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I have the following time series that contains the past 12 months data as well as data for the 24th month:-

Time           Sales
2021-06-30      0.00
2021-07-31     64.40
2021-08-31     82.61
2021-09-30     93.37
2021-10-31     97.74
2021-11-30     98.56
2021-12-31    103.01
2022-01-31    104.97
2022-02-28    108.55
2022-03-31    115.36
2022-04-30    123.87
2022-05-31    122.36 (12th month observation)
2023-05-31    978.88 (24th month observation, which is 8 times that of sales for 12th month observation)

Here, the 24th month sales can have value anywhere between 2 times to 8 times the sales appeared for the 12th month. While forecasting the sales for the 13th month to the 23rd month time period (2022-06-30 to 2023-04-30), I want the original scale to be maintained among the forecasted sales values for these 11 months and the 24th month sales, otherwise there would be a high difference reflected between the 23rd month sales and the 24th month sales. Here, the point of concern is that the time series that needs to be fed as input to the model is not continuous, as can be seen from the data sample mentioned above, and that I need to perform reverse forecasting for these 11 months as I already have data for the 24th month.

Any help/suggestion/advice on how to solve this problem would be highly appreciated.

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  • $\begingroup$ You actually have 11 months as the shop was not open in June 2021. Not do you have May 2023 (it has not happened yet) - my guess is you have a target. So you need to extrapolate to reach the target - your choice, with linear growth or exponential growth, and you might look at the first 11 months to inform what kind of growth. But it will not be soundly based: you had less than a doubling up to May 2022 (+60ish) so multiplying that level by $8$ by May 2023 (+850ish) looks ambitious $\endgroup$
    – Henry
    Jun 21, 2022 at 15:58

1 Answer 1

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You're essentially look for ways to impute or fill the missing values in your series. There are a number of ways you could do this. For example, you could fill using:

  • The most recent value - this would be the naive way.
  • Drawing different lines between the last and second to last observed points, e.g. straight line, curved line (e.g. quadratic, cubic, splines, etc.).
  • Fit a forecasting model based on the data up to and including 2022-05-31. Use the predictions of this model to fill the missing values.

I've included some examples in this notebook for you, which should be fully reproducible if you open it in Google Colab.

Here's the main plot from the notebook - hopefully this gives you a good starting point.

enter image description here

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