Developing new mathematical method for search of the time series periodicity with deletions and insertions

The purpose of this study was to detect latent periodicity in the presence of deletions or insertions in the analyzed data, when the points of deletions or insertions are unknown. A mathematical method was developed to search for periodicity in the numerical series, using dynamic programming and random matrices. The developed method was applied to search for periodicity in the Euro/Dollar (Eu/$) exchange rate, since 2001. The presence of periodicity within the period length equal to 24 h in the analyzed financial series was shown. Periodicity can be detected only with insertions and deletions. The results of this study show that periodicity phase shifts, depend on the observation time. The reasons for the existence of the periodicity in the financial ranks are discussed.