Direct multi-step forecasting an integrated time series from a stationary model

Question

I am new to time series analysis. But I am well versed in data science and machine learning. One thing that confused me was modeling the data. For example, I want to create an LSTM or regression model, I have stationarized all my variables (first-order differences). My dependent variable/target is stationary and I can now predict $t+1$, but my goal is to predict value $t+8$ with the data at time $t$ with a model $$ \Delta_8 Y_{t+8}\equiv Y_{t+8} - Y_t=\beta X_{1t}+\beta X_{2t}+....+\beta X_{10t} $$ (direct multi-step forecast).

My question here is whether it is the right approach to forecast the change between the target variable ($\Delta_8 Y_{t+8}=Y_{t+8} - Y_t$) , i.e. its value now and its value eight hours later?

According to time series approaches and theories, does summing differences/deltas cause stationarity, unit root or any other time series related problem?

Answer 1

Stationarity is needed for obtaining well-behaved parameter estimates of the model. Once that is done, you can obtain the forecast $\hat Y_{t+8}$ of $Y_{t+8}$ by $Y_t+\widehat{\Delta_8 Y}_{t+8}$. This step is not invalidated by concerns of unit roots and such.