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The study of stationary processes is an important §topic both in the probability and statistics §literatures. This monograph continues the §investigation along the classical lines, but with a §modern viewpoint. For example, to study the behavior §of the partial sums, it features the interplay §between ergodic theory and probability from an §operator-theoretical point of view. As a §consequence, the results tend to be much more §refined, and nearly optimal on many occasions. With §the tools developed to understand the probabilistic §behavior of the processes, one statistical §application is considered in the context of global §warming. The goal is to nonparametrically estimate §the trend of a time series under monotonicity §assumptions. Some interesting features in time §series analysis are carefully explored.
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