Hi, iterated multistep forecasts are quite different from direct multistep forecasts.

If you are interested in forecasts h-step ahead, in the iterated approach you construct this forecast as a function of forecasts at shorter horizons (h-1,h-2,h-3, etc).

In the direct approach you build your h-step ahead forecasts directly, without relying on forecasts at shorter horizons.

For instance, in an driftless AR(1) process with Rho autoregressive parameter, your h-step ahead forecasts (f(h)) is given by f(h)= Rho*f(h-1). So you have a recursion or an iterative method in which h-step-ahead forecasts depend on forecasts at shorter horizons.

You do need some sort of autoregressive structure to compute iterated multistep forecasts.

In sharp contrast, you can build h-step ahead forecasts directly using a regression between Y(t+h) and x(t) for instance:

Y(t+h)=a+b*x(t)+error

Here your forecast for Y(t+h) will be f(h)=a+b*x(t)

You can do the same if you are interested in a different forecast horizon "k". You can use the following regression:

Y(t+k)=A+B*x(t)+ERROR

and your k-step ahead forecast will be f(k)=A+B*x(t)

Cap "A" and small "a" will be different, however. The same happens with "B" and "b" .

These are direct forecasts and you don´t need to know f(k) to build f(h) or viceversa.

I guess with probit and logit models the same logic applies.

Hope it helps!!

Iterated forecast need a series of steps to arrive at the final solution. Direct foreast arrive at the final solution without these iterated steps.