Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors

A positive Lyapunov exponent is one practical definition 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 significantly rejected in many cases. One possible interpretation of this result is that the traditional exogenous models are better able to explain business cycle fluctuations than is the chaotic endogenous approach. However, our results are subject to a number of caveats, in particular our results could have been influenced by small sample bias, high noise level, incorrect filtering, and long memory of the data.

[1]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[2]  M. Wand,et al.  Multivariate Locally Weighted Least Squares Regression , 1994 .

[3]  Douglas W. Mitchell,et al.  Nonlinear Monetary Dynamics , 1991 .

[4]  R. Gencay,et al.  Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis , 1992 .

[5]  Abhay Abhyankar,et al.  Uncovering nonlinear structure in real-time stock-market indexes: the S&P 500, the DAX, the Nikkei 225, and the FTSE-100 , 1997 .

[6]  W. Brock.  Distinguishing random and deterministic systems: Abridged version , 1986 .

[7]  A neural' network applied to tlie calculation of lyapunov exponents 1 , 1994 .

[8]  Cars H. Hommes,et al.  A reconsideration of Hicks' non-linear trade cycle model , 1995 .

[9]  A. Gallant,et al.  Finding Chaos in Noisy Systems , 1992 .

[10]  W. Brock,et al.  Is the business cycle characterized by deterministic chaos , 1988 .

[11]  O. Linton,et al.  The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series , 1999 .

[12]  Peter C. B. Phillips,et al.  ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES , 1999, Econometric Theory.

[13]  P. Phillips,et al.  Nonstationary Density Estimation and Kernel Autoregression , 1998 .

[14]  Kazuo Nishimura,et al.  The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth , 1979 .

[15]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[16]  D. Nychka,et al.  Local Lyapunov exponents: Predictability depends on where you are , 1995 .

[17]  Oliver Linton,et al.  SECOND ORDER APPROXIMATION IN THE PARTIALLY LINEAR REGRESSION MODEL , 1995 .

[18]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[19]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[20]  J. Hicks,et al.  A Contribution To The Theory Of The Trade Cycle , 1951 .

[21]  P. Doukhan.  Mixing: Properties and Examples , 1994 .

[22]  William A. Barnett,et al.  A single-blind controlled competition among tests for nonlinearity and chaos , 1997 .

[23]  Simon M. Potter.  A Nonlinear Approach to US GNP , 1995 .

[24]  Douglas W. Nychka,et al.  Chaos with Confidence: Asymptotics and Applications of Local Lyapunov Exponents , 1997 .

[25]  James B. Ramsey,et al.  The statistical properties of dimension calculations using small data sets , 1990 .

[26]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[27]  Jianqing Fan,et al.  Variable Bandwidth and Local Linear Regression Smoothers , 1992 .

[28]  William A. Barnett,et al.  Dynamic econometric modeling: The aggregation-theoretic monetary aggregates are chaotic and have strange attractors: an econometric application of mathematical chaos , 1988 .

[29]  Bruce E. Hansen,et al.  Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis , 1996 .

[30]  Elias Masry,et al.  MULTIVARIATE LOCAL POLYNOMIAL REGRESSION FOR TIME SERIES:UNIFORM STRONG CONSISTENCY AND RATES , 1996 .

[31]  H. R. Hudson,et al.  A MODEL OF THE TRADE CYCLE , 1957 .

[32]  Jianqing Fan.  Design-adaptive Nonparametric Regression , 1992 .

[33]  J. Campbell.  Inspecting the Mechanism: An Analytical Approach to the Stochastic Growth Model , 1992, Journal of Monetary Economics.

[34]  Philip Rothman,et al.  The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications , 1990 .

[35]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[36]  Apostolos Serletis,et al.  Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money , 1995 .

[37]  Thomas F. Cooley.  Frontiers of business cycle research , 1995 .

[38]  B. Lautrup,et al.  Products of random matrices. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[40]  N. Herrndorf.  A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables , 1984 .

[41]  Rodney C. Wolff,et al.  Local Lyapunov Exponents: Looking Closely at Chaos , 1992 .

[42]  Francis X. Diebold,et al.  A Nonparametric Investigation of Duration Dependence in the American Business Cycle , 1990, Journal of Political Economy.

[43]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[44]  William A. Barnett,et al.  Dynamic Econometric Modeling , 1988 .

[45]  W. Brock,et al.  Heterogeneous beliefs and routes to chaos in a simple asset pricing model , 1998 .

[46]  M. Hashem Pesaran,et al.  A floor and ceiling model of US output , 1997 .

[47]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

[48]  William A. Brock,et al.  A rational route to randomness , 1997 .

[49]  William A. Barnett,et al.  Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size , 1995 .

[50]  R. Day.  Irregular Growth Cycles , 2016 .

[51]  Eugen Slutzky.  Summation of random causes as the source of cyclic processes , 1937 .

[52]  R. Gencay,et al.  An algorithm for the n Lyapunov exponents of an n -dimensional unknown dynamical system , 1992 .

[53]  Mototsugu Shintani,et al.  Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos , 2002 .

[54]  Thanasis Stengos,et al.  Some evidence concerning macroeconomic chaos , 1988 .

[55]  Jean-Michel Grandmont,et al.  On Endogenous Competitive Business Cycles , 1985, Cycles and Chaos in Economic Equilibrium.

[56]  Rodney C. Wolff,et al.  ON THE STRENGTH OF DEPENDENCE OF A TIME SERIES GENERATED BY A CHAOTIC MAP , 1995 .

[57]  C. Sims.  MACROECONOMICS AND REALITY , 1977 .

[58]  A. Gallant,et al.  Estimating the Lyapunov Exponent of a Chaotic System with Nonparametric Regression , 1992 .