Fractals and Intrinsic Time - a Challenge to Econometricians

Posted: 2 Sep 1999

See all articles by Ulrich A. Müller

Ulrich A. Müller

Olsen & Associates

Michel M. Dacorogna

DEAR-Consulting

Rakhal Dave

Olsen Financial Technologies

Olivier V. Pictet

Pictet Asset Management

Richard B. Olsen

Lykke Corp

J. Robert Ward

Olsen Group (Olsen & Associates Ltd.)

Abstract

A fractal approach is used to analyze financial time series, applying different degrees of time resolution, and the results are interrelated. Some fractal properties of foreign exchange (FX) data are found. In particular, the mean size of absolute values of price changes follows a "fractal" scaling law (a power law) as a function of the analysis time interval ranging from a few minutes up to a year. In an autocorrelation study of intraday data, the absolute values of price changes are seen to behave like the fractional noise of Mandelbrot and Van Ness rather than those of a GARCH process. Intraday FX data exhibit strong seasonal and autoregressive heteroskedasticity. This can be modeled with the help of new time scales, one of which is termed intrinsic time. These time scales are successfully applied to a forecasting model with a fractal structure for both the FX and interbank interest rates, which present similar market structures as the Foreign Exchange. The goal of this paper is to demonstrate how the analysis of high-frequency data and the finding of fractal properties lead to the hypothesis of a heterogeneous market, where different market participants analyze past events and news with different time horizons. This hypothesis is further supported by the success of trading models with different dealing frequencies and risk profiles. Intrinsic time is proposed for modeling the frame of reference of each component of a heterogeneous market.

JEL Classification: C22, C32, F31

Suggested Citation

Müller, Ulrich A. and Dacorogna, Michel M. and Dave, Rakhal D. and Pictet, Olivier V. and Olsen, Richard B. and Ward, J. Robert, Fractals and Intrinsic Time - a Challenge to Econometricians. Available at SSRN: https://ssrn.com/abstract=5370

Ulrich A. Müller

Olsen & Associates ( email )

Seefeldstrasse 233
CH-8008 Zurich
Switzerland
+41 (1) 386 48 16 (Phone)
+41 (1) 422 22 82 (Fax)

Michel M. Dacorogna

DEAR-Consulting ( email )

Scheuchzerstrasse 160
Zurich, 8057
Switzerland
+41795447327 (Phone)

Rakhal D. Dave

Olsen Financial Technologies ( email )

Ottenbergstrasse 81
Zurich, 8049
Switzerland
+41 44 342 3566 (Phone)
+41 44 342 3561 (Fax)

HOME PAGE: http://www.olsendata.com

Olivier V. Pictet

Pictet Asset Management ( email )

Geneva
Switzerland

Richard B. Olsen (Contact Author)

Lykke Corp ( email )

Baarerstrasse 2
Zug, Zug 6300
Switzerland
41793368950 (Phone)

HOME PAGE: http://www.lykke.com

J. Robert Ward

Olsen Group (Olsen & Associates Ltd.) ( email )

Seefeldstrasse 233
CH-8008 Zurich
Switzerland
+41 1 386 4848 (Phone)
+41 1 422 2282 (Fax)

Register to save articles to
your library

Register

Paper statistics

Abstract Views
2,097
PlumX Metrics