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42
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 39 (5 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 23 (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.
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 11 (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
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 9 (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
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 8 (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 7 (0 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.
Is there chaos in the world economy? A nonparametric test using consistent standard errors.” International Economic Review, forthcoming
, 2001
"... A positive Lyapunov exponent is one practical deÞnition of chaos. We develop a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators. When our procedures are applied to international real output series, the hypothesis of the ..."
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Cited by 5 (3 self)
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A positive Lyapunov exponent is one practical deÞnition of chaos. We develop a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators. When our procedures are applied to international real output series, the hypothesis of the positive Lyapunov exponent is signiÞcantly rejected in many cases. One possible interpretation of this result is that the traditional exogenous models are better able to explain business cycle ßuctuations than is the chaotic endogenous approach. However, our results are subject to a number of caveats, in particular our results could have been inßuenced by small sample bias, high noise level, incorrect Þltering, and long memory of the data.
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 4 (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.
Voles and Lemmings: Chaos and Uncertainty in Fluctuating Populations
 Proc. R. Soc. Lond B
, 1995
"... Turchin (Oikos 68, 167172 (1993)) provided point estimates of the dominant Lyapunov exponent suggesting that chaos occurs in microtines north of 60 N. Falck et al. (Proc. R. Soc. B 261, 159165 (1995)) proposed to use bootstrapping methodology in order to investigate the uncertainty associated with ..."
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Cited by 4 (2 self)
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Turchin (Oikos 68, 167172 (1993)) provided point estimates of the dominant Lyapunov exponent suggesting that chaos occurs in microtines north of 60 N. Falck et al. (Proc. R. Soc. B 261, 159165 (1995)) proposed to use bootstrapping methodology in order to investigate the uncertainty associated with the reported estimates. Based on this, Falck et al. (1995) found no reason to conclude that the northern populations are chaotic. The methodology employed, and the conclusions reached, were criticised by Turchin (Proc. R. Soc. B 262, 357361 (1995)). Here we discuss the critique as well as analyse the new data set introduced by Turchin (1995). In addition to analysing pooled data for all microtines at eighteen localities (as Turchin does), we also analyse data for each species at the sites separately. As an integral part of our response, we address some fundamental statistical and biological issues. We reach the same conclusion as earlier: there is no statistical evidence to conclude that n...
Estimating Lyapunov Exponents In Chaotic Time Series With Locally Weighted Regression
, 1994
"... Nonlinear dynamical systems often exhibit chaos, which is characterized by sensitive dependence on initial values or more precisely by a positive Lyapunov exponent. Recognizing and quantifying chaos in time series represents an important step toward understanding the nature of random behavior and re ..."
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Cited by 4 (1 self)
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Nonlinear dynamical systems often exhibit chaos, which is characterized by sensitive dependence on initial values or more precisely by a positive Lyapunov exponent. Recognizing and quantifying chaos in time series represents an important step toward understanding the nature of random behavior and revealing the extent to which shortterm forecasts may be improved. We will focus on the statistical problem of quantifying chaos and nonlinearity via Lyapunov exponents. Predicting the future or determining Lyapunov exponents requires estimation of an autoregressive function or its partial derivatives from time series. The multivariate locally weighted polynomial fit is studied for this purpose. In the nonparametric regression context, explicit asymptotic expansions for the conditional bias and conditional covariance matrix of the regression and partial derivative estimators are derived for both the local linear fit and the local quadratic fit. These results are then generalized to the time s...