[Gretl-devel] multivariate ARCH test for VARs

Following up on Sven at http://lists.wfu.edu/pipermail/gretl-devel/2017-March/007508.html Thanks for another nice hansl prototype! I've now implemented this in C and you can access it after estimating a VAR, with modtest [horizon] --arch --multivariate (--multivariate is currently a "secret" option). Lutkepohl provides some example results (2005, p. 578) but unfortunately in this case they're based on a dataset that has apparently not been made public (Volkswagen daily stock returns). However I've done some basic testing: * The test seems to be sized about right, based on Monte Carlo using varsimul() -- thanks, Jack! -- with plain mnormal() errors. * I've verified that the new test collapses to equivalence with our existing univariate ARCH test for a "VAR" with a single variable. Well, almost: there's a small difference in that our univariate test skips missing lagged residuals at the start of the sample range while the new one substitutes zeros. For anyone wanting to mess with this, here's my Monte Carlo script: <hansl> set verbose off scalar T = 200 # coeffs from Lutkepohl's VW example matrix A = {0, 0.02, -0.18, 0.16, -0.08, 0.11 ;\ 0.12, -0.13, -0.08, 0.03, -0.01, 0.01 } matrix y0 = zeros(3, 2) n = T + 3 nulldata n --preserve setobs 12 2000:01 K = 5000 matrix rej05 = zeros(K, 3) matrix rej01 = zeros(K, 3) matrix pv loop i=1..K -q matrix U = mnormal(T, 2) matrix Y = varsimul(A, U, y0) series y1 = Y[,1] series y2 = Y[,2] smpl 4 ; var 3 y1 y2 --silent modtest 6 --arch --multivariate --quiet pv = $pvalue rej05[i, 1] = pv[1] < 0.05 rej05[i, 2] = pv[3] < 0.05 rej05[i, 3] = pv[6] < 0.05 rej01[i, 1] = pv[1] < 0.01 rej01[i, 2] = pv[3] < 0.01 rej01[i, 3] = pv[6] < 0.01 smpl full endloop sz05 = sumc(rej05) / K sz01 = sumc(rej01) / K print sz05 print sz01 </hansl> Allin