TY - JOUR
T1 - Forecasting for Stationary Binary Time Series
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
PY - 2003/10
Y1 - 2003/10
N2 - The forecasting problem for a stationary and ergodic binary time series {Xn}n=0∞ is to estimate the probability that Xn+1 = 1 based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. It is known that this is not possible if one estimates at all values of n. We present a simple procedure which will attempt to make such a prediction infinitely often at carefully selected stopping times chosen by the algorithm. We show that the proposed procedure is consistent under certain conditions, and we estimate the growth rate of the stopping times.
AB - The forecasting problem for a stationary and ergodic binary time series {Xn}n=0∞ is to estimate the probability that Xn+1 = 1 based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. It is known that this is not possible if one estimates at all values of n. We present a simple procedure which will attempt to make such a prediction infinitely often at carefully selected stopping times chosen by the algorithm. We show that the proposed procedure is consistent under certain conditions, and we estimate the growth rate of the stopping times.
KW - Nonparametric estimation
KW - Stationary processes
UR - http://www.scopus.com/inward/record.url?scp=0142250480&partnerID=8YFLogxK
U2 - 10.1023/A:1025862222287
DO - 10.1023/A:1025862222287
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AN - SCOPUS:0142250480
SN - 0167-8019
VL - 79
SP - 25
EP - 34
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
IS - 1-2
ER -