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I have a time series at day level granularity:

Date.      Value
2023-10-01 78945
2023-10-02 78990
2023-10-03 79005
2023-10-04 78999
...

While there are some fluctuations, the overall trend is increasing and we want to estimate when this value will reach a threshold, say, 90000. While standard time series models like Holt-Winters, ARIMA are good for forecasting, I am not sure how to use them to get the exact "runway" like in this case. One way is to calculate growth rate and assume linear growth and find the time, but correct calculation of growth rate is also one problem.

So, I have two questions:

  1. Is there a standard method for calculating when the time series will reach a certain value?
  2. How to correctly measure the growth rate?

One additional requirements: Sudden spikes (absurd increase and decrease) should not decrease/increase the runway abruptly.

Ricky
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    The exact calculation will depend on your model, but this can usually be done. Note that this would estimate when the mean of the series reaches that value; because of "noise", you may see observations beyond your threshold far earlier - simulations can help you here. Your question 2 is hard, especially since forecasters (me included) are big fans of dampening trends, and of course the specific dampening has a huge impact on this calculation. – Stephan Kolassa Dec 06 '23 at 15:17
  • One example with a simple model (uncorrelated conditional responses) is given at https://stats.stackexchange.com/questions/206531. – whuber Dec 06 '23 at 15:20

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