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The existing statistics in unit root tests of ESTAR-GARCH model often need to calculate the variance of specimen. In this paper, the empirical likelihood ratio statistics are proposed to deduce the limiting distribution of them, so that the random errors caused by variance calculation are avoided. And then, a critical value of the statistics can be received through simulation, the power of the QML test and the empirical likelihood ratio statistics has been compared and
studied. Monte Carlo simulation shows that compared with the QML test, the power and the criterion of tests is more fruitful and more scientific, through the empirical likelihood ratio statistics. Avoiding the random errors of the calculation of variance, the accuracy of tests is clearly increased by using the empirical likelihood ratio statistics. Finally, the empirical study of SSE can further illustrate the higher test efficiency of this statistic.
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In this paper, we discuss the exponential ergodicity of Markov switching diffusion processes, presenting criteria of f-exponential ergodicity for the processes with reflecting boundary at origin. When the one-dimensional diffusion processes are stochastically ordered for any fixed environment, the explicit estimates of the exponential ergodic rate for the process are investigated by means of the coupling method.
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Since the jump of an asset price has a strong effect on the estimate and forecast volatility, it has received widespread attention. Following HAR-CJ model introduced by Andersen et al, lots of works focus on this problem. In this paper, through a threshold technique, we distinguish the true and false jumps. Then we introduce two models, HAR-CTFJ model and LHAR-CTFJ model. Our result shows that the effect from the true jumps is significant while that from the false jumps is not. Moreover, the SPA test shows that our models (i.e. HAR-CTJ and LHAR-CTJ) are better than the classical HAR-CJ model in the prediction of volatility.
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Modal regression based on nonparametric quantile estimator is given. Unlike the traditional mean and median regression, modal regression uses mode but not mean or median to represent the center of a conditional distribution, which helps the model to be more robust for outliers, asymmetric or heavy-tailed distribution. Most of solutions for modal regression are based on kernel estimation of density. This paper studies a new solution for modal regression by means of nonparametric quantile estimator. This method builds on the fact that the distribution function is the inverse of the quantile function, then the flexibility of nonparametric quantile estimator is utilized to improve the estimation of modal function. The simulations and application show that the new model outperforms the modal regression model via linear quantile function estimation.
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When the sample size is $N$, the computational complexity of the least squares estimate of mean change point is O(N^2), and it's necessary to reduce the computational complexity in the case of huge data. In this paper, a two-stage fast scanning algorithm is proposed for the estimation of mean change point, and it is proved that this method has the same convergence speed and limiting distribution as the least squares estimation of mean change point, and the optimal complexity of the new algorithm is O(N^{4/3}\cdot b_n^{2/3}). We have conducted sufficient data experiments in terms of computation time and estimated efficiency, and the results show that the estimated efficiency of the new and old methods is similar, but the computation time of our method is obviously shortened.
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In the reserve model of B-F, in order to make the estimated reserve of the accident year mean independent of the specific form of prior distribution, the credibility method is adopted. On the basis of \ncite{10} model, considering the relationship between the amount of claims in different years of progress in the same accident year, the optimal non-homogeneous and homogeneous credibility estimates of the accident year means are obtained under the balanced loss function. When \omega=0, the result is consistent with that of the original model, and the original model is generalized.
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For calculating the predictive powers, we suggest an elegant expectation identity to directly calculate the expectations. We calculate the predictive powers of the hypotheses with a nonzero threshold for five different categories, which are non-sequential trials with classical power and Bayesian power, and sequential trials with hybrid predictions, Bayesian predictions, and classical predictions. Moreover, the calculations of the various predictive powers are illustrated through
three examples. Finally, when calculating the average success probability in \ncite{9}, it is tricky to find the predictive distribution for the predictive power, whereas, it is straightforward to utilize the expectation identity for the calculation.
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This paper studies the optimal asset allocation and reinsurance problem under mean-variance-CVaR criteria for an insurer in continuous-time. We obtain the closed-form solution of optimization problem by using martingale method. Numerical results show the trends of optimal wealth, investment and reinsurance strategies with various parameter values.
