On Parameter Estimation of Stochastic Delay Difference Equation using the Two $m$-delay Autoregressive Coefficients

This paper aims to present how to estimate a model parameter, namely the fixed rate of the investment return in the stochastic delay difference equation in financial time series using the two m-delay autoregressive coefficients. The autoregressive coefficients (ARC) algorithm is proposed and compares with the classical differential evolution (DE) algorithm. For a Monte-Carlo simulation tool, the results obtained from the model with the estimated parameter are validated with historical financial data of IBEX 35, JPM and GOOG from Thomson Reuters database in the period between 2008 and 2010. The numerical results confirm that the two $m$-delay autoregressive coefficients perform well to estimate the fixed rate of the investment return and reduce the computation time for the matching process.