Most financial and investment decisions are based on considerations of
possible future changes and require forecasts on the evolution of the
financial world. Time series and processes are the natural tools for
describing the dynamic behavior of financial data, leading to the
required forecasts. This book presents a survey of the empirical
properties of financial time series, their descriptions by means of
mathematical processes, and some implications for important financial
applications used in many areas like risk evaluation, option pricing or
portfolio construction. The statistical tools used to extract
information from raw data are introduced. Extensive multiscale empirical
statistics provide a solid benchmark of stylized facts
(heteroskedasticity, long memory, fat-tails, leverage...), in order to
assess various mathematical structures that can capture the observed
regularities. The author introduces a broad range of processes and
evaluates them systematically against the benchmark, summarizing the
successes and limitations of these models from an empirical point of
view. The outcome is that only multiscale ARCH processes with long
memory, discrete multiplicative structures and non-normal innovations
are able to capture correctly the empirical properties. In particular,
only a discrete time series framework allows to capture all the stylized
facts in a process, whereas the stochastic calculus used in the
continuum limit is too constraining. The present volume offers various
applications and extensions for this class of processes including
high-frequency volatility estimators, market risk evaluation, covariance
estimation and multivariate extensions of the processes. The book
discusses many practical implications and is addressed to practitioners
and quants in the financial industry, as well as to academics, including
graduate (Master or PhD level) students. The prerequisites are basic
statistics and some elementary financial mathematics.
