Higher Moments and Exchange Rate Behavior

Published date01 February 2019
Date01 February 2019
The Financial Review 54 (2019) 201–229
Higher Moments and Exchange Rate
Siroos Khademalomoom
Department of Treasury and Finance,Victoria, Australia
Paresh Kumar Narayan
Deakin University
Susan Sunila Sharma
Deakin University
This paper uses 15-minute exchange rate returns data for the six most liquid currencies
(i.e., the Australian dollar,British pound, Canadian dollar, Euro, Japanese yen, and Swiss franc)
a-vis the United States dollar to examine whether a GARCH model augmented with higher
moments (HM-GARCH) performs better than a traditional GARCH (TG) model. Two find-
ings are unraveled. First, the inclusion of odd/even moments in modeling the return/variance
Corresponding author: Centre for Financial Econometrics, Deakin Business School, Deakin University,
221 Burwood Highway,Burwood, VIC 3125, Australia; Phone: +61 3 9244 6871; Fax: +61 3 9244 6034;
E-mail: s.sharma@deakin.edu.au.
The views expressed in this paper are those of the authors and do not necessarily reflect the views of the
Department of Treasury and Finance, Victoria, Australia.
This paper is original and has not been submitted elsewhere for publication. It is a chapter of the first
author’s PhD thesis undertaken at Deakin University, Melbourne, Australia. Earlier versions of this paper
were presented at the Centre for Financial Econometrics—Journal of Banking and Finance 2015 con-
ference on “Recent Developments in Financial Econometrics” at Deakin University,Geelong, Australia.
We acknowledge helpful comments and suggestions provided by conference participants, seminar par-
ticipants at Deakin University, and Professors Jonathan Batten and Niklas Wagner. Helpful comments
and suggestions from the Editor (Dr. Richard Warr) and anonymous reviewers of this journal are duly
C2019 The Eastern Finance Association 201
202 S. Khademalomoom et al./The Financial Review 54 (2019) 201–229
improves the statistical performance of the HM-GARCH model. Second, trading strategies
that extract buy and sell trading signals based on exchange rate forecasts from HM-GARCH
models are more profitable than those that depend on TG models.
Keywords: foreign exchange, high frequency, modeling, higher moments, trading strategy
JEL Classifications: C5, C58, F31, G15
1. Introduction
In this paper, we examine the role of high-order moments in influencing ex-
change rate behavior. We are not the first to explore the role of higher moments in
understanding exchange rate behavior. There is a literature on this; see Aggarwal
(1990), Harvey and Siddique (1999), and Mittnik and Paolella (2000). These studies
show that higher moments improve the statistical performance of the models. How-
ever, these studies only consider up to the fourth moment. High-order moments in
excess of the fourth moment have not been considered in terms of how theyinfluence
exchange rate behavior.1
There are several economic channels/mechanisms through which higher mo-
ments can impact exchange rate behavior. The firstchannel of effect is “liquidity spi-
rals” that results from the theoretical model of Brunnermeier and Pedersen (2009).
The basic idea of their model is that invested securities contain positive average
returns and a negative skewness. They explain the source of this positive returns
and negative skewness. Positive returns owe to the premium resulting from specula-
tors’ provision of liquidity while negative skewness is because investors make heavy
losses and relatively mild gains from negative shocks (such as financial constraints)
and positive shocks (such as liquidity), respectively. In other words, the impact of
shocks is asymmetric, skewed heavily in favorof negative shocks. More specifically,
their work implies that funding constraints determine market liquidity. When there
are funding shocks, market liquidity declines leading to higher margins, which exerts
1The motivation for this is rooted in the fact that these high-order moments contain different types of
risk-related information. The second-order moment (variance), for instance, represents volatility,the third-
order moment (skewness) accounts for the probability of positiveand negative values, and the fourth-order
moment (kurtosis) is indicative of the relative importance of tails versus shoulders in causing dispersion.
High kurtosis is linked to heavy tails, and low kurtosis corresponds to heavy shoulders. In other words,
the fourth moment or volatility of variance indicates how uncertain the uncertainty is. The fifth moment
(hyper-skewness) indicates the relative importance of tails versus the center in causing skewness and
corresponds to a heavy tail. There is little movement in the mode when the hyper-skewness is high and
a greater change in the shoulders when hyper-skewness is low.In other words, hyper-skewness measures
the asymmetric sensitivity of the kurtosis. For instance, in the case of the stock market, the fifth moment
can explain a symmetric or asymmetric distribution of fluctuations in assets with high/lowvolatilities. The
sixth moment, hyper-kurtosis measures both the peakedness and tails relative to the normal distribution.
See also Kostakis, Muhammad and Siganos (2012).

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