In time series forecasting using various models like AR,MA,ARMA, etc, we usually focus on the modeling of the data in the change of time. But when we have 2 time series that Pearson correlation coefficient show they are highly correlated, is it possible to model their dependency and forecast values of one from the other? For example, when one serie have a linear relationship with the other, it seems possible. But is there a general method for this kind of dependency analysis?
The AR, MA, and ARMA models are examples of univariate time series models. Each of these models has a multivariate counterpart: Vector Autogression (VAR), Vector Moving Average (VMA), and Vector Autoregressive Moving Average (VARMA), respectively.
VAR might be the simplest to reason about if you are more familiar with linear regression. An AR(p) model regresses a time series against its p lags. Correspondingly, a VAR(p) model is a series of regressions, such that each series is regressed against its p lags and the p lags of all the other variables. After performing the regressions, you can calculate residuals from each series and evaluate how correlated the residuals are.
As with univariate models, stationarity is also an important issue for multivariate models. This leads to models like the Vector Error Correction Model (VECM), which allows for variables to have share a stable long-term trend with short-term deviations.