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2.1. UNRESTRICTED VECTOR AUTOREGRESSIONS 29The effect on q 1t at time k of a one standard deviation orthogonalizedinnovation in η 1 at time 0, is b 11,k . Similarly, the effect on q 2k is b 21,k .Graphing the transformed moving-average coefficients is an efficientmethod to examine the impulse responses.You may also want to calculate standard error bands for the impulseresponses. You can do this using the following parametric bootstrapprocedure. 5 Let T be the number of time-series observations you haveand let a ‘tilde’ denote pseudo values generated by the computer, then ⇐(12) ‘tilde’1. Take T + M independent draws from the N(0, ˆΣ) to form thevector series {˜² t }.2. Set startup values of q tat their mean values of 0 then recursivelygenerate the sequence {˜q t } of length T + M according to (2.1)using the estimated A j matrices.3. Drop the Þrst M observations to eliminate dependence on startingvalues. Estimate the simulated VAR. Call the estimated coefficientsà j .4. Form the matrices ˜B j = ˜C j ˜Λ −1˜S. You now have one realization ⇐(13)of the parametric bootstrap distribution of the impulse responsefunction.5. Repeat the process say 5000 times. The collection of observationson the ˜B j forms the bootstrap distribution. Take the standarddeviation of the bootstrap distribution as an estimate of the standarderror.Forecast-Error Variance DecompositionIn (2.7), you have decomposed q 1t into orthogonal components. Theinnovation η 1t is attributed to q 1t and the innovation η 2t is attributed5 The bootstrap is a resampling scheme done by computer to estimate the underlyingprobability distribution of a random variable. In a parametric bootstrapthe observations are drawn from a particular probability distribution such as thenormal. In the nonparametric bootstrap, the observations are resampled from thedata.