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Estimation of General Stationary Processes by Variable Length Markov Chains
Author(s) -
Ferrari Fiorenzo,
Wyner Abraham
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00342
Subject(s) - mathematics , markov chain , markov process , state space , categorical variable , context (archaeology) , variable (mathematics) , probability distribution , sieve (category theory) , discrete mathematics , statistics , mathematical analysis , paleontology , biology
. We develop new results about a sieve methodology for the estimation of minimal state spaces and probability laws in the class of stationary processes defined on finite categorical spaces. Using a sieve approximation with variable length Markov chains of increasing order, we show that an adapted version of the Context algorithm yields asymptotically correct estimates for the minimal state space and for the underlying probability distribution. As a side product, the method of sieves yields a nice graphical tree representation for the potentially infinite dimensional minimal state space of the data generating process, which is very useful for exploration of the memory.