ﻻ يوجد ملخص باللغة العربية
Bailey showed that the general pointwise forecasting for stationary and ergodic time series has a negative solution. However, it is known that for Markov chains the problem can be solved. Morvai showed that there is a stopping time sequence ${lambda_n}$ such that $P(X_{lambda_n+1}=1|X_0,...,X_{lambda_n}) $ can be estimated from samples $(X_0,...,X_{lambda_n})$ such that the difference between the conditional probability and the estimate vanishes along these stoppping times for all stationary and ergodic binary time series. We will show it is not possible to estimate the above conditional probability along a stopping time sequence for all stationary and ergodic binary time series in a pointwise sense such that if the time series turns out to be a Markov chain, the predictor will predict eventually for all $n$.
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
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_
Let ${(X_i,Y_i)}$ be a stationary ergodic time series with $(X,Y)$ values in the product space $R^dbigotimes R .$ This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance)
Trace reconstruction considers the task of recovering an unknown string $x in {0,1}^n$ given a number of independent traces, i.e., subsequences of $x$ obtained by randomly and independently deleting every symbol of $x$ with some probability $p$. The