Each error term is supposed to be uncorrelated with all lags of itself and lags of the other error terms.Īn arbitrary number of successive forecasts can be calculated, and you must specify an end date for the forecast calculation. The present value of y depends on the intercept v, the lagged value of itself and the other variable, and the error term u. The expression can be written in expanded form as: y 1, t y 2, t = v 1 v 2 + a 1 1 a 1 2 a 2 1 a 2 2 y 1, t - 1 y 2, t - 1 + u 1, t u 2, t If there are 2 variables in a VAR (1) model, the system of equations can be written as: y t = v + A y t - 1 + u t A model may be denoted as being of order p, called VAR(p), containing K endogenous variables. Such variables are only explanatory and are not modelled in the system. ![]() In the analysis, the dependent variables are called endogenous variables. The estimation is made using all common valid observations for the model series in the selected estimation. The analysis yields a report that contains the estimated parameters of the system as well as several statistics that can be used as a test of the system's validity and stability. There is an equation for each variable that explains its evolution based on its own lags and the lags of other variables in the model. A VAR can be thought of as a system of linear regressions, but the emphasis is on using lagged values of the dependent variables to model a set of variables. The main difference from regression analysis is that in VAR you have several dependent variables instead of one. Finally, the VAR analysis has a feature for calculating impulse response, the response of one variable to an impulse in another. By calculating VECM you can estimate the speed at which a dependent variable returns to equilibrium after a change in other variables. The VAR analysis also allows for modelling of cointegrated variables. ![]() In addition to estimating a given system, you can also automatically test different models and let the analysis pick the best one based on information criteria. The analysis can produce fitted values and forecasts for those series. ![]() The Vector autoregression analysis (VAR) estimates the linear dependencies among a few series.
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