Financial Data Analysis by SDE Modeling with YUIMA

Abstract

YUIMA is the name of a project for software implementation of statistical analysis methods for data modeled by stochastic differential equations (SDEs). In this paper, we explain how to implement statistical modeling of financial time series by SDEs using the R package yuima, which is the main development result of the YUIMA project. As a concrete example, we focus on daily time series of the exchange rate between the U.S. dollar and the Japanese yen from 2001 to 2024. The model selection results suggest that the volatility-induced stationarity observed in previous studies on the modeling of the U.S. short-term interest rate might also exist in the USD/JPY exchange rate.