Maximum spacing estimation for dependent variables

For independent and identically distributed univariate observations a new estimation method, the maximum spacing (MSP) method, was defined in Ranneby (Scand. J. Statist. 11 (1984)) and independently by Cheng and Amin (J. Roy. Statist. Soc. B 45 (1983)). The idea behind the method, as described by Ranneby (1984), is to approximate the Kullback-Leibler information so that each contribution is bounded from above. In the present paper, the MSP method is extended to Markov and semi-Markov chains with continuous time. Consistency of the MSP estimate is proved. Furthermore, the extension to m-dependent stationary processes is discussed.