Limitations on intermittent forecasting

Details Limitations on intermittent forecasting Limitations on intermittent forecasting

2007-10-19

arxiv.org/abs/0710.3773v1

Statist. Probab. Lett. 72 (2005), no. 4, 285--290

Mathematics

Probability

Scientific paper

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 $n$.

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