  In this paper, we investigate the problem of system identification for
autonomous Markov jump linear systems (MJS) with complete state observations.
We propose switched least squares method for identification of MJS, show that
this method is strongly consistent, and derive data-dependent and
data-independent rates of convergence. In particular, our data-independent rate
of convergence shows that, almost surely, the system identification error is
$\mathcal{O}\big(\sqrt{\log(T)/T} \big)$ where $T$ is the time horizon. These
results show that switched least squares method for MJS has the same rate of
convergence as least squares method for autonomous linear systems. We derive
our results by imposing a general stability assumption on the model called
stability in the average sense. We show that stability in the average sense is
a weaker form of stability compared to the stability assumptions commonly
imposed in the literature. We present numerical examples to illustrate the
performance of the proposed method.
