TY - JOUR
T1 - Forward estimation for ergodic time series
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
PY - 2005/9
Y1 - 2005/9
N2 - The forward estimation problem for stationary and ergodic time series {Xn}n=0∞ taking values from a finite alphabet X is to estimate the probability that Xn+1 = x based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. We present a simple procedure gn which is evaluated on the data segment (X0,...,Xn) and for which, error (n) = gn(x) - P (Xn+1= x X0,..., Xn) → 0 almost surely for a subclass of all stationary and ergodic time series, while for the full class the Cesaro average of the error tends to zero almost surely and moreover, the error tends to zero in probability.
AB - The forward estimation problem for stationary and ergodic time series {Xn}n=0∞ taking values from a finite alphabet X is to estimate the probability that Xn+1 = x based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. We present a simple procedure gn which is evaluated on the data segment (X0,...,Xn) and for which, error (n) = gn(x) - P (Xn+1= x X0,..., Xn) → 0 almost surely for a subclass of all stationary and ergodic time series, while for the full class the Cesaro average of the error tends to zero almost surely and moreover, the error tends to zero in probability.
KW - Nonparametric estimation
KW - Stationary processes
UR - http://www.scopus.com/inward/record.url?scp=23944515510&partnerID=8YFLogxK
U2 - 10.1016/j.anihpb.2004.07.002
DO - 10.1016/j.anihpb.2004.07.002
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AN - SCOPUS:23944515510
SN - 0246-0203
VL - 41
SP - 859
EP - 870
JO - Annales de l'institut Henri Poincare (B) Probability and Statistics
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
IS - 5
ER -