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C++ API

: [a, b] = arch_fit (y, x, p, iter, gamma, a0, b0)

Fit an ARCH regression model to the time series y using the scoring algorithm in Engle’s original ARCH paper.

The model is 

y(t) = b(1) * x(t,1) + … + b(k) * x(t,k) + e(t),
h(t) = a(1) + a(2) * e(t-1)^2 + … + a(p+1) * e(t-p)^2

in which e(t) is N(0, h(t)), given a time-series vector y up to time t-1 and a matrix of (ordinary) regressors x up to t. The order of the regression of the residual variance is specified by p.

If invoked as arch_fit (y, k, p) with a positive integer k, fit an ARCH(k, p) process, i.e., do the above with the t-th row of x given by 

[1, y(t-1), …, y(t-k)]

Optionally, one can specify the number of iterations iter, the updating factor gamma, and initial values a0 and b0 for the scoring algorithm.

Package: octave