The Beveridge–Nelson decomposition of Markov-switching processes

This paper modifies the well-known Beveridge–Nelson [Beveridge, S., Nelson, C.R., 1981. A new approach to the decomposition of economic time erie into permanent and transitory component with particular attention to measurement of the ‘busines cycle’, Journal of Monetary Economic 7, 151–174] decomposition to an N-state Markov-switching autoregressive (AR) model proposed by Hamilton [Hamilton, J.D., 1989. A new approach to the economic analy is of non-tationary time erie and the busine cycle, Econometrica 57, 357–384], and shows that this modified Beveridge–Nelson decomposition can be carried out without the necessity of truncating an infinite sum.