Study on the nonlinear and chaotic behavior of exchange traded funds listed in Hong Kong Stock Exchanges

Article Sidebar

Requires Subscription or Fee PDF (GBP 25)
Published: Mar 9, 2020
DOI: https://doi.org/10.5750/jpm.v13i2.1781
Keywords:
exchange traded fund AR-GARCH Hong Kong Stock Exchange nonlinearity chaotic behavior time series

Main Article Content

Patrick Kuok Kun Chu
University of Macau
http://orcid.org/0000-0002-8395-8534

Abstract

This study examines the nonlinearity and chaotic behavior of the time series of returns of two exchange traded funds (ETFs) listed in Hong Kong Stock Exchanges, namely Hong Kong Tracker Fund (HKTF) and iShares FTSE A50 (ISFT), and the adequacy of autoregressive-generalized autoregressive conditional heteroskedasticity (AR-GARCH) models to capture nonlinearity. A set of nonlinearity tests consistently indicates the presence of nonlinearity in both return time series and the Brock–Dechert–Scheinkman (BDS) test of nonlinearity on AR-GARCH residuals, and the inability of AR-GARCH models to capture the nonlinearity in the return series at different stages of the model-building process. Testing for chaos is a rather delicate part in this study and is done by estimating the correlation dimension for both ETFs’ return series. The correlation dimension saturates at a finite value, and the saturation indicates the presence of chaos in two ETFs considered for this study.

Article Details

Issue
Vol. 13 No. 2 (2019)
Section
Articles
Author Biography

Patrick Kuok Kun Chu, University of Macau

Assistant Professor in Decision Sciences,Department of Accounting and Information Management,Faculty of Business Administration.

References

Atchison, M.D., White, M.A. 1996. Disappearing evidence of chaos in security returns: a Simulation. Quarterly Journal of Business and Economics 35, 21–37.

Bask, M. 1996. Dimensions, and Lyapunov exponents from exchange rate series. Chaos Solitons Fractals 7 (12), 2199–2214.

Bask, M. 2002. A positive Lyapunov exponent in Swedish exchange rates? Chaos Solitons Fractal 14 (8), 1295–1304.

BenSaida, A., Litimi, H. 2013. High level chaos in the exchange and index markets. Chaos, Solitons & Fractals 54, 90–95.

Blank, S. 1991. “Chaos” in futures markets? A non-linear dynamical analysis. Journal of Future Markets 11 (6), 711–728.

Brock, W.A., Dechert, W.D., Scheinkman, J.A. 1987. A test for independence based on the correlation dimension, Working Paper 8702, Department of Economics. University of Wisconsin at Madison.

Brock, W.A., Hsieh, D.A. , LeBaron, B. 1991. Nonlinear dynamics, chaos, and instability: statistical theory and economic evidence, MIT Press.

Brooks, C. 1998. Chaos in foreign exchange markets: a skeptical view. Computational Economics 11 (3), 265–281.

Chen, P. 1988. Empirical and theoretical evidence of economic chaos. System Dynamics Review 4 (1–2), 81–108.

Das, A., and Das, P. 2006. Does composite index of NYSE represents chaos in the long time scale? Applied Mathematics and Computation 174 (1), 483–489.

Das, A., Das, P. 2007. Chaotic analysis of the foreign exchange rates. Applied Mathematics and Computation 185 (1), 388–396.

De Grauwe, P., Vansteenkiste, I. 2007. Exchange rates and fundamentals: a non-linear relationship? International Journal of Finance and Economics 12 (1), 37–54.

Denker, G., Keller, G. 1986. Rigorous statistical procedures for data from dynamical systems. Journal of Statistical Physics 44 (1–2), 67–93.

Engle, R.F. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.

Fama, E.F. 1965. The behavior of stock market prices. Journal of Business 38 (1), 34–105.

Frank, M.Z., Stengos, T. 1989. Measuring the strangeness of gold and silver rates of return. Review of Economic Studies 56 (4), 553–567.

Gilmore, C.G. 1996. Detecting linear and nonlinear dependence in stock returns: new methods derived from chaos theory. Journal of Business Finance and Accounting, 23, 1357-1377.

Gilmore, C.G. 2001. An examination of nonlinear dependence in exchange rates using recent methods from chaos theory. Global Finance Journal 12 (1), 139–151.

Greene, M.T., Fieltz, B.D. 1977. Long term dependence in common stock returns. Journal of Financial Economics 4 (3), 249–339.

Hamill, P., Opong, K.K. 1997. Nonlinear determinism in the Irish equity market. Unpublished paper, School of Management, University of Ulster, Newtonabbey, 34–63.

Hampton, J. 1996. Rescaled range analysis: approaches for the financial practitioner, Part 3. Journal of Neuro Vest Journal 4 (4), 27–30.

Hinich, M.J. 1982. Testing for Gaussianity and linearity of a stationary time series. Journal of Time Series Analysis 3 (3), 169–176.

Howe, J.S., Martin, W., Wood Jr., B. 1997. Fractal structure in the Pacific Rim. Southwestern Finance Annual Meeting, New Orleans, March 1997.

Hsieh, D.A. 1991. Chaos and nonlinear dynamics: application to financial markets. The Journal of Finance 46 (5), 1839–1877.

Hsieh, D.A. 1993. Implications of nonlinear dynamics for financial risk management. Journal of Financial and Quantitative Analysis 28 (1), 41–64.

Iseri, M., Caglar, H., Caglar, N. 2008. A model proposal for the chaotic structure of Istanbul stock exchange. Chaos Solitons & Fractals 36 (5), 1392–1398.

Lin, K. 1997. The ABC’s of BDS. Journal of Computational Intelligence in Finance 97 (July/Aug), 23-26.

Liu, T., Granger, C.W.J., Heller, W.P. 1993. Using the correlation exponent to decide whether an economic series is chaotic. Nonlinear Dynamics, Chaos and Econometrics, John Wiley & Sons.

Madhavan, V. 2013a. Nonlinearity in investment grade Credit Default Swap (CDS) Indices of US and Europe: evidence from BDS and close-returns tests. Global Finance Journal 24 (3), 266–279.

Madhavan, V. 2013b. Investigating the nature of nonlinearity in Indian Exchange Traded Funds (ETFs). Managerial Finance 40 (4), 395–415.

Mandelbrot, B. 1964. The variation of certain speculative prices. The Random Character of Stock Prices, MIT Press.

McKenzie, M. 2001. Chaotic behavior in national stock market indices, new evidence from the close returns test. Global Finance Journal 12 (1), 35–53.

McLeod, A.I., Li, W.K. 1983. Diagnostic checking ARMA time series models using squared residual autocorrelations. Journal of Time Series Analysis 4 (4), 269–273.

Mishra, R., Sehgal, S., Bhanumurthy, N. 2011. A search for long-range dependence and chaotic structure in Indian stock market. Review of Financial Economics 20 (2), 96–104.

Opong, K.K., Mulholland, G., Fox, A.F., Farahmand, K. 1999. The behavior of some UK equity indices: an application of Hurst and BDS tests. Journal of Empirical Finance 6 (3), 267–282.

Papaioannou, G., Karytinos, A. 1995. Nonlinear time series analysis of the stock exchange: the case of an emerging market. International Journal of Bifurcation and Chaos 5, 1557–1584.

Peters, E.E. 1989. Fractal structure in the capital markets. Financial Analyst Journal 45, 33-37.

Peters, E.E. 1991a. Chaos and order in the capital markets: a new view of cycles, prices, and market volatility (Vol. 1), John Wiley & Sons.

Peters, E.E. 1991b. A chaotic attractor for the S&P 500. Financial Analyst Journal 47 (2), 55–62.

Peters, E.E. 1992. R/S analysis using logarithmic returns. Financial Analyst Journal 48 (6), 81–82.

Peters, E.E. 1994. Fractal market analysis: applying chaos theory to investment and economics (Vol. 24), John Wiley & Sons.

Scarlat, E., Stan, C., Cristescu, C. 2007. Chaotic features in Romanian transition economy as reflected onto the currency exchange rate, Chaos, Solitons & Fractals 33 (2), 396–404.

Scheinkman, J., LeBaron, B. 1989. Nonlinear dynamics and stock returns. Journal of Business 62, 311–337.

Serletis, A., Gogas, D., Calgary, P. 1997. Chaos in east European black-market exchange rates. Research in Economics 51 (4), 359–385.

Serletis, A., Shintani, M. 2003. No evidence of chaos but some evidence of dependence in the US stock market. Chaos Solitons Fractals 17 (2–3), 449–454.

Willey, T. 1992. Testing for nonlinear dependence in daily stock indices. Journal of Economics and Business 44 (1), 63–76.