IJPAM: Volume 110, No. 2 (2016)

Title

THE MAHALANOBIS DISTANCE
BETWEEN THE HURST COEFFICIENT
AND THE ALPHA-STABLE PARAMETER:
AN EARLY WARNING INDICATOR OF CRISES

Authors

Román Rodríguez-Aguilar$^1$, Salvador Cruz-Aké$^2$,
Francisco Venegas-Martínez$^3$
$^{1,2,3}$Escuela Superior de Economía
Instituto Politécnico Nacional
Plan de Agua Prieta No. 66, Miguel Hidalgo, C.P. 11340
Mexico City, MÉXICO

Abstract

The Hurst coefficient and the alpha-stable parameter are useful indicators in the analysis of time series to detect normality and absence of self-similarity. In particular, when these two features met simultaneously the series is driven by white noise. This paper is aimed at developing an index to measure the degree to which a time series departs from white noise. The proposed index is built by using the principal component analysis of the Mahalanobis distances between the Hurst coefficient and the alpha-stable parameter from theoretical values of normality and absence of self-similarity. The proposed index is applied to examine the Mexican Peso exchange rate against the US Dollar. The distinctive characteristic of the index is that it can be used as an early warning indicator of crises, as it is shown for the Mexican case.

History

Received: August 1, 2016
Revised: October 19, 2016
Published: November 5, 2016. Download retracted version from here.
Revised (on author's request: error in the name of 3-rd author): November 30, 2016

AMS Classification, Key Words

AMS Subject Classification: G15, F31, C43 and C53
Key Words and Phrases: Fractional Brownian motion, Hurst coefficient, self-similarity, alpha-stable distributions, heavy tails, early warning indicator.

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How to Cite?

DOI: 10.12732/ijpam.v110i2.5 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 110
Issue: 2
Pages: 283 - 310


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