期刊
MULTISCALE MODELING & SIMULATION
卷 6, 期 4, 页码 1125-1145出版社
SIAM PUBLICATIONS
DOI: 10.1137/060670535
关键词
principle component analysis; hidden Markov models; multidimensional stochastic differential equations; metastability; seasonal autoregressive integrable model with moving average
资金
- DFG research center Matheon Mathematics for key technologies in Berlin
We present a method for simultaneous dimension reduction, model fitting, and metastability analysis of high-dimensional time series. The approach is based on the combination of hidden Markov models (HMMs) with localized principal component analysis (PCA) (which is used to identify the essential dimensions in the form of empirical orthogonal functions (EOFs) for each of the hidden states) and fitting of multidimensional stochastic differential equations (SDEs). This means that the analyzed data is clustered according to differences in essential dimensions and SDE models specific to each of the hidden states. We derive explicit estimators for PCA-SDE model parameters in the case of fixed sequences of HMM states and employ the expectation-maximization algorithm for numerical optimization of HMM-PCA-SDE parameters. We demonstrate the performance of the method by application to historical temperature data in Europe during 1976-2002. In a comparison with the standard SARMA (seasonal autoregressive moving average model) technique for time series analysis, the HMM-PCA-SDE method exhibits better numerical performance and efficiency, especially on high-dimensional data sets and for a 20-dimensional reduced state space. We also compare the results of both models w.r.t. errors of one-day temperature predictions.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据