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-rw-r--r--macros/arch_fit.sci44
1 files changed, 22 insertions, 22 deletions
diff --git a/macros/arch_fit.sci b/macros/arch_fit.sci
index 2fa462c..b38996a 100644
--- a/macros/arch_fit.sci
+++ b/macros/arch_fit.sci
@@ -1,26 +1,26 @@
-/*
-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)
+// Fit 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)
+// [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.
+
nargin = argn(2)
if (nargin < 3 || nargin == 6)
error("invalid inputs");