Abstract
This paper discusses the importance of modeling financial time series as a chaotic dynamic rather than a stochastic system. The dynamical properties of a financial time series of an economic institution in Iran were analyzed to identify the potential occurrence of the low-dimensional deterministic chaos. This paper applies several classic nonlinear techniques for detecting the chaotic nature of the time series of loan payment portion and proposes a modified nonlinear predictor scheme for forecasting the future levels of the nonperforming loan. The auto mutual information was implemented to estimate the delay time dimension, and Cao’s approach, along with correlation dimension methodology, quantified the embedding dimension of the time series. The results reveal a low embedding dimension implying the chaotic nature exists in the financial data. The maximum Lyapunov exponent measure is also adopted to investigate the divergence or convergence of the trajectories. Since positive Lyapunov exponents are revealed, the long-term unpredictability of the time series is proved. Lastly, a modified nonlinear local approximator is developed to forecast the short-term history of the time series. Numerical simulations are provided to illustrate the adopted nonlinear techniques. The results reported in this paper could have implications for commercial bank managers who could use the nonlinear models for early detection of the possible nonperforming loans before they become uncontrollable.
Highlights
Banks and financial institutions have played a significant role in balancing the economic life of the people in recent decades owing to the development of the countries and the development of new financial opportunities for the merchants
Embedding Dimension. e minimum number of the state variables needed to display the system behavior is called the embedding dimension m. e Grassberger–Procaccia (GP) [35], the singular value decomposition (SVD) [36], the false nearest neighbor (FNN) [37], and Cao’s scheme [38] are the main approaches for obtaining the minimum embedding dimension from a scalar time series. e delay coordinates at a specified time delay τ are used in the GP method to rebuild the dynamics of a scalar time series in an embedding space of dimension m
Concluding Remarks is paper has introduced the concept of chaotic predictions over short periods for the loan time series. e main idea is that if one can forecast the future behavior of the loan payment percent, the nonperforming loans will be identified
Summary
Banks and financial institutions have played a significant role in balancing the economic life of the people in recent decades owing to the development of the countries and the development of new financial opportunities for the merchants. The chaotic time series are not periodic and random, they exhibit a sense of order and pattern Such unique and complicated appearances can be detected using nonlinear techniques, including phase space reconstruction, false nearest neighbor (FNN) algorithm, correlation dimension method, and Lyapunov exponent. E delay coordinates at a specified time delay τ are used in the GP method to rebuild the dynamics of a scalar time series in an embedding space of dimension m This procedure is data demanding and subjective and consumes more time in the simulation, it can determine the time series’s chaotic and/or random nature. A mean norm of this divergence and the unpredictability of a chaotic time series are given by the Lyapunov exponent measure, in which it expresses the rate of division of infinitesimally close states. (e) Steps (c) and (d) are repeated to achieve a given accuracy
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
