  This paper investigates change point detection in state space models, in
which the pre-change distribution $f^{\theta_0}$ is given, while the poster
distribution $f^{\theta}$ after change is unknown. The problem is to raise an
alarm as soon as possible after the distribution changes from $f^{\theta_0}$ to
$f^{\theta}$, under a restriction on the false alarms. We investigate
theoretical properties of a weighted Shiryayev-Roberts-Pollak (SRP) change
point detection rule in state space models. By making use of a Markov chain
representation for the likelihood function, exponential embedding of the
induced Markovian transition operator, nonlinear Markov renewal theory, and
sequential hypothesis testing theory for Markov random walks, we show that the
weighted SRP procedure is second-order asymptotically optimal. To this end, we
derive an asymptotic approximation for the expected stopping time of such a
stopping scheme when the change time $\omega = 1$. To illustrate our method we
apply the results to two types of state space models: general state Markov
chains and linear state space models.
