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Parameter estimation in CKLS model by continuous observations

Author

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  • Mishura, Yuliya
  • Ralchenko, Kostiantyn
  • Dehtiar, Olena

Abstract

We consider a stochastic differential equation of the form drt=(a−brt)dt+σrtβdWt, where a, b and σ are positive constants, β∈(12,1). We study the estimation of an unknown drift parameter (a,b) by continuous observations of a sample path {rt,t∈[0,T]}. We prove the strong consistency and asymptotic normality of the maximum likelihood estimator. We propose another strongly consistent estimator, which generalizes an estimator proposed in Dehtiar et al. (2021) for β=12. The identification of the diffusion parameters σ and β is discussed as well.

Suggested Citation

  • Mishura, Yuliya & Ralchenko, Kostiantyn & Dehtiar, Olena, 2022. "Parameter estimation in CKLS model by continuous observations," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000153
    DOI: 10.1016/j.spl.2022.109391
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