Econometrics Toolbox: estimate the probability of different time series predicitions

Hello,

Please help me with the following:

Consider a time series of length N=100 (100 observations).

An ARIMA model is constructed to fit the series with "estimate".

Different future realizations can be calculated with "forecast", for example 30.

This means that we have 30 different forecasts of the initial time series (consider also that prediction horizon spans at 100 future time steps).

Is there a way to find the probability of each of the 30 realizations?

Thank you very much.

Best,

Pavlos

Answer 1

[Roger Wohlwend]

If you know the distribution of the returns you could calculate the probability. However, the probability of a path with 30 steps is probably very, very small. I doubt that such a number is useful. I have never seen somebody do it - neither in an article nor in a book. What people usually do is calculating the probability that the final value - only the final value, not the entire path - is in a certain range.