Abstract: This paper presents some empirical
evidences on the presence of nonlinearity of exchange rates of six
emerging markets by using Brock-Dechert-Scheinkman (BDS) test and
Volterra-Wiener-Korenberg (VWK) model, respectively. The nonlinear
dependences are found in the exchange rates of six emerging markets.
Furthermore, this paper applies the VWK model with surrogate data
method to detect if their nonlinear dependences are deterministic or
not. The results show that the above exchange rates are
deterministic and nonlinear time series. These imply that the
exchange rate markets do not conform to the requirements of the
random walk hypothesis. Therefore, the nonlinear dynamic model
should be used to analyze the exchange rates.
LEI Qiang (雷 强), PAN Ying-li (潘英丽)
. Nonlinear Analyses of Exchange Rates of Six Emerging Markets[J]. Journal of Shanghai Jiaotong University(Science), 2012
, 17(1)
: 108
-113
.
DOI: 10.1007/s12204-012-1236-6
1 Bask M. Dimensions and Lyapunov exponents from exchange rate
series [J]. Chaos, Solitons and Fractals, 1996, 7:
2199-2214.
2 Bask M. A positive Lyapunov exponent in Swedish exchange rates? [J].
Chaos, Solitons and Fractals, 2002, 14: 1295-1304.
3 Schwartz B, Yousefi S. On complex behavior and exchange rate
dynamics [J]. Chaos, Solitons and Fractals, 2003, 18:
503-523.
4 Jonsson M. Studies in business cycles [D]. Stockholm: Institute for
International Economic Studies, Stockholm University, 1997.
5 Serletis A, Gogas P. Chaos in East European black market exchange
rates [J]. Research in Economics, 1997, 5(51): 359-385.
6 Gencay R, Dechert W D. An algorithm for the n Lyapunov exponents
of an n-dimensional unknown dynamical system [J]. Physica
D, 1992, 59: 142-157.
7 D\'\iaz F A, Grall-Carles P, Mangas E L. Nonlinearities in the exchange
rates returns and volatility [J]. Physica A, 2002, 316:
469-482.
8 Cao L, Soofi A. Nonlinear deterministic forecasting of daily dollar
exchange rates [J]. International Journal of Forecasting,
1999, 15: 421-430.
9 Soofi A S, Galka A. Measuring the complexity of currency markets by
fractal dimension analysis [J]. International Journal of
Theoretical and Applied Finance, 2003, 6(6): 553-563.
10 Kugiumtzis D. On the reliability of the surrogate data test for
nonlinearity in the analysis of noisy time series [J].
International Journal of Bifurcation and Chaos, 2001, 11(7):
1881-1896.
11 Strozzi F, Comenges J M Z. Towards a non-linear trading strategy for
financial time series [J]. Chaos, Solitons and Fractals,
2006, 28: 601-615.
12 Chiarella C, Peat M, Stevenson M. Detecting and modeling
nonlinearity in flexible exchange rate time series [J]. Asia
Pacific Journal of Management, 1994, 11(2): 159-186.
13 Hsieh D A. Testing for nonlinear dependence in daily foreign
exchange rates [J]. Journal of Business, 1989, 62(3):
339-368.
14 Cecen A A, Erkal C. Distinguishing between stochastic and
deterministic behavior in foreign exchange rate returns: Further
evidence [J]. Economics Letters, 1996, 51: 323-329.
15 Cecen A A, Erkal C. Distinguishing between stochastic and
deterministic behavior in high frequency foreign exchange rate
returns: Can non-linear dynamics help forecasting? [J]
International Journal of Forecasting, 1996, 12: 465-473.
16 Lai D. Comparison study of AR models of the Canadian lynx data: A
close look at BDS statistic [J]. Computational Statistics
& Data Analysis, 1996, 22: 409-423.
17 Chu P K K. Study on the non-random and chaotic behavior of Chinese
equities market [J]. Review of Pacific Basin Financial Markets
and Policies, 2003, 6(2): 199-222.
18 Brock W A, Dechert W D, Scheinkman J A, et al. A test for
independence based on the correlation dimension [R]. Madison:
University of Wisconsin, 1987.
19 Brock W A, Hsieh D A, Lebaron B. Nonlinear dynamics, chaos and
instability: Statistical theory and economic evidence [M].
Cambridge, USA: MIT Press, 1991.
20 Barahona M, Poon C S. Detection of nonlinear dynamics in short,
noisy time series [J]. Nature, 1996, 381: 215-217.
21 Lei M, Meng G, Feng Z. Security analysis of chaotic communication
systems based on Volterra-Wiener-Korenberg model [J]. Chaos,
Solitons and Fractals, 2006, 28: 264-270.
22 Theiler J, Eubank S, Longtin A, et al. Testing for nonlinearity in
time series: The method of surrogate data [J]. Physica D,
1992, 58: 77-94.
23 Theiler J, Prichard D. Constrained-realization Monte-Carlo method
for hypothesis testing [J]. Physica D, 1996, 94:
221-235.
24 Lima E J A, Tabak B M. Testing for inefficiency in emerging markets
exchange rates [J]. Chaos, Solitons and Fractals, 2007,
33: 617-622.