The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The es...The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.展开更多
In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg...In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.展开更多
This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic functio...This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.展开更多
基金This work was supported by National Natural Science Foundation of China (Grant No. 10371074).
文摘The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.
基金Supported by the National Natural Science FundZhejiang Provincial Natural Science Foundation.
文摘In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.
基金supported by National Natural Science Foundation of China (Grant No. 10671037)the Science Foundation of Shanghai Educational Department (Grant No. 06FZ035)
文摘This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.
