Some statistical properties of a vector autoregressive
process with Markov-switching coefficients are considered.
Sufficient conditions for this nonlinear process to be
covariance stationary are given. The second moments of
the process are derived under the conditions. The autocovariance
matrix decays at exponential rate, permitting the application
of the law of large numbers. Under the stationarity conditions,
although sharing the “mean-reverting” property
with conventional linear stationary processes, the process
offers richer short-run dynamics such as conditional heteroskedasticity,
asymmetric responses, and occasional nonstationary behavior.