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Diffstat (limited to 'macros/arch_test.sci')
| -rw-r--r-- | macros/arch_test.sci | 104 |
1 files changed, 58 insertions, 46 deletions
diff --git a/macros/arch_test.sci b/macros/arch_test.sci index 3c53fc5..5cb8ed8 100644 --- a/macros/arch_test.sci +++ b/macros/arch_test.sci @@ -1,46 +1,58 @@ -function [PVAL, LM]= arch_test(Y,X,P) -// perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P) -//Calling Sequence -//arch_test(Y,X,P) -//PVAL = arch_test(Y,X,P) -//[PVAL, LM]= arch_test(Y,X,P) -//Parameters -//P: Degrees of freedom -//PVAL:PVAL is the p-value (1 minus the CDF of this distribution at LM) of the test -//Description -//perform a Lagrange Multiplier (LM) test of thenull 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 sametest in a linear autoregression model of orderk, i.e., with -// -// [1, y(t-1), ..., y(t-K)] as the t-th row of X. -// -// Under the null, LM approximatel 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. - funcprot(0) - rhs= argn(2); - lhs= argn(1); - if(rhs<3 | rhs>3) - error("Wrong number of input arguments"); - end - if(lhs<1 | lhs>2) - error("Wrong number of output arguments"); - end - select(rhs) - case 3 then - select(lhs) - case 1 then - PVAL= callOctave("arch_test", Y, X, P); - case 2 then - [PVAL,LM]= callOctave("arch_test", Y, X, P); - end - end -endfunction
\ No newline at end of file +/* +Description: + Perform a Lagrange Multiplier (LM) test for conditional heteroscedasticity. + 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. + Calling Sequence + [pval, lm] = arch_test (y, x, p) + Parameters + y: Array-like. Dependent variable of the regression model. + x: Array-like. Independent variables of the regression model. If x is a scalar integer k, it represents the order of autoregression. + p : Integer. Number of lagged squared residuals to include in the heteroscedasticity model. + Returns: + pval: Float. p-value of the LM test. + lm: Float. Lagrange Multiplier test statistic.*/ + Dependencies : ols, autoreg_matrix +//helper function +function cdf = chi2cdf ( X, n) + df = resize_matrix ( n , size (X) , "" , n); + [cdf,Q] = cdfchi ( "PQ" , X ,df); +endfunction +//main function +function [pval, lm] = arch_test (y, x, p) + nargin = argn(2) + if (nargin ~= 3) + error ("arch_test: 3 input arguments required"); + end + if (~ (isvector (y))) + error ("arch_test: 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_test: either rows (X) == length (Y), or X is a scalar"); + end + if (~ (isscalar (p) && (modulo (p, 1) == 0) && (p > 0))) + error ("arch_test: P must be a positive integer"); + end + [b, v_b, e] = ols (y, x); + Z = autoreg_matrix (e.^2, p); + f = e.^2 / v_b - ones (T, 1); + f = Z' * f; + lm = f' * inv (Z'*Z) * f / 2; + pval = 1 - chi2cdf (lm, p); +endfunction |