  We apply the Zipf power law to financial time series of WIG20 index daily
changes (open-close). Thanks to the mapping of time series signal into the
sequence of 2k+1 'spin-like' states, where k=0, 1/2, 1, 3/2, ..., we are able
to describe any time series increments, with almost arbitrary accuracy, as the
one of such 'spin-like' states. This procedure leads in the simplest
non-trivial case (k = 1/2) to the binary data projection. More sophisticated
projections are also possible and mentioned in the article. The introduced
formalism allows then to use Zipf power law to describe the intrinsic structure
of time series. The fast algorithm for this implementation was constructed by
us within Matlab^{TM} software. The method, called Zipf strategy, is then
applied in the simplest case k = 1/2 to WIG 20 open and close daily data to
make short-term predictions for forthcoming index changes. The results of
forecast effectiveness are presented with respect to different time window
sizes and partition divisions (word lengths in Zipf language). Finally, the
various investment strategies improving ROI (return of investment) for WIG20
futures are proposed. We show that the Zipf strategy is the appropriate and
very effective tool to make short-term predictions and therefore, to evaluate
short-term investments on the basis of historical stock index data. Our
findings support also the existence of long memory in financial data, exceeding
the known in literature 3 days span limit.
