Asymptotic Behavior of the Maximum Likelihood Estimator for Ergodic and Nonergodic Square-Root Diffusions

作者：Ben Alaya Mohamed; Kebaier Ahmed^*

来源：Stochastic Analysis and Applications, 2013, 31(4): 552-573.

DOI：10.1080/07362994.2013.798175

• Cox-Ingersoll-Ross processes
• Laplace transform
• Limit theorems
• Nonergodic diffusion
• Parameter inference
• 44A10
• 60F05
• 62F12

This article deals with the problem of global parameter estimation in the Cox-Ingersoll-Ross (CIR) model (X-t)(t0). This model is frequently used in finance for example, to model the evolution of short-term interest rates or as a dynamic of the volatility in the Heston model. In continuity with a recent work by Ben Alaya and Kebaier [%26lt;xref rid=%26quot;CIT0001%26quot; ref-type=%26quot;bibr%26quot;%26gt;1%26lt;/xref%26gt;], we establish new asymptotic results on the maximum likelihood estimator (MLE) associated to the global estimation of the drift parameters of (X-t)(t0). To do so, we need to study the asymptotic behavior of the quadruplet . This allows us to obtain various and original limit theorems on our MLE, with different rates and different types of limit distributions. Our results are obtained for both cases: ergodic and nonergodic diffusion.

• 出版日期2013-7-1