基于高斯过程的时间序列分析

《基于高斯过程的时间序列分析》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、上海交通大学硕士学位论文基于高斯过程的时间序列分析姓名：沈赟申请学位级别：硕士专业：计算机软件与理论指导教师：张丽20090101TimeSeriesAnalysisusingGaussianProcessABSTRACTTheGaussianprocess(GP)regressionmodelisappliedforpredictionoftimeseries.Theautoregressivemodelisusedinsteadoftime-drivenmodel.Wefirstlyintroducethesinglesteppredictionusin

2、gGPandthenextendittomulti-steppredictionoftimeseries.TheconnectionbetweenstationarityofkernelfunctionofGPandthatoftimeseriesunderinvestigationisfoundthattheGPwiththestationarykernelfunctionproducespoorpredic-tionresultsfornon-stationarytimeseries.TheconventionalGPmodelhastobemodifi

3、edtofitthenon-GPtimeseries,e.g.thefamousautoregressiveconditionalheteroskedasticity(ARCH)series.AnovelexponentialARCHmodelbasedonGPisintroducedtoinvestigatethevolatilityofdata.Numericalexperimentsshowgoodperformanceofthismodel.FinallywepresentanovelprobabilisticmethodemployingGPpri

4、ortodealwithspeechenhance-mentaswellasvoiceactivitydetection.Thecomputersimulationsshowbetteroratleastcomparativeperformancethanconventionalmethods.KEYWORDS:TimeSeriesAnalysis,StochasticVolatilityAnalysis,GaussianProcess,KernelMethods,BayesianLearning,SpeechEnhancementIII插图2.1白噪声.

5、...................................62.2RandomWalk.................................72.3AR(2).....................................102.4ARCH(1)数据.................................112.5EGARCH数据................................124.1二氧化碳含量预测..............................244.2正弦函数预测.......

6、.........................255.1白噪声....................................345.2AR(2)单步预测结果.............................355.3AR(2)单步预测误差分析..........................375.4AR(2)核矩阵.................................385.5AR(2)多步预测................................385.6纯净的预测结果...................

7、............395.7纯净的多步预测结果............................405.8随机漫步的预测结果（平稳核函数）...................415.9随机漫步的预测结果（非平稳核函数）..................425.10ARCH(1)单步预测..............................435.11EGARCH单步预测..............................445.12EGPARCH预测................................456.1白噪

8、声(0dB)的增强结果......................