In this paper we test for deterministic chaos (i.e., nonlinear deterministic processes which look random) in seven Mont Belview, Texas, hydrocarbon markets, using monthly data from 1985:1 to 1996:12--the markets are those of ethane, propane, normal butane, iso-butane, naptha, crude oil, and natural gas. In doing so, we use the Lyapunov exponent estimator of Nychka, Ellner, Gallant, and McCaffrey (1992). We conclude that there is evidence, consistent with a chaotic nonlinear generation process in all five natural gas liquids markets.
BarnettW.A.GallantA.R.HinichM.J.JungeilgesJ.KaplanD.JensenM.J. (1995). “Robustness of Nonlinearity and Chaos Test to Measurement Error, Inference Method, and Sample Size.” Journal of Economic Behavior and Organization27: 301-320.
2.
BarnettW.A.GallantA.R.HinichM.J.JungeilgesJ.KaplanD.JensenM.J. (1997). “A Single-Blind Controlled Competition Between Tests for Nonlinearity and Chaos.” Journal of Econometrics82: 157-192.
3.
BarnettW.A.SerletisA. (1999). “Martingales, Nonlinearity, and Chaos.” Journal of Economic Dynamics and Control, forthcoming.
4.
BollerslevT. (1986). “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics31: 307-327.
5.
BrockW.A.DechertW.D.ScheinkmanJ.LeBaronB. (1996). “A Test for Independence Based on the Correlation Dimension.” Econometric Reviews15: 197-235.
6.
DickeyDavid A.FullerWayne A. (1981). “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root.” Econometrica49: 1057-72.
7.
DoldadoDoldadoJenkinsonT.Sosvilla-RiveroS. (1990). “Cointegration and Unit Roots.” Journal of Economic Surveys4: 249-273.
8.
EckmannJ.P.RuelleD. (1985). “Ergodic Theory of Strange Attractors.” Reviews of Modem Physics57: 617-656.
9.
EllnerS.NychkaD.W.GallantA.R. (1992). “LENNS, a Program to Estimate the Dominant Lyapunov Exponent of Noisy Nonlinear Systems from Time Series Data.” Institute of Statistics Mimeo Series #2235 (BMA Series #39), Statistics Department, North Carolina State University, Raleigh, NC 27695-8203.
10.
EngleR.F. (1982). “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation.” Econometrica50: 987-1008.
11.
FrankFrankStengosThanasis (1989). “Measuring the Strangeness of Gold and Silver Rates of Return.” Review of Economic Studies56: 553-567.
12.
FullerWayne A. (1976). Introduction to Statistical Time Series. New York: Wiley.
13.
GallantA.R.WhiteH. (1992). “On Learning the Derivatives of an Unknown Mapping with Multilayer Feedforward Networks.” Neural Networks5: 129-138.
14.
GencayGencayDechert DavisW. (1992). “An Algorithm for the n Lyapunov Exponents of an n-Dimensional Unknown Dynamical System.” Physica D59: 142-157.
15.
HinichM.J. (1982). “Testing for Caussianity and Linearity of a Stationary Time Series.” Journal of Time Series Analysis3: 169-176.
16.
KaplanDaniel T. (1994). “Exceptional Events as Evidence for Determinism.” Physica D73: 38-48.
LamoureuxC.LastrapesW. (1990). “Persistence in Variance, Structural Change, and the GARCH Model.” Journal of Business and Economic Statistics8: 225-234.
19.
LjungG.M.BoxG.E.P. (1978). “On a Measure of Lack of Fit in Time Series Models.” Biometrica65: 297-303.
20.
NelsonCharles R.PlosserCharles I. (1982). “Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications.” Journal of Monetary Economics10: 139-62.
21.
NelsonD.B. (1991). “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica59: 347-370.
22.
NychkaD.W.EllnerS.GallantA.R.McCaffreyD. (1992). “Finding Chaos in Noisy Systems.” Journal of the Royal Statistical Society B54: 399-426.
23.
PantulaSastry G.Gonzalez-FariasG.FullerW.A. (1994). “A Comparison of Unit-Root Test Criteria.” Journal of Business and Economic Statistics12: 449-459.
24.
PindyckR.S.RotembergJ. J. (1990). “The Excess Co-movement of Commodity Prices.” The Economic Journal100: 1173-1189.
25.
ScheinkmanJose A.LeBaronBlake (1989). “Nonlinear Dynamics and Stock Returns.” Journal of Business62: 311-337.
26.
SchwartzG. (1978). “Estimating the Dimension of a Model.” The Annals of Statistics6: 461-464.
27.
SerletisApostolos (1997). “Is There an East-West Split in North American Natural Gas Markets?” The Energy Journal18(1): 47-62.
28.
SerletisSerletisGogasPeriklis (1997). “Chaos in East European Black-Market Exchange Rates.” Research in Economics51: 359-385.
29.
WhiteH. (1989). “Some Asymptotic Results for Learning in Single Hidden-Layer Foodforward Network Models.” Journal of the American Statistical Association84: 1003-1013.
