On impossibility of sequential algorithmic forecasting

The problem of prediction future event given an individual sequence of past events is considered. Predictions are given in form of real numbers pn which are computed by some algorithm using initial fragments 1, . . . , n-1 of an individual binary sequence = 1, 2, . . . and can be interpreted as probabilities of the event n = 1 given this fragment. According to Dawid's prequential framework we consider partial forecasting algorithms which are defined on all initial fragments of and can be undefined outside the given sequence of outcomes. We show that even for this large class of forecasting algorithms combining outcomes of coin-tossing and transducer algorithm it is possible to efficiently generate with probability close to one sequences for which any partial forecasting algorithm is failed by the method of verifying called calibration.

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Vladimir V. V'yugin
• Keywords: Algorithm, DAGSTUHL 2006, DAGSTUHL 2007, Initial Fragments, Partial Forecasting Algorithm