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We have a series of monthly data for 20 months (it is not possible to obtain more data). These are the number of medical consultations encoded in a public hospital and we only have monthly data for two years.

We would like to predict some future values for this series since our goal is to see if doctors are adopting the coding system. Which method do you suggest to use to forecast this kind of series?

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I very much recommend this free online forecasting textbook.

In your specific case, you have a short monthly series, but from what you describe, there likely is not much seasonality involved. It sounds like Exponential Smoothing with trend but without seasonality (also known as "Holt's method") might be right for you. You can implement it easily in Excel, or use the HoltWinters() function in R, or the ets() function in the forecast package for R.

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