In order to carry out statistical inference for time series it is necessary to be able to derive the distributions of various statistics used for the estimation of parameters from the data. For finite n the exact distribution of such a statistic f n (X 1,..., X n) is usually (even for Gaussian processes) prohibitively complicated. In such cases, we can still however base the inference on large-sample approximations to the distribution of the statistic in question. The mathematical tools for deriving such approximations are developed in this chapter. A comprehensive treatment of asymptotic theory is given in the book of Serfling (1980). Chapter 5 of the book by Billingsley (1986) is also strongly recommended.
KeywordsRandom Vector Central Limit Theorem Asymptotic Theory Asymptotic Normality Stationary Sequence
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