# Predict change in variable

Probably this is easy to answer, but let me formulate the question: If we have a variable $$Y_t$$ measured over time and cross-sectionally, and we calculate the change of this variable from $$t-1$$ to $$t$$, let's call it $$\Delta Y_t$$. Next, we want to predict this $$\Delta Y_t$$ at time $$t$$ using several predictors (let's call them $$a$$ and $$b$$ for simplicity). My question is as follows: Can we use $$a$$ and $$b$$ at time $$t-1$$, or do they need to be measured at $$t-2$$? I am asking because $$\Delta Y_t$$ also contains information from period $$t-1$$ (logically, as it is the change from $$t-1$$ to $$t$$), so does that lead to any problems in the regression model?

Before trying any modeling with time series, it is important to make sure that time-series you have is stationary. In simple words, it means that, if you select random consecutive sample sizes of n from this time-series they will have equal covariances. One considers time series purely stationary if and only if it complies to the following: