Citation:
Weiss, Gusztav Morvai, and Benjamin, Nathans. “Forecasting For Stationary Times Series”. Discussion Papers 2002. Web.
Abstract:
The forecasting problem for a stationary and ergodic binary time series Xn 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.