Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation

It is well known in the literature that obtaining the parameter estimates for the Smooth Transition Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (STAR-GARCH) can be problematic due to computational difficulties. Conventional optimization algorithms do not seem to perform well in locating the global optimum of the associated likelihood function. This makes Quasi-Maximum Likelihood Estimator (QMLE) difficult to obtain for STAR-GARCH models in practice. Curiously, there has been very little research investigating the cause of the numerical difficulties in obtaining the parameter estimates for STAR-GARCH using QMLE. The aim of the paper is to investigate the nature of the numerical difficulties using Monte Carlo Simulation. By examining the surface of the log-likelihood function based on simulated data, the results provide several insights into the difficulties in obtaining QMLE for STAR-GARCH models. Based on the findings, the paper also proposes a simple transformation on the parameters to alleviate these difficulties. Monte Carlo simulation results show promising signs for the proposed transform. The asymptotic and robust variance-covariance matrices of the original parameter estimates are derived as a function of the transformed parameter estimates, which greatly facilitates inferences on the original parameters.     

基于新型PID控制器的列车自动驾驶调速系统

基于对列车自动驾驶系统(ATO)的研究,提出了基于重新参数化的B样条神经网络以及粒子群算法的PSO-B-PID控制器;该控制器能通过PSO搜索找到最佳适合的β因子,从而得到适合本网络权值搜索的最佳的重新参数化B样条基函数,同时,文中还提出了由粒子群算法取代传统BP后向传播算法来作为网络学习算法,从而有效克服传统算法易于陷入局部最优的缺点。通过比较实验中建立的PSO-B-PID、BP-B-PID以及PSO-BP-PID 3种控制器的控制性能,结果表明PSO-B-PID控制过程的误差变化最为缓和,其超调量也最小,因此,该控制器能够提高ATO系统控制的快速性、乘坐舒适度以及停车精度。