Identification of Chaos in Financial Time Series to Forecast Nonperforming Loan

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.