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Asymptotic laws of successive least squares estimates for seasonal arima models and application
Author(s) -
Truongvan B.,
Varachaud P.
Publication year - 2002
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 - 10.1111/1467-9892.00287
Subject(s) - autoregressive integrated moving average , mathematics , autoregressive–moving average model , moving average , series (stratigraphy) , least squares function approximation , stochastic modelling , econometrics , statistics , time series , autoregressive model , paleontology , estimator , biology
. In view of detecting the stochastic non‐stationarity in time series, successive Yule–Walker estimates are considered for general seasonal ARIMA models and their asymptotic laws are obtained. This extends results known on least squares estimates for stable–unstable ARMA. Furthermore, these asymptotic laws are then compared with analogous results obtained under some additive seasonal model that corresponds to the case of deterministic seasonal behaviour. These results, combined with a simulation study, reveal that successive autoregressions provide a very useful tool both for identifying seasonal ARIMA processes and for distinguishing between stochastic and deterministic seasonal behaviours.