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I have found Holt-Winters seasonal method a very decent method for forecast, specifically for cases where more recent observations are more representative of the near future. The method equally sounds very promising for imputation of missing intervals. However, I have not found even a single implementation of this method for imputation. Why is that?

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Data imputation is best done using the data on both sides of the missing interval. A forecast method such as Holt-Winters uses data on only one side --- the past must be used to predict the future, and not vice-versa.

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  • $\begingroup$ Thanks Rob. It is very helpful. I agree. What I still see perplexing is that aren’t we using the future as well to know the unknown past (i.e., the missing interval) when we are using data on “both” side of the missing interval? $\endgroup$ – Reveille Apr 13 '16 at 15:10
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My subjective impression is that forecasters and data imputers are simply different people. The data imputers don't know much about forecasting, so they don't think about methods like Holt-Winters. The forecasters, from what I have seen, usually expect their time series not to have missing values. (Yes, that's unrealistic, but as far as I see, they will usually do some ad hoc way of imputation, if they don't throw out series with missing values altogether. They are simply not all that interested in imputation.)

Plus, as Rob writes, to use Holt-Winters to impute values, you'd have to fit the model to the data up to the first missing value, then forecast into the missing period. The problem is that if the first missing value occurs near the beginning of your time series, the model used for imputation will be based on very few observations, so it will be unstable and won't be able to fit seasonality etc. You would not be using the data after the missing period.

Of course, in such a case you could reverse the time series and work backward in time. But that won't help you if you have multiple missing values, some near the beginning and some near the end of the time series.

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  • $\begingroup$ Thanks much Stephan. The reason this question crossed my mind is actually because I am doing both imputation and forecast on massive data and see that there are way many more methods available in R for uni-variate forecast than for imputation. It may be fundamentally wrong, as Rob mentioned, but would be interesting to see how this would perform compare to other imputation methods; approaching the missing interval from both directions in time using Holt-Winters and aggregate (e.g., average) the two estimates in to one value for that missing interval. $\endgroup$ – Reveille Apr 13 '16 at 15:11

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