马尔可夫状态转换GARCH族模型的选择与估计

Selection and Estimation of Markov State Transition GARCH Family Model

文章基于比特币波动率数据,采用马尔可夫状态转换GARCH族模型对常用的两种估计方法--极大似然估计和贝叶斯估计进行比较研究。结果显示,在模型参数估计方面,不同估计下的标准GARCH族模型的参数估计结果差异不大,但随着状态数量增加和残差分布改变其差异会变大。在模型应用方面,对比特币收益率序列进行风险测度发现,其风险水平总体上差别不大,引起差异的原因可能与模型选择、残差分布、状态数量及置信水平有关。由于MCMC算法比较依赖计算机技术,随着状态数量的增加,在MCMC估计下的马尔可夫状态转换GARCH族模型的程序运行时间更长,风险预测值差别不大时可考虑采用经典的极大似然估计。

Based on the volatility data of bitcoin, this paper adopts the Markov state transition GARCH family model to compare and study the two commonly used estimation methods—maximum likelihood estimation and Bayesian estimation. The results are shown as follows: In terms of model parameter estimation, there is little difference in the parameter estimation results of standard GARCH models under different estimates, but the difference will become larger with the increase of state number and the change of residual distribution. In terms of the application of the model, the risk measurement on bitcoin yield series shows that there is little difference in risk level on the whole, and that the reasons for the differences may be related to model selection, residual distribution, number of states and confidence level. Because MCMC algorithm is more dependent on computer technology, with the increase of the number of states, the program running time of the Markov state transition GARCH family model under MCMC estimation is longer, and the classical maximum likelihood estimation can be used when the difference of risk prediction values is not large.