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2022•Fractal and FractionalOpen access

Maximum Likelihood Estimation for Mixed Fractional Vasicek Processes

Chunhao Cai, Yinzhong Huang, Lin Sun, Weilin Xiao

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Abstract

In this paper, we consider the problem of estimating the drift parameters in the mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators are studied for all H∈(0,1), H≠1/2. On the other hand, we present that the MLE can be simulated when the Hurst parameter H>1/2.

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What this paper is about

In this paper, we consider the problem of estimating the drift parameters in the mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators are studied for all H∈(0,1), H≠1/2. On the other hand, we present that the MLE can be simulated when the Hurst parameter H>1/2.

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Available abstract

In this paper, we consider the problem of estimating the drift parameters in the mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators are studied for all H∈(0,1), H≠1/2. On the other hand, we present that the MLE can be simulated when the Hurst parameter H>1/2.

Key concepts: Vasicek model, Estimator, Mathematics, Maximum likelihood, Hurst exponent, Applied mathematics, Strong consistency, Martingale (probability theory)

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