| Abstract: | We propose a general class of Markov-switching-ARFIMA (MS-ARFIMA) processes in order to combine strands of long memory and Markov-switching literature. Although the coverage of this class of models is broad, we show that these models can be easily estimated with the Durbin–Levinson–Viterbi algorithm proposed. This algorithm combines the Durbin–Levinson and Viterbi procedures. A Monte Carlo experiment reveals that the finite sample performance of the proposed algorithm for a simple mixture model of Markov-switching mean and ARFIMA(1, d, 1) process is satisfactory. We apply the MS-ARFIMA models to the US real interest rates and the Nile river level data, respectively. The results are all highly consistent with the conjectures made or empirical results found in the literature. Particularly, we confirm the conjecture in Beran and Terrin J. Beran and N. Terrin, Testing for a change of the long-memory parameter. Biometrika 83 (1996), pp. 627–638.] that the observations 1 to about 100 of the Nile river data seem to be more independent than the subsequent observations, and the value of differencing parameter is lower for the first 100 observations than for the subsequent data. |
