Study of the periodicity in Euro-US Dollar exchange rates using local alignment and random matrices

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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. The presence of periodicity within the period length equal to 24 hours and 25 hours, 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. A period of 24 hours is a common phenomenon for foreign exchange rates, indices and stocks of different companies. We show it for the Bank of America and Microsoft stocks, S&P500 and NASDAG indexes and for the gold and silver prices as examples. The reasons for the existence of the periodicity in the financial ranks are discussed. The results can find application in computer systems, for the purpose of forecasting exchange rates.