This, to me, is a huge mistake, as a cross sectional survey is designed to estimate what is currently happening. A time series forecast for that period can incorporate seasonality, but not a new change that would break the time series. Thus, a time series forecast as an imputation for a cross sectional survey may work well most of the time, but not when it really matters.
I was recently reminded of situations where another regressor on an ARIMA model may have a time series that reaches to the current period, when the variable of interest does not, and that can be helpful, but for a current/cross sectional survey, often needed for Official Statistics, focus is on the current data, which may be modeled in groups/strata, not on forecasting from past data.
The notes at the attached link argue that to impute into a cross sectional survey using a [strictly] time series forecast, misses the point of discovering if there has been a change, say in a market for example, that has just occurred or is occurring now, when the time series by definition cannot detect a current break when it only uses past data. An example is given where this has been used, regardless. But I think it is a big mistake, which 'muddies the water,' misses what is important, and complicates a basically otherwise simple situation.
Has anyone else seen this kind of application?
Note that there are related questions on ResearchGate, considering "prediction," "forecasting," and similar sounding terms, so you may want to search for them as well.
Research When Prediction is Not Time Series Forecasting
have you looked at any of the longitudinal studies of women's health publications? I don't know whether they would help, but they have repeated measures over time, so I can imagine if they are collecting info on risk factors then they will be used to model outcomes, just an idea, as I said I have not looked at any of these, just thought of this when you asked this ?
For imputation, you can go for imputePSF R Package.
If you are interested in univariate time series data predictions, have a look in PSF algorithm and it's R Packages available at :
CRAN: https://cran.r-project.org/web/packages/PSF/index.html
GitHub: https://github.com/neerajdhanraj/PSF
How to use: https://www.researchgate.net/publication/304131481_PSF_Introduction_to_R_Package_for_Pattern_Sequence_Based_Forecasting_Algorithm
and
https://www.researchgate.net/publication/304580701_Introduction_of_seasonality_concept_in_PSF_algorithm_to_improve_univariate_time_series_predictions
For further details contact me at: http://www.neerajbokde.com
Article PSF: Introduction to R Package for Pattern Sequence Based Fo...
Article Introduction of seasonality concept in PSF algorithm to impr...
My point was that when you can model current data, it may not be a good idea to impute for missing data in a sample using a time series which projects to the data of interest based only on previous data, not a relationship to current data.
Both prediction for cases not in the sample, and for imputation for nonresponse, can use a model-based approach with the current population, rather than an individual time series for each member of the population, which ignores the current conditions which are of importance.
In https://www.researchgate.net/publication/261586154_Using_Prediction-Oriented_Software_for_Survey_Estimation I experimented to look into modeling for both out-of-sample cases, and imputation. This is just an example and results would vary by application.
Here are examples using prediction for current data, with regard to establishment surveys for Official Statistics:
https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development
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