Preamble by Nobel Prize winner Robert F. Engle
The Handbook of Financial Time Series, edited by Andersen, Davis, Kreiss
and Mikosch, is an impressive collection of survey articles by many of the
leading contributors to the field. These articles are mostly very clearly written
and present a sweep of the literature in a coherent pedagogical manner.
The level of most of the contributions is mathematically sophisticated, and
I imagine many of these chapters will find their way onto graduate reading
lists in courses in financial economics and financial econometrics. In reading
through these papers, I found many new insights and presentations even in
areas that I know well.
The book is divided into five broad sections: GARCH-Modeling, Stochastic
Volatility Modeling, Continuous Time Processes, Cointegration and Unit
Roots, and Special Topics. These correspond generally to classes of stochastic
processes that are applied in various finance contexts. However, there are
other themes that cut across these classes. There are several papers that carefully
articulate the probabilistic structure of these classes, while others are
more focused on estimation. Still others derive properties of extremes for each
class of processes, and evaluate persistence and the extent of long memory.
Papers in many cases examine the stability of the process with tools to check
for breaks and jumps. Finally there are applications to options, term structure,
credit derivatives, risk management, microstructure models and other
forecasting settings.
The GARCH family of models is nicely introduced by Teräsvirta and then
the mathematical underpinning is elegantly and readably presented by Lindner
with theorems on stationarity, ergodicity and tail behavior. In the same
vein, Giraitis, Leipus and Surgailis examine the long memory properties of
infinite order ARCH models with memory decay slower than GARCH, and
Davis and Mikosch derive tail properties of GARCH models showing that
they satisfy a power law and are in the maximum domain of attraction of
the Fréchet distribution. The multivariate GARCH family is well surveyed
by Silvennoinen and Teräsvirta. Linton and Čížek and Spokoiny, respectively,
specify models which are non- or semi-parametric or which are only constant
over intervals of homogeneity.