Suppose, I have a data for rate that shows growth and decay of a process that is function of time. So, I can forecast the rate n-steps ahead in time. But how do I forecast what will be time for a certain value of the rate?
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As I understand it, you are interested in the times when a particular time-dependent function reaches a target value. One possibility would be to densely interpolate the process (i.e. with small time steps), subtract the threshold, and then take the absolute value of these residuals. The closer a point is to zero, the closer it is to your target threshold.
You might want to include a small 'noise' buffer, accepting all points within some range of zero, to account for the fact that the data is noisy and may not intersect precisely at the timepoints you have interpolated the function to. The operation would simply be the following, where theta is your target value and epsilon is your noise buffer.
$$ abs(f[t] - \theta) \leqslant \epsilon $$
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$\begingroup$ This is exactly I wanted to do with this : stats.stackexchange.com/questions/244524/… $\endgroup$ Commented Nov 7, 2016 at 16:36
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$\begingroup$ Ah I see, that wasn't so clear from your last question. Sorry about that! $\endgroup$ Commented Nov 7, 2016 at 16:38
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$\begingroup$ So, what I do know? Please help. $\endgroup$ Commented Nov 7, 2016 at 16:39
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$\begingroup$ Are you having a problem conceptually or with implementing it as code? $\endgroup$ Commented Nov 7, 2016 at 16:41
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$\begingroup$ This question is the conceptual problem. The last question stats.stackexchange.com/questions/244524/… was requiring the implementation of this concept $\endgroup$ Commented Nov 7, 2016 at 16:42