Parameter estimation for moving averages with positive innovations. (English) Zbl 0881.62093

Summary: This paper continues the study of time series models generated by nonnegative innovations which was begun by P. Feigin and S. Resnick [Commun. Stat. Stochastic Models 8, No. 3, 479-498 (1992; Zbl 0762.62024); Stochastic Processes Appl. 51, No. 1, 135-165 (1994; Zbl 0819.62070)]. We concentrate on moving average processes. Estimators for moving average coefficients are proposed and consistency and asymptotic distributions established for the case of an order-one moving average assuming either the right or the left tail of the innovation distribution is regularly varying. The rate of convergence can be superior to that of the Yule-Walker or maximum likelihood estimators.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60B10 Convergence of probability measures
60F05 Central limit and other weak theorems
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62E20 Asymptotic distribution theory in statistics
62F10 Point estimation
Full Text: DOI


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