A DOUBLY MARKOV SWITCHING AR MODEL: SOME PROBABILISTIC PROPERTIES AND STRONG CONSISTENCY

In this work, we consider doubly Markov switching AR models, where analytic tractability and flexibility are quite simply a competitive advantage, which becomes an attractive tool for modeling economic financial time series. these the parameters allowed to depend on unobservable time-homogeneous chain with finite state space. So, discuss some basic probabilistic properties of $$D-MSAR\left( p,q\right)$$ model such as conditions ensuring existence strict, second-order stationarity solution, causal ergodic solution its moments properties. The quasi-maximum likelihood estimator in is shown be strongly consistent.