Parameter estimation for moving averages with positive innovations
Open Access
- 1 November 1996
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 6 (4) , 1157-1190
- https://doi.org/10.1214/aoap/1035463327
Abstract
This paper continues the study of time series models generated by nonnegative innovations which was begun by Feigin and Resnick. 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.Keywords
This publication has 12 references indexed in Scilit:
- Limit theory for bilinear processes with heavy-tailed noiseThe Annals of Applied Probability, 1996
- Semidefinite ProgrammingSIAM Review, 1996
- Second-order regular variation and rates of convergence in extreme-value theoryThe Annals of Probability, 1996
- Consistency of Hill's estimator for dependent dataJournal of Applied Probability, 1995
- Testing for independence in heavy tailed and positive innovation time seriesCommunications in Statistics. Stochastic Models, 1995
- Limit distributions for linear programming time series estimatorsStochastic Processes and their Applications, 1994
- Estimation for autoregressive processes with positive innovationsCommunications in Statistics. Stochastic Models, 1992
- Extremes of moving averages of random variables from the domain of attraction of the double exponential distributionStochastic Processes and their Applications, 1988
- Limit Theory for the Sample Covariance and Correlation Functions of Moving AveragesThe Annals of Statistics, 1986
- On Some Limit Theorems Similar to the Arc-Sin LawTheory of Probability and Its Applications, 1965