P-adic modeling of the RTS index dynamics depending on timeframes

Similarity of physical and economic processes provides us with the opportunity to study price fluctuations in financial markets with the help of methods of econophysics. These both kinds of processes are chaotic, determined in time, but cannot be predicted on its basis. The p-adic analysis, one of econophysics methods, is chosen as the approach for consideration of price changes. The research purpose is application of methods of p-adic modeling and forecasting for price fluctuations, the research subject is the RTS Index dynamics. The article provides mathematical description of the p-adic analysis, which is considered to be determination of p-adic numbers and their representation in  space. This is complete metric (generated by a p-adic non-Archimedean norm) space, which allows us to apply p-adic numbers to modeling stochastic phenomena. Models of the main elementary figures of price dynamics in financial markets, such as a linear function, step function and R.N. Elliott's wave model, are constructed. In the history of financial markets, examples which are characteristic of p-adic mapping are found. An attempt to create a method of p-adic modeling and forecasting is made. According to this method, analysis of the RTS Index dynamics is performed. For the RTS Index dynamics, four models are constructed: depending on months, weeks, days and hours. The main types of the p-adic forecasts are revealed, those being optimistic, pessimistic, average and the forecast of the continuing development. Conclusions are drawn about accuracy of both p-adic models depending on timeframes and their forecasts depending on the revealed types. Benefits and faults of the p-adic analysis are found. The research results can be used for further studying of wave patterns with the use of p-adic mapping, the patterns being applied not only to price fluctuations but also to other economic processes. Moreover, p-adic models can serve as a tool of the technical analysis.