Time Series Forecasting by Imitation of Preceding Patterns
Barbara Motnikar, Drago Čepar, Peter Žunko, Marijan Ribarič, Boštjan Vovk · 1992
We propose a new approach to time series forecasting based on the imitation of the preceding local shapes of a given time series z t , t = 1,...,n. We define a pattern $$ \vec r \equiv \left( {{z_{b\left( r \right)}},{z_{b\left( r \right)}} + 1,...,{z_{b\left( r \right) + s - 1}}} \right) $$ as a sequence of s observations starting at index b(r), where s is the pattern size and we compare various patterns by some similarity measure chosen in advance. In the belief that the similarity between two patterns can be extended to their subsequent observations, we try to find the pattern r⃗ 1 among all possible patterns, that is most similar to the very last pattern p⃗ of the time series. Time series observations that follow the pattern r⃗ 1 are transformed into forecasts of future observations (following p⃗). If there are k patterns sufficiently similar to p⃗, we rank them according to the similarity measure and denote them by r⃗ 1,...,r⃗ k . Each of these patterns generates one potential forecast; and we calculate the actual forecast as their linear combination.