The Application of Chaos Theory and Nonlinear Structures in Financial Time Series

Hosseini Tash, Fatemeh Sadat | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41411 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Modarres Yazdi, Mohammad
  7. Abstract:
  8. Financial and monetary markets are appropriate areas of applying Chaos Theory. Firstly, current theories of financial and monetary economics state that economic and financial variables such as exchange rates and stock prices are stochastic, so forecasting them is almost impossible. Secondly, if we find the hidden ordered and deterministic trends, we can achieve considerable profits. In this piece of research, we evaluate different methods and tests of detecting chaos in financial time series, and choose the most applicable methods to test financial markets’ indices. The main three indices of Tehran Stock Exchange, including Price, Finance and Industry indices, are examined. A sample of the size 2919 (11 years) is gathered for each index. First, we estimate an autoregressive model for the log return of the indices, and then we put the residuals of the model in chaos tests. Finally, we find strong evidence of nonlinearity in the series and reject the null hypothesis of IID. However, we don’t observe certain evidence of low-dimension chaos. In addition, using a feature of chaotic models, which is unstable periodic orbits, we forecast the value of the indices for different forecasting horizons. Moreover, to justify the nonlinear behavior of the time series and find the causes of this behavior, we use nonlinear GARCH models to establish the variance of the indices’ returns. We also use the estimated AR/GARCH model to predict returns, indices’ values, and volatility for different prediction horizons
  9. Keywords:
  10. Chaos Theory ; Nonlinear Model ; Tehran Stock Exchange ; General Autoregressive Conditional Heteroskedastic (GARCH) ; Financial Time Series ; Forecasting Financial Variables

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