5) How mathematicians predict the future?

posted Jul 1, 2011, 3:19 AM by Ecmi Milano   [ updated Jul 7, 2011, 11:59 PM ]

Instructor: Agnieszka Wylomanska

This project aims at developing and validating suitable mathematical model for the interpretation and description of financial data, like interest rates. It is very important to find the proper system that describes real data sets and it is well known that it can be useful especially in the prediction problem. Because data from financial markets indicate very characteristic behavior therefore it is not easy to find the appropriate model that takes into consideration such many aspects as: seasonality, deterministic trend and relationship observed in the data.The work will be divided into four steps:1.Analysis of three data sets from financial markets - seasonality and deterministic trend detection.2. The common analysis of the mentioned time series – relationship between real financial data.3. Modeling the data sets on the basis of points 1 and 2.4. Validating the obtained model and prediction.In our analysis we will use the techniques based on the least squares method that provide to detection and removing the seasonality and deterministic trend from the real data sets. Moreover to find the relationship between two or more time series we will take into consideration the multiple regression method that assumes the linear relation between observed data sets and is also based on the least squares technique. On the basis of the obtained results we will validate the model and predict the real financial data.

Preferred mathematical background:
fundamentals of statistics, fundamentals of probability, differential equations.