间歇性预测的局限性
Limitations on intermittent forecasting
摘要：
Bailey证明了平稳和遍历时间序列的一般逐点预测有一个负解。然而，众所周知，对于马尔可夫链，这个问题是可以解决的。Morvai表明，有一个停时序列$\{λ_n\}$，使$P(X_{λ_n+1}=1|X_0,...,X_{λ_n}) $可以估计样本$(X_0,...,X_{λ_n})$，使之间的差异条件概率和估计消失沿这些停止时间为所有平稳和遍历的二值时间序列。我们将表明，这是不可能的，以估计上述条件概率沿停时序列的所有平稳和遍历的二值时间序列在逐点意义上，如果时间序列原来是一个马尔可夫链，预测将预测最终为所有$n$。
英文摘要：
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 $\{λ_n\}$ such that $P(X_{λ_n+1}=1|X_0,...,X_{λ_n}) $ can be estimated from samples $(X_0,...,X_{λ_n})$ 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 $n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
