In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA‐GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coefficient. As it is often of interest to identify all those components which exhibit stochastic volatility features we suggest a test statistic for this problem. We also show that a slightly modified version of the principal volatility component analysis can be seen as an ICA method. Finally, we apply the estimators in analysing a data set which consists of time series of exchange rates of seven currencies to US dollar. Supporting information including proofs of the theorems is available online.

中文翻译：

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使用独立分量分析提取条件异方差分量

在独立成分模型中，假设多变量数据是相互独立的潜在成分的混合。然后，独立成分分析（ICA）旨在估计这些潜在成分。在本文中，我们研究了一种 ICA 方法，该方法结合使用线性和二次自相关来实现各种平稳时间序列的有效估计。通过寻找一般条件下估计量的极限分布来研究估计量的统计特性，并在 ARMA-GARCH 模型的情况下推导渐近方差。我们使用渐近结果和有限样本模拟研究来比较权重系数的不同选择。由于通常有兴趣识别所有表现出随机波动特征的成分，因此我们建议对此问题使用检验统计量。我们还表明，主波动率成分分析的稍微修改版本可以被视为 ICA 方法。最后，我们应用估计量来分析由七种货币兑美元汇率的时间序列组成的数据集。包括定理证明在内的支持信息可在线获取。