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Limitations on intermittent forecasting

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  • Morvai, Gusztáv
  • Weiss, Benjamin
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    Abstract

    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=1X0,...,X[lambda]n) can be estimated from samples (X0,...,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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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 72 (2005)
    Issue (Month): 4 (May)
    Pages: 285-290

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    Handle: RePEc:eee:stapro:v:72:y:2005:i:4:p:285-290

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    Related research

    Keywords: Nonparametric estimation Prediction theory Stationary and ergodic processes Finite-order Markov chains;

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    Cited by:
    1. Gusztav Morvav & Benjamin Weiss, 2007. "On Sequential Estimation and Prediction for Discrete Time Series," Discussion Paper Series dp464, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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