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This book is an introductory exposition of different topics that
emerged in the literature as unifying themes between two fields of
econometrics of time series, namely nonlinearity and
nonstationarity. Papers on these topics have exploded over the last
two decades, but they are rarely ex amined together. There is,
undoubtedly, a variety of arguments that justify such a separation.
But there are also good reasons that motivate their combination.
People who are reluctant to a combined analysis might argue that
nonlinearity and nonstationarity enhance non-trivial problems, so
their combination does not stimulate interest in regard to
plausibly increased difficulties. This argument can, however, be
balanced by other ones of an economic nature. A predominant idea,
today, is that a nonstationary series exhibits persistent
deviations from its long-run components (either deterministic or
stochastic trends). These persistent deviations are modelized in
various ways: unit root models, fractionally integrated processes,
models with shifts in the time trend, etc. However, there are many
other behaviors inherent to nonstationary processes, that are not
reflected in linear models. For instance, economic variables with
mixture distributions, or processes that are state-dependent,
undergo episodes of changing dynamics. In models with multiple
long-run equi libria, the moving from an equilibrium to another
sometimes implies hys teresis. Also, it is known that certain
shocks can change the economic fundamentals, thereby reducing the
possibility that an initial position is re-established after a
shock (irreversibility)."
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