### abstract ###
In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy
We make mild compactness assumptions but no stochastic assumptions about the environment
In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered strategies only means that they do not depend explicitly on time; we argue that it is natural to consider only stationary strategies even for highly non-stationary environments
### introduction ###
This paper belongs to the area of learning theory that has been variously referred to as prediction with expert advice, competitive on-line prediction, prediction of individual sequences, and universal on-line learning; see  CITATION  for a review
There are many proof techniques known in this field; this paper is based on Kalnishkan and Vyugin's Weak Aggregating Algorithm  CITATION , but it is possible that some of the numerous other techniques could be used instead
In Section  we give the main definitions and state our main results, Theorems --; their proofs are given in Sections --
In Section  we informally discuss the notion of stationarity, and Section  concludes
