  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.
