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QMLE of the
General Periodic
GARCH Models
Ahmed Ghezal (1) and Imane Zemmouri
(2)
(1) Department
of Mathematics
and Computer
Sciences,
University
Center of
Mila, Algeria
Email address:
a.ghezal@centre-univ-mila.dz
(2) Department of
Mathematics,
University of
Annaba, Elhadjar 23,
Annaba,
Algeria
Email address:
imanezemmouri25@gmail.com
Doi :
https://doi.org/10.47013/17.1.3
Cited by :
Jordan J. Math &
Stat.,
17 (1) (2024),
45 - 64
PDF
Received on:
Jan. 30,
2023;
Accepted
on: Jun. 5,
2023
Abstract. In this
article, we
study the
necessary and
sufficient
conditions that
guarantee the
strict
stationarity of
general periodic
generalized
autoregressive
conditional
heteroskedasticity
models (in the
periodic sense).
We also obtain
conditions for
the existence of
finite
higher-order
moments under
general and
tractable
assumptions. We
propose the
quasi-maximum
likelihood
estimation of
general periodic
generalized
autoregressive
conditional
heteroskedasticity
parameters and
derive their
asymptotic
properties. We
demonstrate the
strong
consistency and
asymptotic
normality of the
quasi-maximum
likelihood
estimation in
special cases.
Keywords: GARCH model and
its extension,
strict
stationarity,
QMLE, ergodicity,
strong
consistency,
asymptotic
normality.
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