On uniform asymptotic normality of sequential estimates of the parameters in unstable autoregression V. V. Konev, B. N. Nazarenko
Material type:
ArticleOther title: О равномерной асимптотической нормальности последовательных оценок параметров в неустойчивой авторегрессии [Parallel title]Subject(s): последовательная оценка | авторегрессия | неасимптотические выводы | равномерная асимптотическая нормальостьGenre/Form: статьи в сборниках Online resources: Click here to access online
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Международная научная конференция "Робастная статистика и финансовая математика - 2018" 09-11 июля 2018 г. : сборник статей С. 38-47Abstract: The paper proposes new sequential least squares estimates
for the parameters in autoregressive processes of order 𝑝. The
construction of the procedure, in contrast to those known in the
literature, makes use of only one least squares estimate (LSE)
for the vector of unknown parameter for any order 𝑝. The main
point is that the sample Fisher information matrix in the LSE
is properly modified by introducing special stopping rules for
collecting the data. It is shown that in the i.i.d. case with unspecified
error distributions, the new estimates have the property
of uniform asymptotic normality for unstable autoregressive
processes under some general condition on the parameters. The
cases of AR(1), AR(2) and AR(3) processes are considered in
detail. The results of numerical simulations are given.
Библиогр.: 15 назв.
The paper proposes new sequential least squares estimates
for the parameters in autoregressive processes of order 𝑝. The
construction of the procedure, in contrast to those known in the
literature, makes use of only one least squares estimate (LSE)
for the vector of unknown parameter for any order 𝑝. The main
point is that the sample Fisher information matrix in the LSE
is properly modified by introducing special stopping rules for
collecting the data. It is shown that in the i.i.d. case with unspecified
error distributions, the new estimates have the property
of uniform asymptotic normality for unstable autoregressive
processes under some general condition on the parameters. The
cases of AR(1), AR(2) and AR(3) processes are considered in
detail. The results of numerical simulations are given.
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