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Function List:

C++ API

: [pval, lm] = arch_test (y, x, p)

For a linear regression model 

y = x * b + e

perform a Lagrange Multiplier (LM) test of the null hypothesis of no conditional heteroscedascity against the alternative of CH(p).

I.e., the model is 

y(t) = b(1) * x(t,1) + … + b(k) * x(t,k) + e(t),

given y up to t-1 and x up to t, e(t) is N(0, h(t)) with 

h(t) = v + a(1) * e(t-1)^2 + … + a(p) * e(t-p)^2,

and the null is a(1) == … == a(p) == 0.

If the second argument is a scalar integer, k, perform the same test in a linear autoregression model of order k, i.e., with 

[1, y(t-1), …, y(t-k)]

as the t-th row of x.

Under the null, LM approximately has a chisquare distribution with p degrees of freedom and pval is the p-value (1 minus the CDF of this distribution at LM) of the test.

If no output argument is given, the p-value is displayed.

Package: octave