The North American Natural Gas Liquids Markets are Chaotic

Abstract

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.

Keywords

Natural gas liquids prices statistical analysis financial markets GARCH chaos Lyapunov exponent

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References

Barnett

W.A.

Gallant

A.R.

Hinich

M.J.

Jungeilges

Kaplan

Jensen

M.J.

(1995). “Robustness of Nonlinearity and Chaos Test to Measurement Error, Inference Method, and Sample Size.” Journal of Economic Behavior and Organization 27: 301-320.

Barnett

W.A.

Gallant

A.R.

Hinich

M.J.

Jungeilges

Kaplan

Jensen

M.J.

(1997). “A Single-Blind Controlled Competition Between Tests for Nonlinearity and Chaos.” Journal of Econometrics 82: 157-192.

Barnett

W.A.

Serletis

(1999). “Martingales, Nonlinearity, and Chaos.” Journal of Economic Dynamics and Control, forthcoming.

Bollerslev

(1986). “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31: 307-327.

Brock

W.A.

Dechert

W.D.

Scheinkman

LeBaron

(1996). “A Test for Independence Based on the Correlation Dimension.” Econometric Reviews 15: 197-235.

Dickey

David A.

Fuller

Wayne A.

(1981). “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root.” Econometrica 49: 1057-72.

Doldado

Jenkinson

Sosvilla-Rivero

(1990). “Cointegration and Unit Roots.” Journal of Economic Surveys 4: 249-273.

Eckmann

J.P.

Ruelle

(1985). “Ergodic Theory of Strange Attractors.” Reviews of Modem Physics 57: 617-656.

Ellner

Nychka

D.W.

Gallant

A.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.

Engle

R.F.

(1982). “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation.” Econometrica 50: 987-1008.

11.

Frank

Stengos

Thanasis

(1989). “Measuring the Strangeness of Gold and Silver Rates of Return.” Review of Economic Studies 56: 553-567.

12.

Fuller

Wayne A.

(1976). Introduction to Statistical Time Series. New York: Wiley.

13.

Gallant

A.R.

White

(1992). “On Learning the Derivatives of an Unknown Mapping with Multilayer Feedforward Networks.” Neural Networks 5: 129-138.

14.

Gencay

Dechert Davis

(1992). “An Algorithm for the n Lyapunov Exponents of an n-Dimensional Unknown Dynamical System.” Physica D 59: 142-157.

15.

Hinich

M.J.

(1982). “Testing for Caussianity and Linearity of a Stationary Time Series.” Journal of Time Series Analysis 3: 169-176.

16.

Kaplan

Daniel T.

(1994). “Exceptional Events as Evidence for Determinism.” Physica D 73: 38-48.

17.

Kearns

Pagan

A.R.

(1993). “Australian Stock Market Volatility: 1875-1987.” The Economic Record 69: 163-178.

18.

Lamoureux

Lastrapes

(1990). “Persistence in Variance, Structural Change, and the GARCH Model.” Journal of Business and Economic Statistics 8: 225-234.

19.

Ljung

G.M.

Box

G.E.P.

(1978). “On a Measure of Lack of Fit in Time Series Models.” Biometrica 65: 297-303.

20.

Nelson

Charles R.

Plosser

Charles I.

(1982). “Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications.” Journal of Monetary Economics 10: 139-62.

21.

Nelson

D.B.

(1991). “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica 59: 347-370.

22.

Nychka

D.W.

Ellner

Gallant

A.R.

McCaffrey

(1992). “Finding Chaos in Noisy Systems.” Journal of the Royal Statistical Society B 54: 399-426.

23.

Pantula

Sastry G.

Gonzalez-Farias

Fuller

W.A.

(1994). “A Comparison of Unit-Root Test Criteria.” Journal of Business and Economic Statistics 12: 449-459.

24.

Pindyck

R.S.

Rotemberg

J. J.

(1990). “The Excess Co-movement of Commodity Prices.” The Economic Journal 100: 1173-1189.

25.

Scheinkman

Jose A.

LeBaron

Blake

(1989). “Nonlinear Dynamics and Stock Returns.” Journal of Business 62: 311-337.

26.

Schwartz

(1978). “Estimating the Dimension of a Model.” The Annals of Statistics 6: 461-464.

27.

Serletis

Apostolos

(1997). “Is There an East-West Split in North American Natural Gas Markets?” The Energy Journal 18(1): 47-62.

28.

Serletis

Gogas

Periklis

(1997). “Chaos in East European Black-Market Exchange Rates.” Research in Economics 51: 359-385.

29.

White

(1989). “Some Asymptotic Results for Learning in Single Hidden-Layer Foodforward Network Models.” Journal of the American Statistical Association 84: 1003-1013.