One of the most frequently used methods to model the autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an autocovariance structure via nonparametric estimation of the autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic.

中文翻译：

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通过高斯插补从删失时间序列进行非参数自协方差估计

对二阶平稳时间序列的自协方差函数进行建模的最常用方法之一是使用 Box 和 Jenkins 开发的自回归和移动平均模型的参数框架。然而，这种参数模型虽然非常灵活，但可能并不总是足以对具有急剧变化的自协方差函数进行建模。此外，如果数据不遵循参数模型并在某个值处进行删失，则估计结果可能不可靠。我们开发了一种高斯插补方法，通过自协方差函数的非参数估计来估计自协方差结构，以解决审查和不正确的模型规范。我们在各种审查率和基础模型下进行模拟，证明了该技术在偏差和效率方面的有效性。我们描述了它在北极硅浓度时间序列中的应用。