Further Results on a Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors
Further Results on a Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors
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DOI：
10.1007/978-3-319-96944-2_3
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发表时间：
2017-09
期刊：
影响因子：
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通讯作者：
H. Alkhatib;B. Kargoll;J. Paffenholz
中科院分区：
文献类型：
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作者：
H. Alkhatib;B. Kargoll;J. Paffenholz
我们研究了一类时间序列模型，它一般可以解释为具有多个单变量、协方差平稳自回归(AR)过程的多变量非线性回归模型的加性组合，这些过程的白噪声分量服从独立的标度t分布。这些分布使得能够对重尾或受异常值影响的观测进行随机建模，并为确定性模型参数、AR系数、尺度参数和基础t分布的自由度的部分自适应、稳健的最大似然(ML)估计提供了框架。为了实现最大似然估计，我们推导了一种广义期望最大化(GEM)算法，该算法采用线性化、迭代加权最小二乘的形式。为了得到最终估计的质量评估，我们用基于蒙特卡洛的Bootstrap算法对GEM算法进行了扩展，该算法允许计算关于所有估计参数的协方差矩阵。将扩展的GEM算法应用于全球导航卫星系统(GNSS)多变量时间序列，在考虑有色观测噪声和部分重尾白噪声分量的情况下，将其近似为一个三维圆。用GEM算法拟合的圆周模型的精度优于以往的标准估计方法。
We investigate a time series model which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance stationary autoregressive (AR) processes whose white noise components obey independent scaled t-distributions. These distributions enable the stochastic modeling of heavy tails or outlier-afflicted observations and present the framework for a partially adaptive, robust maximum likelihood (ML) estimation of the deterministic model parameters, of the AR coefficients, of the scale parameters, and of the degrees of freedom of the underlying t-distributions. To carry out the ML estimation, we derive a generalized expectation maximization (GEM) algorithm, which takes the form of linearized, iteratively reweighted least squares. In order to derive a quality assessment of the resulting estimates, we extend this GEM algorithm by a Monte Carlo based bootstrap algorithm that enables the computation of the covariance matrix with respect to all estimated parameters. We apply the extended GEM algorithm to a multivariate global navigation satellite system (GNSS) time series, which is approximated by a three-dimensional circle while taking into account the colored measurement noise and partially heavy-tailed white noise components. The precision of the circle model fitted by the GEM algorithm is superior to that of the previous standard estimation approach.