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Rate of convergence in the central limit theorem for parameter estimation in a causal, invertible ARMA( p, q ) model
Author(s) -
Roy Sugata Sen,
Bhattacharya Sankha
Publication year - 2013
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2012.00817.x
Subject(s) - mathematics , estimator , autoregressive model , invertible matrix , central limit theorem , autoregressive–moving average model , rate of convergence , convergence (economics) , setar , asymptotic distribution , estimation theory , normality , statistics , star model , autoregressive integrated moving average , pure mathematics , time series , channel (broadcasting) , economic growth , electrical engineering , economics , engineering
In this study we consider the estimators of the parameters of a stable ARMA( p, q ) process. The autoregressive parameters are estimated by the instrumental variable technique while the moving average parameters are estimated using a derived autoregressive process. The estimators are shown to be asymptotically normal and their rate of convergence to normality is derived.