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I have a revenue dataset for various businesses. For about half of those businesses, monthly data is available. For the other half, only annual revenue data is present. I know the seasonality of the revenues fairly well from the half of the businesses who have reported their monthly revenue. In addition, the data goes back at least five years, so I know that seasonal effects are real. What is the best way to go about extrapolating monthly revenue for businesses with missing data given the information I have on hand? Even though it is not strictly true, I am assuming that the businesses with missing data and businesses with complete data are sufficiently similar that we need not worry about any underlying issues.

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    $\begingroup$ Whatever approaches are suggested, you should obviously hold out some of the monthly-revenue companies as test cases and see what happens when you impute monthly values from their annual totals. $\endgroup$ – Wayne Mar 29 '16 at 13:10
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    $\begingroup$ This probably can be done with the proportional Denton method of interpolation of a low-frequency time series by use of an associated higher-frequency indicator series, imposing the constraints that the interpolated series obeys the original low-frequency series totals. There's an IMF document that goes through the approach and various implementations in several languages. $\endgroup$ – Dimitriy V. Masterov Feb 9 '18 at 18:51
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Time series analysis incorporating Intervention Detection can estimate these missing values. Essentially the "0" value at a particular point in time is treated as an exception and the size of the exception is the estimated coefficient associated with that point in time. You can search for Intervention Detection OR AUTOMATIC Intervention Detection using a browser. If the number of missing values is "large" relative to normal data points then you might have to iteratively pursue this.

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