APPLICATIONS OF THE DISCRETE AND CONTINUOUS WAVELET TRANSFORM TO THE PORTFOLIO MANAGEMENT
Abstract
The current paper demonstrates that the wavelet transform is a very
powerful tool for financial analysis. Some of the opportunities that it provides to the
financial analyst and in particular to the portfolio manager are discussed in the context of
two empirical examples. The first example illustrates how the notion of wavelet coherency
might be utilized in the process of risk diversification. In the second example is applied the
discrete wavelet transform to the preliminary stage of the portfolio return modeling. On the
basis of the delivered empirical findings it might be concluded that the application of the
wavelet transform reveals relevant decision-making information that is otherwise not that
obvious.
References
Ramsey, J. 1999, Philosophical Transactions of the Royal Society of London A, Vol. 357,
pp. 2593-606.
2. Gençay, R., Selçuk, F. and Whitcher, B. An Introduction to Wavelets and Other
Filtering Methods in Finance and Economics. New York : Academic Press, 2001.
3. Wavelets in economics and finance: past and future. Ramsey, J. 3, 2002, Studies
in Nonlinear Dynamics & Econometrics, Vol. 6, p. Article 1.
4. A theory for multiresolution signal decomposition: the wavelet representation.
Mallat, S. 1989, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11,
pp. 674-93.
5. Percival D.B. and Walden A.T. Wavelet Methods for Time Series Analysis.
Cambridge : Cambridge Press, 2000.
6. Maginn, J., Tuttle, D., Pinto, J. and McLeavey, D. Managing Invetment Portfolios:
A Dynamic Process (CFA Institute Investment Series). 3rd. Hoboken, New Jersey : John
Wiley & Sons, Inc, 2007.
7. The continuous wavelet transform: a primer. Aguirar-Conraria, L. and Soares,
M.J. 2011, NIPE Working Papers from NIPE - Universidade do Minho, WP 16/2011.
8. Country versus region effects in international stock returns. Brooks, R. and Del
Negro, M. 4, 2005, Journal of Portfolio Management, Vol. 31, pp. 67-72.
9. Estrada, J., Kritzman, M. and Page, S. Countries versus industries in emerging
markets: a normative portfolio approach. s.l. : EFMA 2004 Basel Meetings Papers, 2004.
10. Country and industry factors in returns: evidence from emerging markets'
stocks. Serra, A.P. 2, 2000, Emerging Markets Review, Vol. 1, pp. 127-51.
11. International portfolio diversification: US and Central European equity markets.
Gilmore, C. and McManus, G. 1, 2002, Emerging Markets Review, Vol. 3, pp. 69-83.
12. The evolution of stock market efficiency over time: a survey of the empirical
literature. Lim, K.P. and Brooks, R. 1, 2011, Journal of Economic Surveys, Vol. 25, pp. 69-
108.
13. Testing for long-range dependence in world stock markets. Cajueiro, D.O. and
Tabak, B.M. 2008, Chaos, Solutions & Fractals, Vol. 37, pp. 918-27.
14. Self-similarity and long-range dependence through the wavelet lens. Arby, P.,
Flandirn, P., Taqqu, M.S. and Vietch, D. s.l. : Birkhaeuser, 2003, Theory and Applications
of Long-range Dependence, pp. 527-56.
15. An introduction to long-memory time series models and fractional differencing.
Granger, C.W. and Joyeux, R. 1, 1980, Journal of Time Series Analysis, Vol. 1, pp. 15-29.
16. Fractional differencing. Hosking, J.R.M. 1, 1981, Biometrika, Vol. 68, pp. 165-
76.

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