Vector autoregression  Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregressive model (AR model) by allowing for more than one evolving variable. All variables in a VAR enter the model in the same way: each variable has an equation explaining its evolution based on its own lagged values, the lagged values of the other model variables, and an error term. VAR modeling does not require as much knowledge about the forces influencing a variable as do structural models with simultaneous equations: The only prior knowledge required is a list of variables which can be hypothesized to affect each other intertemporally. A VAR model describes the evolution of a set of "k" variables (called "endogenous variables") over the same sample period ("t" = 1, ..., "T") as a linear function of only their past values. The variables are collected in a "k"-vector (("k" × 1)-matrix) "yt", which has as the "i" th element, "y""i","t", the observation at time "t" of the "i" th variable. For example, if the "i" th variable is GDP, then "y""i","t" is the value of GDP at time "t". A "p-th order VAR", denoted VAR("p"), is  where the observation "y""t"−i (i periods back) is called the i-th lag of "y", "c" is a "k"-vector of constants (intercepts), "Ai" is a time-invariant ("k" × "k")-matrix and "e""t" is a "k"-vector of error terms satisfying   A "p"th-order VAR is also called a VAR with "p" lags. The process of choosing the maximum lag "p" in the VAR model requires special attention because inference is dependent on correctness of the selected lag order. Note that all variables have to be of the same order of integration. The following cases are distinct:   One can stack the vectors in order to write a VAR("p") as a stochastic matrix difference equation, with a concise matrix notation:  Details of the matrices are in a separate page. For a general example of a VAR("p") with "k" variables, see General matrix notation of a VAR(p).