Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations

Dehtiar, Olena; Mishura, Yuliya; Ralchenko, Kostiantyn

doi:10.1080/03610926.2020.1866611

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…In this section we generalize an approach to drift parameters estimation proposed in Dehtiar et al (2021) for the CIR process. We start with two auxiliary lemmas.…”

Section: Estimation Of a When B Is Knownmentioning

confidence: 99%

“…For the case of CIR process, the problem of the drift parameters estimation was extensively studied in the literature, see e. g. Ben Kebaier (2012, 2013); De Rossi (2010); Dehtiar et al (2021); Overbeck and Rydén (1997) and references cited therein. However in the case β = 1/2 we can mention only the work by Dokuchaev (2017), who studied the estimation of the diffusion term parameters β and σ.…”

Section: Introductionmentioning

confidence: 99%

“…First, we extend the results of Ben Kebaier (2012, 2013) concerning the maximum likelihood estimation of (a, b). Then we generalize an alternative approach to drift parameters estimation developed in the recent paper by Dehtiar et al (2021) for the CIR process.…”

Section: Introductionmentioning

confidence: 99%

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Parameter estimation in CKLS model by continuous observations

Mishura¹,

Ralchenko²,

Dehtiar³

2021

Preprint

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We consider a stochastic differential equation of the form dr t = (a − br t )dt + σr β t dW t , where a, b and σ are positive constants, β ∈ ( 1 2 , 1). We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path {r t , 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 = 1 2 . The identification of the diffusion parameters σ and β is discussed as well.

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“…In this section we generalize an approach to drift parameters estimation proposed in Dehtiar et al (2021) for the CIR process. We start with two auxiliary lemmas.…”

Section: Estimation Of a When B Is Knownmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation in CKLS model by continuous observations

Mishura¹,

Ralchenko²,

Dehtiar³

2021

Preprint

Self Cite

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Parameter estimation in CKLS model by continuous observations

Mishura¹,

Ralchenko²,

Dehtiar³

2022

Statistics & Probability Letters

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Method of moments estimation for the superposition of square-root diffusions

Wu,

2024

Prob. Eng. Inf. Sci.

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We consider the problem of parameter estimation for the superposition of square-root diffusions. We first derive the explicit formulas for the moments and auto-covariances based on which we develop our moment estimators. We then establish a central limit theorem for the estimators with the explicit formulas for the asymptotic covariance matrix. Finally, we conduct numerical experiments to validate our method.

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Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations

Cited by 4 publications

References 17 publications

Parameter estimation in CKLS model by continuous observations

Parameter estimation in CKLS model by continuous observations

Parameter estimation in CKLS model by continuous observations

Method of moments estimation for the superposition of square-root diffusions

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