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Diffstat (limited to 'macros/arch_fit.sci')
| -rw-r--r-- | macros/arch_fit.sci | 120 |
1 files changed, 85 insertions, 35 deletions
diff --git a/macros/arch_fit.sci b/macros/arch_fit.sci index 3e431a6..2fa462c 100644 --- a/macros/arch_fit.sci +++ b/macros/arch_fit.sci @@ -1,35 +1,85 @@ -function [A, B] = arch_fit(Y, varargin) -//This functions fits an ARCH regression model to the time series Y using the scoring algorithm in Engle's original ARCH paper. -//Calling Sequence -//[A, B] = arch_fit (Y, X, P, ITER, GAMMA, A0, B0) -//Parameters -//Description -//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. -funcprot(0); -rhs = argn(2); -lhs=argn(1); -if(rhs<7 | rhs>7) -error("Wrong number of input arguments."); -end -if (lhs<2 | lhs>2) - error("Wrong number of output arguments."); -end - - select(rhs) - case 7 then - [A, B] = callOctave("arch_fit",Y, varargin(1), varargin(2), varargin(3), varargin(4), varargin(5), varargin(6)); - end -endfunction +/* +Dependencies : ols, autoreg_matrix +Calling Sequence + [a, b] = arch_fit (y, x, p) + [a, b] = arch_fit (y, x, p, iter, gamma, a0, b0) +Parameters + y(vector) : A time-series data vector up to time t-1 . + x (Matrix): A matrix of (ordinary) regressors x up to t. + p (scalar): The order of the regression of the residual variance. + iter (scaler) : Number of iterations + gamma (real number) : updating factor + a0 b0 (real numbers) : Initial values for the scoring algorithm +Description: + 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 upto 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. +*/ +function [a, b] = arch_fit (y, x, p, iter, gamma, a0, b0) + nargin = argn(2) + if (nargin < 3 || nargin == 6) + error("invalid inputs"); + end + if (~ (isvector (y))) + error ("arch_fit: Y must be a vector"); + end + T = max(size(y)); + y = matrix (y, T, 1); + [rx, cx] = size (x); + if ((rx == 1) && (cx == 1)) + x = autoreg_matrix (y, x); + elseif (~ (rx == T)) + error ("arch_fit: either rows (X) == length (Y), or X is a scalar"); + end + [T, k] = size (x); + if (nargin == 7) + a = a0; + b = b0; + e = y - x * b; + else + [b, v_b, e] = ols (y, x); + zer = zeros(1,p); + a = [v_b zer]'; + if (nargin < 5) + gamma = 0.1; + if (nargin < 4) + iter = 50; + end + end + end + esq = e.^2; + Z = autoreg_matrix (esq, p); + for i = 1 : iter + h = Z * a; + tmp = esq ./ h.^2 - 1 ./ h; + s = 1 ./ h(1:T-p); + for j = 1 : p + s = s - a(j+1) * tmp(j+1:T-p+j); + end + r = 1 ./ h(1:T-p); + for j = 1:p + r = r + 2 * h(j+1:T-p+j).^2 .* esq(1:T-p); + end + r = sqrt (r); + X_tilde = x(1:T-p, :) .* (r * ones (1,k)); + e_tilde = e(1:T-p) .*s ./ r; + delta_b = inv (X_tilde' * X_tilde) * X_tilde' * e_tilde; + b = b + gamma * delta_b; + e = y - x * b; + esq = e .^ 2; + if isempty(esq) then + esq = zeros(size(y)) + end + Z = autoreg_matrix (esq, p); + h = Z * a; + f = esq ./ h - ones (T,1); + Z_tilde = Z ./ (h * ones (1, p+1)); + delta_a = inv (Z_tilde' * Z_tilde) * Z_tilde' * f; + a = a + gamma * delta_a; + end + endfunction |