Segmentation Study of Foreign Exchange Market
This chapter explains a recursive segmentation procedure under normal distribution assumptions. The Akaike information criterion between independently identically distributed Gaussian samples and two successive segments drawn from different Gaussian distributions is used as a discriminator to segment time series. The Jackknife method is employed in order to evaluate a statistical significance level. This chapter shows univariate and multivariate cases. The proposed method is performed for artificial time series consisting of two segments with different statistics. Furthermore, log-return time series of currency exchange rates for 30 currency pairs for the period from January 4, 2001 to December 30, 2011 are divided into 11 segments with the proposed method. It is confirmed that some segment corresponds to historical events recorded as critical situations.
KeywordsMultivariate Gaussian Distribution Multivariate Time Series Segmentation Procedure Financial Time Series Foreign Exchange Rate
The author would like to express his sincere gratitude to Prof. Zdzislaw Burda of Jagiellonian University for constructive comments and stimulating discussions.
- 1.Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Caski, F. (eds.) Proceeding of the Second International Symposium on Information Theory, pp. 267–281. Akademiai Kiado, Budapest (1973)Google Scholar
- 4.Basseville, M., Nikiforov, I.V.: Detection of Abrupt Changes—Theory and Application. Prentice-Hall, Upper Saddle Revier (1993)Google Scholar
- 10.Cheong, S.A., Fornia, R.P., Lee, G.H.T., Kok, J.L., Yim, W.S., Xu, D.Y., Zhang, Y.: The Japanese economy in crises—a time series segmentation study. Econ. E-J., 2012–5 (2012) URL http://www.economics-ejournal.org
- 20.Gullett, D.W., Vincent, L., Sajecki, P.J.F.: Testing homogeneity in temperature series at Canadian climate stations. CCC report 90–4, Climate Research Branch, Meteorological Service of Canada, Ontario, Canada (1990).Google Scholar
- 21.Hamilton, J.D.: Regime-switching models (2005) URL dss.ucsd.edu/ jhamilto/palgrav1.pdf.Google Scholar
- 25.Karl, T.R., Williams, C.N. Jr: An approach to adjusting climatological time series for discontinuous inhomogeneities. J. Clim. Appl. Meteorol. 26, 1744–1763 (1987)Google Scholar
- 27.Kim, C.J., Piger, J.M., Startz, R.: Estimation of Markov Regime-switching regression Models with endogenous swithing. Working Paper 2003–015C, Federal Researve Bank of St. Luis (2003) URL http://research.stlouisfed.org/wp/2003/2003-015.pdf
- 31.Mantegna, R.N., Stanley, H.E.: An Introduction to Econophysics- Correlations and Complexity in Finance. Cambridge University Press, Cambridge (2000)Google Scholar
- 41.Sato, A.-H.: Recursive segmentation procedure based on the Akaike information criterion test. 2013 IEEE 37th Annual Signature Conference of Computer Software and Applications Conference (COMPSAC), pp. 226–233 (2013)Google Scholar
- 43.Shiryaev, A.N., Zhitlukhin, M.V.: Optimal stopping problems for a Brownian motion with a disorder on a finite interval (2012) arXiv:1212.3709
- 44.Vert, J., Bleakley, K.: Fast detection of multiple change-points shared by many signals using group LARS. Adv. Neural Info. Process. Syst. 23, 2343–2351 (2010)Google Scholar