# Reverse prediction in a time series

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?

• Side note: consider also models that target time specifically, e.g. autoregressive conditional duration (ACD) models. – Richard Hardy Nov 5 '18 at 8:14

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.

• Yes, and multiple values are not invalid solution. Anyway, I was wondering if there is a way to do this. Right now I'm thinking of employing a root search kind of method to do this. Any other ideas will be great to know. – Ira Nov 6 '18 at 9:46