I am working with a multivariate time series (with daily data) of approximately 40 years.

It consists of the data of two stations (dataset A & dataset B) measuring both the river level and the streamflow of two neighbouring (but not connected) rivers. The datasets are correlated (specificly the streamflow), however the variance of both time series is pretty different.

Additionally I have the data of two closeby percipitation stations.

Dataset B ends 6 years before dataset A ends. I am looking for a way to impute the 6 years of missing data of station B at the end of the time series using the data of station A and the percipitation stations.

Many papers have been published about the imputation of missing values at random, however I have not found a good method for imputation of a single, long period of missing data. I have tried multiple methods in R (mtsdi, mice, iVAR), all without satisfactory results.

1) What is the best method to impute a single, long period of missing data?

2) What is the best way to test the functionality of the used method? Up until now i picked a period directly before the data gap, deleted the last 6 years, imputed these 6 years and compared them to the original time series. I am wondering if this process can be automated not only for the 6 years before the data gap but also for other 6 year periods within the dataset.


1 Answer 1


To partially answer question 1, you could look at this paper:

Park, J., Müller, J., Arora, B. et al. Long-term missing value imputation for time series data using deep neural networks. Neural Comput & Applic 35, 9071–9091 (2023). https://doi.org/10.1007/s00521-022-08165-6

The authors write:

We assume that the target time series variable has one large gap and that the supporting variables that explain the target variable are fully observed.


Unlike the referenced studies, the main contribution of our work is a method for filling a long continuous gap (e.g., multiple continuous months of missing daily observations) in a single variable of a multivariate time series dataset. Another key difference between the previous studies and our research is the size of the datasets used. Our focus is on smaller datasets that have fewer variables than the cited works. Usually, these types of datasets are hard to use and tend to be discarded in analysis and modeling efforts. Our approach would enable greater use of time series datasets that have multi-year gaps in a variable, which are common in many long-term environmental monitoring observations.


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