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comparison scripts/signal/arch_test.m @ 3499:3e3e14ad5149

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[project @ 2000-01-31 05:18:07 by jwe]
author jwe
date Mon, 31 Jan 2000 05:18:13 +0000
parents d25bc039237b
children e54140b9ebe1
comparison
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3498:e391aeef2b3c 3499:3e3e14ad5149
27 ## conditional heteroscedascity against the alternative of CH(@var{p}). 27 ## conditional heteroscedascity against the alternative of CH(@var{p}).
28 ## 28 ##
29 ## I.e., the model is 29 ## I.e., the model is
30 ## 30 ##
31 ## @example 31 ## @example
32 ## y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t), 32 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t),
33 ## @end example 33 ## @end example
34 ## 34 ##
35 ## @noindent 35 ## @noindent
36 ## given @var{y} up to @var{t}-1 and @var{x} up to @var{t}, 36 ## given @var{y} up to @math{t-1} and @var{x} up to @math{t},
37 ## @var{e}(@var{t}) is @var{N}(0, @var{h}(@var{t})) with 37 ## @math{e}(t) is @math{N(0, h(t))} with
38 ## 38 ##
39 ## @example 39 ## @example
40 ## h(t) = v + a(1) * e(t-1)^2 + ... + a(p) * e(t-p)^2, 40 ## h(t) = v + a(1) * e(t-1)^2 + @dots{} + a(p) * e(t-p)^2,
41 ## @end example 41 ## @end example
42 ## 42 ##
43 ## @noindent 43 ## @noindent
44 ## and the null is @var{a}(1) == ... == @var{a}(@var{p}) == 0. 44 ## and the null is @math{a(1)} == @dots{} == @math{a(p)} == 0.
45 ## 45 ##
46 ## If the second argument is a scalar integer, @var{k}, perform the same 46 ## If the second argument is a scalar integer, @math{k}, perform the same
47 ## test in a linear autoregression model of order @var{k}, i.e., with 47 ## test in a linear autoregression model of order @math{k}, i.e., with
48 ## 48 ##
49 ## @example 49 ## @example
50 ## [1, y(t-1), ..., y(t-@var{k})] 50 ## [1, y(t-1), @dots{}, y(t-@var{k})]
51 ## @end example 51 ## @end example
52 ## 52 ##
53 ## @noindent 53 ## @noindent
54 ## as the @var{t}-th row of @var{x}. 54 ## as the @math{t}-th row of @var{x}.
55 ## 55 ##
56 ## Under the null, LM approximately has a chisquare distribution with 56 ## Under the null, LM approximately has a chisquare distribution with
57 ## @var{p} degrees of freedom and @var{pval} is the @var{p}-value (1 57 ## @var{p} degrees of freedom and @var{pval} is the @math{p}-value (1
58 ## minus the CDF of this distribution at LM) of the test. 58 ## minus the CDF of this distribution at LM) of the test.
59 ## 59 ##
60 ## If no output argument is given, the @var{p}-value is displayed. 60 ## If no output argument is given, the @math{p}-value is displayed.
61 ## @end deftypefn 61 ## @end deftypefn
62 62
63 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> 63 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
64 ## Description: Test for conditional heteroscedascity 64 ## Description: Test for conditional heteroscedascity
65 65