北京师范大学学报(自然科学版)
北京師範大學學報(自然科學版)
북경사범대학학보(자연과학판)
Journal of Beijing Normal University (Natural Science)
2015年
5期
484-491
,共8页
MRS-GARCH 模型%Gibbs抽样%EM算法%极大似然估计%股市波动
MRS-GARCH 模型%Gibbs抽樣%EM算法%極大似然估計%股市波動
MRS-GARCH 모형%Gibbs추양%EM산법%겁대사연고계%고시파동
MRS-GARCH model%Gibbs sampling%EM algorithm%maximum likelihood estimation%volatility of stock market
考虑 MRS-GARCH 模型中存在的“路径依赖”问题,采用混合 Gibbs 抽样与 EM算法的两步 MCEM-MCML法求参数的极大似然估计,避免了对原模型的简化或近似而导致的信息损失及估计精度下降。以上证综指和深圳成指日(周)收益数据为样本,利用 MRS-GARCH 模型对沪深股市收益波动进行估计。结果表明:沪深股市存在显著的高、低波动状态,处于低波动状态的可能性更大,持续时间更长。与 MS、Gray及 Klassen模型相比,MRS-GARCH 模型估计的波动状态持续性有所降低。比较各模型的BIC值,MRS-GARCH 模型的拟合性能最优。
攷慮 MRS-GARCH 模型中存在的“路徑依賴”問題,採用混閤 Gibbs 抽樣與 EM算法的兩步 MCEM-MCML法求參數的極大似然估計,避免瞭對原模型的簡化或近似而導緻的信息損失及估計精度下降。以上證綜指和深圳成指日(週)收益數據為樣本,利用 MRS-GARCH 模型對滬深股市收益波動進行估計。結果錶明:滬深股市存在顯著的高、低波動狀態,處于低波動狀態的可能性更大,持續時間更長。與 MS、Gray及 Klassen模型相比,MRS-GARCH 模型估計的波動狀態持續性有所降低。比較各模型的BIC值,MRS-GARCH 模型的擬閤性能最優。
고필 MRS-GARCH 모형중존재적“로경의뢰”문제,채용혼합 Gibbs 추양여 EM산법적량보 MCEM-MCML법구삼수적겁대사연고계,피면료대원모형적간화혹근사이도치적신식손실급고계정도하강。이상증종지화심수성지일(주)수익수거위양본,이용 MRS-GARCH 모형대호심고시수익파동진행고계。결과표명:호심고시존재현저적고、저파동상태,처우저파동상태적가능성경대,지속시간경장。여 MS、Gray급 Klassen모형상비,MRS-GARCH 모형고계적파동상태지속성유소강저。비교각모형적BIC치,MRS-GARCH 모형적의합성능최우。
Due to the existence of path dependent problem in MRS-GARCH models,it is impossible to obtain MLE without resorting to modification of the model. We use a two step MCEM-MCML method combined with Gibbs sampling and EM algorithm to obtain maximum likelihood estimator without any modification of the model.Return series of Shanghai Composite Index and Shen Zhen Component Index are chosen as our sample.Estimation results of MRS-GARCH model suggest significantly high volatility and low volatility states in China’s stock market.The duration for low volatility state is longer.Compared with MS model,Gray’s model and Klaassen’s model,estimation of regime persistence is reduced for MRS-GARCH model.Furthermore,MRS-GARCH model is the best among GARCH model,Gray’s model and Klaassen’s model according to BIC for both data sets.