic scale. This property can manifest itself with fractals (spatial scale invariance), flicker noise or 1}fnoise where f denotes the frequency of a signal (temporal scale i ..."
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Cited by 38 (1 self)
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In this article, we present a selfcontained review of recent work on complex biological systems which exhibit no characteristic scale. This property can manifest itself with fractals (spatial scale invariance), flicker noise or 1}fnoise where f denotes the frequency of a signal (temporal scale invariance) and power laws (scale invariance in the size and duration of events in the dynamics of the system). A hypothesis recently put forward to explain these scalefree phenomomena is criticality, a notion introduced by physicists while studying phase transitions in materials, where systems spontaneously arrange themselves in an unstable manner similar, for instance, to a row of dominoes. Here, we review in a critical manner work which investigates to what extent this idea can be generalized to biology. More precisely, we start with a brief introduction to the concepts of absence of characteristic scale (powerlaw distributions, fractals and 1}fnoise) and of critical phenomena. We then review typical mathematical models exhibiting such properties : edge of chaos, cellular automata and selforganized critical models. These notions are then brought together to see to what extent they can account for the scale invariance observed in ecology, evolution of species, type III epidemics and some aspects of the central nervous system. This article also discusses how the notion of scale invariance can give important insights into the workings of biological systems.
Chaos and Nonlinear Forecastability in Economics and Finance
 Philosophical Transactions of the Royal Society of London
, 1994
"... Both academic and applied researchers studying nancial markets and other economic series have become interested in the topic of chaotic dynamics. The possibility ofchaos in nancial markets opens important questions for both economic theorists as well as nancial market participants. This paper will c ..."
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Cited by 16 (1 self)
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Both academic and applied researchers studying nancial markets and other economic series have become interested in the topic of chaotic dynamics. The possibility ofchaos in nancial markets opens important questions for both economic theorists as well as nancial market participants. This paper will clarify the empirical evidence for chaos in nancial markets and macroeconomic series. It will also compare these two concepts from a nancial market perspective contrasting the objectives of the practitioner with those of economic researchers. Finally, the paper will speculate on the impact of chaos and nonlinear modeling on future economic research. The author is grateful to the Alfred P. Sloan Foundation and the University of Wisconsin Graduate School for It has now been almost ten years since economists began searching for chaotic dynamics in economic time series. This search has yielded deeper understandings of the dynamics of many di erent series, and has led to the development of several useful tests for nonlinear structure. However, the direct evidence for deterministic chaos in many economic series remains weak. This paper will survey the
Don't Bleach Chaotic Data
, 1993
"... this paper, that observation is extended. Even when the bleaching is constrained to relatively low order (by the Akaike criterion, for instance), and even for tasks other than detecting nonlinear structure, we find that the effect of bleaching on chaotic data can be detrimental. On the other hand, b ..."
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Cited by 15 (1 self)
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this paper, that observation is extended. Even when the bleaching is constrained to relatively low order (by the Akaike criterion, for instance), and even for tasks other than detecting nonlinear structure, we find that the effect of bleaching on chaotic data can be detrimental. On the other hand, bleaching
Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos
, 2000
"... This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the est ..."
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Cited by 15 (2 self)
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This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1 % level with an exception in some higher power transformed absolute returns.
Martingales, nonlinearity, and chaos
 Journal of Economic Dynamics and Control
, 2000
"... In this article we provide a review of the literature with respect to the e cient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministi ..."
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Cited by 12 (1 self)
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In this article we provide a review of the literature with respect to the e cient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices, and report some evidence. Moreover, we look at the controversies that have arisen about the available tests and results, and raise the issue of whether dynamical systems theory is practical in nance.
Chaos in an Emerging Capital Market? The Case of the Athens Stock Exchange
 Applied Financial Economics
, 1998
"... This paper investigates the existence of a deterministic nonlinear structure in the stock returns of the Athens Stock Exchange (Greece), an emerging capital market. The analysis utilizes the concepts of correlation dimension and Kolmogorov entropy, and it also includes a forecasting experiment. Appl ..."
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Cited by 10 (1 self)
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This paper investigates the existence of a deterministic nonlinear structure in the stock returns of the Athens Stock Exchange (Greece), an emerging capital market. The analysis utilizes the concepts of correlation dimension and Kolmogorov entropy, and it also includes a forecasting experiment. Application of the BDS statistical test to raw and ® ltered returns series suggests the presence of nonlinearities. The ® ndings provide very weak, at best, evidence in support of a nonlinear deterministic data generating process. Numerous studies have investigated the stochastic properties of stock returns of major national stock markets. The obtained empirical evidence suggests that stock returns are not normally distributed but leptokurtic (i.e, fat tailed) and
THE ASYMPTOTIC DISTRIBUTION OF NONPARAMETRIC ESTIMATES OF THE LYAPUNOV EXPONENT FOR STOCHASTIC TIME SERIES
"... COWLES FOUNDATION DISCUSSION PAPER NO. 1130R ..."
Nonlinear Model Specification/Diagnostics: Insights from a Battery of Nonlinearity Tests
, 1999
"... A single statistical test for nonlinearity can indicate whether or not the generating mechanism of a time series is or is not linear. However, if the null hypothesis of linearity is rejected, the test result conveys little information as to what kind of nonlinear model is appropriate. Here we show t ..."
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Cited by 8 (1 self)
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A single statistical test for nonlinearity can indicate whether or not the generating mechanism of a time series is or is not linear. However, if the null hypothesis of linearity is rejected, the test result conveys little information as to what kind of nonlinear model is appropriate. Here we show that a battery of different nonlinearity tests, in contrast, can yield valuable model identification information. Applying such a battery of tests to data on U.S. real GNP, we are able to conclude that the commonly held notion that this time series is generated by some sort of twostate regime switching process is most likely incorrect.