This book integrates the fundamentals of asymptotic theory of
statistical inference for time series under nonstandard settings, e.g.,
infinite variance processes, not only from the point of view of
efficiency but also from that of robustness and optimality by minimizing
prediction error. This is the first book to consider the generalized
empirical likelihood applied to time series models in frequency domain
and also the estimation motivated by minimizing quantile prediction
error without assumption of true model. It provides the reader with a
new horizon for understanding the prediction problem that occurs in time
series modeling and a contemporary approach of hypothesis testing by the
generalized empirical likelihood method. Nonparametric aspects of the
methods proposed in this book also satisfactorily address economic and
financial problems without imposing redundantly strong restrictions on
the model, which has been true until now. Dealing with infinite variance
processes makes analysis of economic and financial data more accurate
under the existing results from the demonstrative research. The scope of
applications, however, is expected to apply to much broader academic
fields. The methods are also sufficiently flexible in that they
represent an advanced and unified development of prediction form
including multiple-point extrapolation, interpolation, and other
incomplete past forecastings. Consequently, they lead readers to a good
combination of efficient and robust estimate and test, and discriminate
pivotal quantities contained in realistic time series models.