Modeling foreign exchange rates as stochastic difference equations with minimum uncertainty for prediction analysis

Abstract Long-term prediction of exchange-rate (XR) signals has been an interesting topic in statistics and finance. However, owing to strong fluctuations in XR signals, long-term prediction remains extremely difficult, and no consensus has been reached on an ideal approach that produces the best estimation accuracy. XR signals are known to be highly volatile (chaotic), which makes it difficult to model them via an accurate statistical framework. In this paper, we attempt to uncover the long-term system dynamics behind AUD/USD and EUR/GBP XR signals by modeling them with reduced stochasticity and minimized volatility in the form of a linear stochastic difference equation (LSDE) via the recursive least squares (RLS) regression approach. On the basis of these two well-known XRs, the simultaneous presence of inherent stochasticity and strong volatility makes prediction difficult for XR signals. Our findings indicate that under the use of a sufficiently large training sample size for RLS regression, the LSDE coefficients of XR signals assume values within a very small range (low variance) and behave relatively consistently in time (low volatility), which concurrently suppresses both their stochasticity and chaoticity, enabling long-term prediction under a reduction of more than 60% in the prediction error. This study aims to decrypt XR signal dynamics in terms of the underlying LSDE coefficients and to develop an accurate LSDE model with minimum uncertainty (stochasticity, volatility) that can overcome the hinderance of precise long-term prediction.