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Vector Autoregressions - Social Science Computing …

Vector Autoregressions VAR: Vector autoregression Nothing to do with VaR: Value at Risk (finance). Multivariate autoregression Multiple equation model for joint determination of two or more variables One of the most commonly used models for applied macroeconometric analysis and forecasting in central banks Two-Variable VAR. Two variables: y and x Example: output and interest rate Two-equation model for the two variables One-Step ahead model One equation for each variable Each equation is an autoregression plus distributed lag, with p lags of each variable VAR(p) in 2 Variables yt = 1 + 11 yt 1 + 12 yt 2 + + 1 p yt p + 11 xt 1 + 12 xt 1 + + 1 p xt p + e1t xt = 2 + 21 yt 1 + 22 yt 2 + + 2 p yt p + 21 xt 1 + 22 xt 1 + + 2 p xt p + e2t Multiple Equation System In general: k variables An equation for each variable Each equation includes p lags of y and p lags of x (In principle, the equations could have different #.)

Vector Autoregressions • VAR: Vector AutoRegression – Nothing to do with VaR: Value at Risk (finance) • Multivariate autoregression • Multiple equation model for joint determination of two or more variables • One of the most commonly used models for applied macroeconometric analysis and forecasting in central banks

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