Estimation of General Stationary Processes by Variable Length Markov Chains
Fiorenzo Ferrari
October 1999
Abstract
We develop new results about a sieve methodology for estimation of minimal
state spaces and probability laws in the class of stationary categorical
processes. We first consider finite categorical spaces. By using a sieve
approximation with variable length Markov chains of increasing order, we
carry out asymptotically correct estimates by an adapted version of the
Context Algorithm. It thereby yields a nice graphical
tree representation for the potentially infinite dimensional minimal state
space of the data generating process. This procedure is also consistent for
increasing size countable categorical spaces. Finally, we show similar
results for real-valued general stationary processes by using a quantization
procedure based on the distribution function.
Download:
Compressed Postscript (115 Kb)
PDF (220 Kb)
Go back to the
Research Reports
from
Seminar für Statistik.