R help - Jun 2013 - “arch.test” in “vars” package with multivariate.only = FALSE

“arch.test” in “vars” package with multivariate.only = FALSE





The function

arch.test(x, lags.single = 16, lags.multi = 5, multivariate.only = FALSE)

produces the univariate and multivariate parts of the ARCH test



By_t = C+A_1 y_{t-1}+….. A_n y_{t-n}+\epsilon  (homoskedastic VAR)

And then

u_t = B^{-1}\epsilon_t = y_t – (B^{-1}C+B^{-1}A_1 y_{t-1}-......+ B^{-1}
A_n y_{t-n})

u_k(t) is the k-th element of u_t

u_k(t)= c+ \theta_1 u_k(t-1) +  \theta_2 u_k(t-2)+...... \theta_q
u_k(t-q)+\nu_k(t)

Do the univariate parts of the ARCH test refer to the significance test of
the last regression, H_0: \theta_i = 0 for all i against H_1: H_0 is false,
for all k?



Thanks,


Miao

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