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The forecasting problem for a stationary and ergodic binary time series ${X_n}_{n=0}^{infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0le ile n$ without prior knowledge of the distribution of the process ${X_n}$. 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.
The forward prediction problem for a binary time series ${X_n}_{n=0}^{infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0le ile n$ without prior knowledge of the distribution of the process ${X_n}$. It is known
The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability of the nex
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but they all dem
Let ${X_n}_{n=0}^{infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0le ile n$ in a strongly consistent way. Bailey and Ryabko
This study concerns problems of time-series forecasting under the weakest of assumptions. Related results are surveyed and are points of departure for the developments here, some of which are new and others are new derivations of previous findings. T