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Wu, Wei Biao

An asymptotic theory for sample covariances of Bernoulli shifts. (English) Zbl 1157.60016

Stochastic Processes Appl. 119, No. 2, 453-467 (2009).
Summary: Covariances play a fundamental role in the theory of stationary processes and they can naturally be estimated by sample covariances. There is a well-developed asymptotic theory for sample covariances of linear processes. For nonlinear processes, however, many important problems on their asymptotic behaviors are still unanswered. The paper presents a systematic asymptotic theory for sample covariances of nonlinear time series. Our results are applied to the test of correlations.

Cited in 1 Review
Cited in 10 Documents

MSC:

60F05 Central limit and other weak theorems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G10 Stationary stochastic processes

Keywords:

asymptotic normality; covariance; dependence; linear process; martingale; moderate deviation; nonlinear time series; stationary process; test of correlation
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References:

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