Merge pull request #17 from avinashlalotra/masterHEADmaster

Abinash's Work

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