Is there a "reverse" time series models?

Traditional time series model of order p take in account periods of time less or equal to p. I would like to know if there is a model that considers periods of time greater or equal than p.

For instance, an AR(2) takes the form:

However, I want a model that would take the form:

Why do I need it? For forecasting. Let's say I want a time series model that can predict something with 3 days in advance. The traditional models with order 3 would not help me, since it also needs values from yesterday and the day before.

In these types of forecasting models, predictions are usually generated recursively: we first predict the first step ahead, then use the first predicted value to predict the second step ahead, then use the second predicted value to predict the third step ahead, and so on. If you're only interested in the third step ahead, you can simply ignore the previous predicted values. So there is no need to reformulate the model.

A more detailed description can be found here: https://otexts.com/fpp2/arima-forecasting.html