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This chapter presents elements of statistical inference and simulation for diffusion processes defined by stochastic differential equations. Many well-known models are treated in detail like geometric Brownian motion, CIR, CEV, Vasicek, CKLS, Heston models. The chapter considers other topics such as quasi-maximum likelihood estimation, Bayesian estimation, hypotheses testing, model selection, lasso estimation, change point analysis, asynchronous covariance estimation, lead–lag analysis and asymptotic expansion. Full R code for completing the above analyses with yuima package is provided.