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Estimation for non-negative time series with heavy-tail innovations. (English) Zbl 1274.62575

Summary: For moving average processes \(x_t=\sum_{i=0}^{\infty} c_iZ_{t-i}\) where the coefficients are non-negative and the innovations are positive random variables with a regularly varying tail at infinity, we provide estimates for the coefficients based on the ratio of two sample values chosen with respect to an extreme value criteria. We then apply this result to obtain estimates for the parameters of non-negative ARMA models. Weak convergence results for the joint distribution of our estimates are established and a simulation study is provided to examine the small sample size behaviour of these estimates.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G32 Statistics of extreme values; tail inference
60F05 Central limit and other weak theorems
65C60 Computational problems in statistics (MSC2010)
62E20 Asymptotic distribution theory in statistics
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