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I have a regular time series of accumulated values of a variable (usage) with some missing (sometimes consecutive) intervals.

Is there an imputation method that methodologically considers this additional information and requirement that the values must add up when it returns the imputed values?

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Ok you have a time series like this:

spend budget: 0, 30, 90, 110, NA, 210, NA, NA, 333,400, NA, 410

So what you probably want to be considered is that:

  1. The NA replacement is bigger than the value before the NA
  2. The NA replacement is smaller than the value after the NA
  3. This still applies for for consecutive missing values

Well, the solution is easy. Linear Interpolation will fulfill this rules all the time. (and actually also gives decent results)

But also all other (advanced) time series methods will recognize the clear trend in the data and make use of this. To get a feeling, what are common time series imputation methods, you could have a look at the manual of my time series imputation R package (imputeTS manual).

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Consecutive accumulated data is functional not stochastic, thus, it does not form the assumption to use time series. It would be better to difference the data first to get the new records at each time point.

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