Terence C. Mills and Kerry Patterson xxvMDH, whereas others have found little evidence against it. In this context, applying
a range of tests, Escanciano and Lobato find general support for the MDH.
Chapter 19 by Dotsiset al. was concerned with models of stochastic volatility,
primarily using the variance as a measure of volatility. Another measure of volatil-
ity is provided by the range of a price; for example, the trading day range of an
asset price. In turn, the range can be related to the interval between consecutive
trades, known as the duration. Duration is a concept that is familiar from counting
processes, such as the Poisson framework for modeling arrivals (for example, at a
supermarket checkout or an airport departure gate).
Chapter 21 by Ruey Tsay provides an introduction to modeling duration that
is illustrated with a number of financial examples. That duration can carry infor-
mation about market behavior is evident not only from stock markets, where a
cluster of short durations indicates active trading relating to, for example, informa-
tion arrival, but from many other markets; for example, durations in the housing
market and their relation to banking failure. The interest in durations modeling
owes much to Engle and Russell (1998), who introduced the autoregressive con-
ditional duration (ACD) model for irregularly spaced transactions data. Just as the
ARCH/GARCH family of models was introduced to capture volatility clusters, the
ACD model captures short-duration clusters indicating the persistence of periods
of active trading, perhaps uncovering and evaluating information arrivals. To see
how an ACD model works, let theith duration be denotedxi=ti−ti− 1 , where
tiis the time of theith event, and modelxiasxi =ψiεi, where {εi} is an i.i.d
sequence andβ(L)ψi=α 0 +α(L)xi, whereα(L)andβ(L)are lag polynomials; this is
the familiar GARCH form, but in this context it is known as the exponential ACD
or EACD. To accommodate the criticism that the hazard function of duration is
not constant over time, unlike the assumption implicit in the EACD model, alter-
native innovation distributions have been introduced, specifically the Weibull and
the Gamma, leading to the Weibull ACD (WACD) and the Gamma ACD (GACD).
The chapter includes some motivating examples. Evidence of duration clusters is
shown in Figures 21.1, 21.4 and 21.7a for IBM stock, Apple stock and General
Motors stock, respectively. The development and application of duration models
can then exploit the development of other forms of time series models, such as
(nonlinear) threshold autoregressive (TAR) models. ACD models have also been
developed to incorporate explanatory variables; an example is provided, which
shows that the change to decimal “tick” sizes in the US stock markets reduced the
price volatility of Apple stock.
The determination of exchange rates has long been an interest to econo-
metricians and, as a result, there is an extensive literature that includes two
constituencies; on the one hand, there have been contributions from economists
who have employed econometric techniques and, on the other, to risk a simple
bifurcation, the modeling of exchange rates has become an area to test out advances
in nonlinear econometrics. Chapter 22, by Efthymios Pavlidis, Ivan Paya and David
Peel, provides an evaluative overview of this very substantial area. As they note,
the combination of econometric developments, the availability of high-quality
and high-frequency data, and the move to floating exchange rates in 1973, has led