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BOOTSTRAPPING STATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODELS
Author(s) -
Kreiss JensPeter,
Franke Jürgen
Publication year - 1992
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.1467-9892.1992.tb00109.x
Subject(s) - mathematics , estimator , autoregressive–moving average model , autoregressive model , bootstrapping (finance) , asymptotic analysis , asymptotic distribution , star model , series (stratigraphy) , moving average , autoregressive integrated moving average , statistics , econometrics , time series , paleontology , biology
. In this paper we develop an asymptotic theory for application of the bootstrap to stationary stochastic processes of autoregressive moving‐average (ARMA) type, with known order ( p, q ). We give a proof of the asymptotic validity of the bootstrap proposal applied to M estimators for the unknown parameter vector of the process. For this purpose we derive an asymptotic expansion for M estimators in ARMA models and construct an estimate for the unknown distribution function of the residuals which in principle are not observable. A small simulation study is also included.