Therefore, the results of an OIR might be sensitive to the order of the variables and it is advised to estimate the above VAR model with different orders to see how strongly the resulting OIRs are affected by that."Remember, it is my will that guided you here. Note that the output of the Choleski decomposition is a lower triangular matrix so that the variable in the first row will never be sensitive to a contemporaneous shock of any other variable and the last variable in the system will be sensitive to shocks of all other variables. In R the irf function of the vars package can be used to optain OIRs by setting the argument ortho = TRUE: oir <- irf(model, impulse = "income", response = "cons", The corresponding orthongonal impulse response function is then # cons 0.002670552 0.004934117 0.007597773įrom this matrix it can be seen that a shock to income has a contemporaneous effect on consumption, but not vice versa. Given the estimated variance-covariance matrix \(P\) the decomposition can be obtained by t(chol(model_summary$covres)) # invest income cons \[\Phi_i = \sum_\), where \(P\) is a lower triangular matrix with positve diagonal elements, which is often obtained by a Choleski decomposition. Mathematically, the FEIR \(\Phi_i\) for the \(i\)th period after the shock is obtained by The departure point of every impluse reponse function for a linear VAR model is its moving average (MA) representation, which is also the forecast error impulse response (FEIR) function. In order to get a better picture of the model’s dynamic behaviour, impulse responses (IR) are used. Since all variables in a VAR model depend on each other, individual coefficient estimates only provide limited information on the reaction of the system to a shock.
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