Time series often reflect variation associated with other related variables. Controlling for the effect of these variables is useful when modeling or analysing the time series. We introduce a novel approach to normalize time series data conditional on a set of covariates. We do this by modeling the conditional mean and the conditional variance of the time series with generalized additive models using a set of covariates. The conditional mean and variance are then used to normalize the time series. We illustrate the use of conditionally normalized series using two applications involving river network data. First, we show how these normalized time series can be used to impute missing values in the data. Second, we show how the normalized series can be used to estimate the conditional autocorrelation function and conditional cross-correlation functions via additive models. Finally we use the conditional cross-correlations to estimate the time it takes water to flow between two locations in a river network.

翻译：时间序列常反映与其他相关变量相关联的变化。在建模或分析时间序列时，控制这些变量的影响非常有用。我们提出了一种创新方法，在给定一组协变量条件下对时间序列数据进行归一化。具体而言，我们使用广义加性模型基于一组协变量对时间序列的条件均值和条件方差进行建模，随后利用这些条件均值和条件方差对时间序列进行归一化。我们通过两个涉及河流网络数据的应用展示了条件归一化序列的用途：首先，说明了如何利用这些归一化时间序列对数据中的缺失值进行插补；其次，展示了如何通过加性模型使用归一化序列估计条件自相关函数和条件互相关函数。最后，我们利用条件互相关估计河流网络中两个地点之间水流传播所需的时间。