Fractional Brownian dynamics in naira/dollar foreign exchange rates
| Published date | 12 July 2013 |
| Date | 12 July 2013 |
| Pages | 191-203 |
| DOI | https://doi.org/10.1108/WJEMSD-01-2013-0003 |
| Author | Olusegun Felix Ayadi |
| Subject Matter | Public policy & environmental management |
Fractional Brownian dynamics
in naira/dollar foreign
exchange rates
Olusegun Felix Ayadi
Department of Accounting and Finance, Texas Southern University, Houston,
Texas, USA
Abstract
Purpose – This paper seeks to characterize the behavior of the naira/dollar foreign exchange rate
series over the period 1999 through 2006 to determine if the process generating the series has
long memory which is a special case of fractional Brownian motion. The existence of long memory
contradicts the notion of market efficiency.
Design/methodology/approach – The paper employs the modified rescaled range R/S test which is
proposed by Lo to test the null hypothesis that daily and weekly NGN/USD exchange rates from
1999 through 2006 exhibit short-memory process. The second test that was also employed is the
Geweke-Porter-Hubak (GPH) test which was refined by Hurvich et al.
Findings – The results show that long memory is present in daily and weekly foreign exchange level
series of the Nigerian naira for the period sampled. This evidence implies that the Nigerian foreign
exchange market may not be efficient. Thus, it is possible for investors to realize abnormal profit
by taking an investment position based on predicted exchange rates. The results reported in this paper
are also indicative of a deviation from long-run PPP.
Originality/value – This paper is the first to empirically apply the modified R/S and GPH tests
to explore the existence of long-memory process in a country study of foreign exchange series using
data from Nigeria.
Keywords Long-memory,Foreign exchange, Fractional Brownian motion, Rescaled R/S test, Nigeria
Paper type Research p aper
1. Introduction
A given time series is said to be governed by some underlyingprocess. A logical question is
whether or not the times series possesses some patterns or regularity which can be
examined through econometric modeling. A fractional Brownian motion is a stochastic
process which possesses stationary increments, self-similarity as well as long-rang e
dependence (Nualart, 2002). A fractional Brownian motion is also associated with regularity
of sample paths. The study of long memory in time series data has been in existence for
quite some time. A renewed application in the financial economics field had recently gained
ground as noted in Peters (1994, 1996), Mandelbrot (1997), Granger and Joyeux (1980),
Beran (1993) and Bouchaud et al. (1999). As far back as 1900 Bachelier argues that
financial asset prices can be described as a random walk because fluctuations in these
prices are assumed to follow a Gaussian probability distribution (Bouchaud et al., 1999).
The focus of researchers was a development of reliable model for predicting
fluctuations which is crucial for managing the risks inherent in asset prices.
The literature on long memory addresses the correlation of times series at long lags
(Box-Steffensmeier and Tomlinson, 1999). Mandelbrot (1972) raises the issue of long
memory in stock prices. The thesis of this area of study is based on the premise that
actual movements in time series are stochastically influenced by the recent to the most
remote past. Furthermore, with an auto regressive moving average (ARMA) model, one
can make more accurate forecasts of foreign exchange rates when long memory exists.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/2042-5961.htm
World Journal of Entrepreneurship,
Management and Sustainable
Development
Vol. 9 No.2/3, 2013
pp. 191-203
rEmeraldGroup Publishing Limited
2042-5961
DOI 10.1108/W JEMSD-01-2013- 0003
191
Fractional
Brownian
dynamics
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