The stability of time-varying autoregressive (TVAR) models is an important
issue in many applications such as time-varying spectral estimation, EEG si
mulation and analysis, and time-varying linear prediction coding (TVLPC). F
or stationary AR models there are methods that guarantee stability, but the
for nonadaptive time-varying approaches there are no such methods. On the
other hand, in some situations, such as in EEG analysis, the models that te
mporarily exhibit roots with almost unit moduli are difficult to use. Thus
we may need a tighter stability condition such as stability with margin 1 -
rho. In this paper we propose a method for the estimation of TVAR models t
hat guarantees stability with margin 1 - rho, that is, the moduli of the ro
ots of the time-varying characteristic polynomial are less than or equal to
some arbitrary positive number rho for every time instant. The model class
is the Subba Rao-Liporace class, in which the time-varying coefficients ar
e constrained to a subspace of the coefficient time evolutions. The method
is based on sequential linearization of the associated nonlinear constraint
s and the subsequent use of a Gauss-Newton-type algorithm. The method is al
so applied to a simulated autoregressive process.