Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-17T18:05:11.308Z Has data issue: false hasContentIssue false
  • English
  • Français

IDENTIFYING NONLINEAR SERIAL DEPENDENCE IN VOLATILE, HIGH-FREQUENCY TIME SERIES AND ITS IMPLICATIONS FOR VOLATILITY MODELING

Published online by Cambridge University Press:  07 April 2010

Phillip Wild ,
John Foster  and
Melvin J. Hinich
Phillip Wild*
Affiliation:
University of Queensland
John Foster
Affiliation:
University of Queensland
Melvin J. Hinich
Affiliation:
University of Texas at Austin
*
Address correspondence to: Phillip Wild, School of Economics, University of Queensland, St. Lucia, QLD 4072, Australia; e-mail: p.wild@uq.edu.au.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we show how tests of nonlinear serial dependence can be applied to high-frequency time series data that exhibit high volatility, strong mean reversion, and leptokurtotis. Portmanteau correlation, bicorrelation, and tricorrelation tests are used to detect nonlinear serial dependence in the data. Trimming is used to control for the presence of outliers in the data. The data that are employed are 161,786 half-hourly spot electricity price observations recorded over nearly a decade in the wholesale electricity market in New South Wales, Australia. Strong evidence of nonlinear serial dependence is found and its implications for time series modeling are discussed.

Keywords

NonlinearityPortmanteau TestsBicorrelationTricorrelationTrimmingDeep Structure
Type
Articles
Information
Macroeconomic Dynamics , Volume 14 , Supplement S1: Nonlinear Time Series , May 2010 , pp. 88 - 110
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ammermann, P.A. and Patterson, D.M. (2003) The cross-sectional and cross-temporal universality of nonlinear serial dependencies: Evidence from world stock indices and the Taiwan Stock Exchange. Pacific-Basin Finance Journal 11, 175–195.Google Scholar
Bera, A.K. and Higgins, M.L. (1993) ARCH models: Properties, estimation and testing. Journal of Economic Surveys 7, 305–362.Google Scholar
Bollerslev, T. (1986) Generalised autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.Google Scholar
Bollerslev, T. (1987) A conditional heteroscedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69, 542–547.Google Scholar
Bollerslev, T., Chou, R.Y., and Kroner, K.F. (1992) ARCH modelling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5–59.Google Scholar
Bollerslev, T., Engle, R.F., and Nelson, D.B. (1995) ARCH models. In Engle, R.F. and McFadden, D. (eds.), The Handbook of Econometrics, Vol. 4, Chapter 49. Amsterdam: North-Holland.Google Scholar
Bonilla, C.A., Romero-Meza, R., and Hinich, M.J. (2007) GARCH inadequacy for modelling exchange rates: Empirical evidence from Latin America. Applied Economics 39, 2529–2533.Google Scholar
Brooks, C. (1996) Testing for non-linearity in daily sterling exchange rates. Applied Financial Economics 6, 307–317.Google Scholar
Brooks, C. and Hinich, M.J. (1998) Episodic nonstationarity in exchange rates. Applied Economic Letters 5, 719–722.Google Scholar
Diebold, F.X. and Lopez, J.A. (1995) ARCH models. In Hoover, K. (ed.), Macroeconomics: Developments, Tensions and Prospects, pp. 427–472. Boston: Kluwer Academic Press.Google Scholar
Edgeworth, F.Y. (1898) On the representation of statistics by mathematical formulae. Journal of the Royal Statistical Society 61, 670–700.Google Scholar
Engle, R.F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.CrossRefGoogle Scholar
Foster, J., Hinich, M.J., and Wild, P. (2008) Randomly modulated periodic signals in Australia's national electricity market. The Energy Journal 29, 105–130.CrossRefGoogle Scholar
Galton, F. (1879) The geometric mean in vital and social statistics. Proceedings of the Royal Society of London 29, 365–367.Google Scholar
Hinich, M.J. (1996) Testing for dependence in the input to a linear time series model. Journal of Nonparametric Statistics 6, 205–221.Google Scholar
Hinich, M.J. (2000) A statistical theory of signal coherence. Journal of Oceanic Engineering 25, 256–261.Google Scholar
Hinich, M.J. and Patterson, D.M. (1989) Evidence of nonlinearity in the trade-by-trade stock market return generating process. In Barnett, W., Geweke, J., and Shell, K. (eds.), Economic Complexity, Chaos, Sunspots, Bubbles, and Nonlinearity, pp. 383–409. New York: Cambridge University Press.Google Scholar
Hinich, M.J. and Patterson, D.M. (1995) Detecting Epochs of Transient Dependence in White Noise. Mimeo, University of Texas at Austin.Google Scholar
Hinich, M.J. and Patterson, D.M. (2005) Detecting epochs of transient dependence in white noise. In Belongia, M. and Binner, J. (ed.), Money, Measurement and Computation, Part 2. London: Palgrave.Google Scholar
Hinich, M.J. and Serletis, A. (2007) Episodic nonlinear event detection in the Canadian exchange rate. Journal of the American Statistical Association, Applications and Case Studies 102, 68–74.Google Scholar
Hinich, M.J. and Wild, P. (2001) Testing time-series stationarity against an alternative whose mean is periodic. Macroeconomic Dynamics 5, 380–412.Google Scholar
Johnson, N.L. (1949) Systems of frequency curves generated by means of translation. Biometrika 36, 149–176.Google Scholar
Lim, K.P. and Hinich, M.J. (2005a) Cross-temporal universality of non-linear dependencies in Asian stock markets. Economics Bulletin 7, 1–6.Google Scholar
Lim, K.P. and Hinich, M.J. (2005b) Non-linear market behavior: Events detection in the Malaysian stock market. Economics Bulletin 7, 1–5.Google Scholar
Lim, K.P., Hinich, M.J., and Liew, V.K.S. (2003) Episodic non-linearity and non-stationarity in ASEAN exchange rates returns series. Labuan Bulletin of International Business and Finance 1, 79–93.Google Scholar
Lim, K.P., Hinich, M.J., and Liew, V.K.S. (2004) Non-linearity in financial markets: Evidence from ASEAN-5 exchange rates and stock markets. ICFAI Journal of Applied Finance 10, 5–18.Google Scholar
Lim, K-P., Hinich, M.J., and Liew, V.K. (2005) Statistical inadequacy of GARCH models for Asian stock markets: Evidence and implications. Journal of Emerging Market Finance 4, 263–279.CrossRefGoogle Scholar
McAlister, D. (1879) The law of the geometric mean. Proceedings of the Royal Society of London 29, 367–376.Google Scholar
National Electricity Market Management Company Limited (2005) An Introduction to Australia's National Electricity Market. National Electricity Market Management Company Ltd. Available at http://www.aemo.com.au/corporate/0000-0006.pdf.Google Scholar
Nelson, D.B. (1991) Conditional heteroscedasticity in asset pricing: A new approach. Econometrica 59, 347–370.Google Scholar
Shephard, N. (1996) Statistical aspects of ARCH and stochastic volatility. In Cox, D.R, Hinkley, D.V., and Barndorff-Nielsen, Ole E. (eds.), Time Series Models in Econometrics, Finance and Other Fields, pp. 1–67. London: Chapman & Hall.Google Scholar
Taylor, S.J. (1986) Modelling Financial Time Series, Chapter 3. Chichester. UK: John Wiley.Google Scholar
Wild, P., Hinich, M.J., and Foster, J. (2008) Are Daily and Weekly Load and Spot Price Dynamics in Australia's National Electric Market Governed by Episodic Nonlinearity? Discussion Paper No. 368, School of Economics, University of Queensland, Australia. Available at http://www.uq.edu.au/economics/abstract/368.pdf.Google Scholar