Time Series Alternating Renewal Process Sojourn Time Laws Persistence
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 27, No 2, (2001), 115p-130p
We study a class of models used with success in the modelling of
climatological sequences. These models are based on the notion of renewal.
At first, we examine the probabilistic aspects of these models to afterwards
study the estimation of their parameters and their asymptotical properties,
in particular the consistence and the normality. We will discuss for applications,
two particular classes of alternating renewal processes at discrete
time. The first class is defined by laws of sojourn time that are translated
negative binomial laws and the second class, suggested by Green is deduced
from alternating renewal process in continuous time with sojourn time laws
which are exponential laws with parameters α^0 and α^1 respectively.