We know using models like ARIMA we can do out of sample predictions for a Time Series. i.e. we can know what would be the value v at time t. Can we do the reverse of it, and find at what t will be v a certain value? Like for linear case, v = mt+c; one can find t = (v-c)/m. Is there a way to do this for nonlinear case?
I don't think it is possible, because this assumes that the function $v=f(t)$ is one on one. But that isn't the case for many time series.
Consider a simple case where a time series looks like a sinusoidal function: One value of v will correspond to multiple values of t.