内容发布更新时间 : 2024/12/23 18:37:49星期一 下面是文章的全部内容请认真阅读。
_cons | .0000119 .0000104 1.14 0.253 -8.52e-06 .0000324 ------------------------------------------------------------------------------
为使上述的模型估计变得清楚明了,我们可以将模型表示为:
虽然arch系数0.204是不显著,但是ARCH(1)和GARCH(1)系数整体是显著的。我们可以通过下面来进行检验:
. test [ARCH]L1.arch [ARCH]L1.garch
( 1) [ARCH]L.arch = 0 ( 2) [ARCH]L.garch = 0
chi2( 2) = 84.92 Prob > chi2 = 0.0000
3.4 非对称效应的EGARCH模型 还是以美国的WPI数据为例,我们可能认为整个经济对于整体物价的异常上涨产生的波动要比异常的下降大。可能异常的上涨导致影响存货的现金流问题从而导致更大的波动。数据中存在这种不对称效应,就需要对原先的ARCH模型加以修正,EGARCH模型就是修正的结果。
. use http://www.stata-press.com/data/r11/wpi1,clear
. arch D.ln_wpi,ar(1) ma(1 4) earch(1) egarch(1)
ARCH family regression -- ARMA disturbances
Sample: 1960q2 - 1990q4 Number of obs = 123 Distribution: Gaussian Wald chi2(3) = 156.04 Log likelihood = 405.3145 Prob > chi2 = 0.0000
------------------------------------------------------------------------------ | OPG
D.ln_wpi | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ln_wpi |
_cons | .0087355 .0034008 2.57 0.010 .0020702 .0154009 -------------+---------------------------------------------------------------- ARMA | ar |
L1. | .76923 .0968298 7.94 0.000 .579447 .959013 |
ma |
L1. | -.3554615 .1265657 -2.81 0.005 -.6035258 -.1073972 L4. | .2414685 .0863807 2.80 0.005 .0721655 .4107715 -------------+---------------------------------------------------------------- ARCH | earch |
L1. | .4064263 .1163501 3.49 0.000 .1783842 .6344684 | earch_a |
L1. | .2467514 .1233374 2.00 0.045 .0050145 .4884883 | egarch |
L1. | .8417241 .0704075 11.96 0.000 .7037279 .9797204 |
_cons | -1.488437 .6604335 -2.25 0.024 -2.782863 -.194011 ------------------------------------------------------------------------------
方差模型的结果如下:
3.4 限制条件的ARCH模型 条件方差模型可以设定为:
在stata里,运行出来的模型是:
例子:
. use http://www.stata-press.com/data/r11/wpi1,clear . constraint 1 (3/4)*[ARCH]l1.arch=[ARCH]l2.arch . constraint 2 (2/4)*[ARCH]l1.arch=[ARCH]l3.arch . constraint 3 (1/4)*[ARCH]l1.arch=[ARCH]l4.arch
. arch D.ln_wpi,ar(1) ma(1 4) arch(1/4) constraints(1/3)
ARCH family regression -- ARMA disturbances
Sample: 1960q2 - 1990q4 Number of obs = 123 Distribution: Gaussian Wald chi2(3) = 123.32 Log likelihood = 399.4624 Prob > chi2 = 0.0000
( 1) .75*[ARCH]L.arch - [ARCH]L2.arch = 0 ( 2) .5*[ARCH]L.arch - [ARCH]L3.arch = 0 ( 3) .25*[ARCH]L.arch - [ARCH]L4.arch = 0
------------------------------------------------------------------------------ | OPG
D.ln_wpi | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ln_wpi |
_cons | .0077204 .0034531 2.24 0.025 .0009525 .0144883 -------------+---------------------------------------------------------------- ARMA | ar |
L1. | .7388168 .1126811 6.56 0.000 .517966 .9596676 | ma |
L1. | -.2559691 .1442861 -1.77 0.076 -.5387646 .0268264 L4. | .2528922 .1140185 2.22 0.027 .02942 .4763644 -------------+---------------------------------------------------------------- ARCH | arch |
L1. | .2180138 .0737787 2.95 0.003 .0734101 .3626174 L2. | .1635103 .055334 2.95 0.003 .0550576 .2719631 L3. | .1090069 .0368894 2.95 0.003 .0367051 .1813087 L4. | .0545034 .0184447 2.95 0.003 .0183525 .0906544 |
_cons | .0000483 7.66e-06 6.30 0.000 .0000333 .0000633 ------------------------------------------------------------------------------
四、VAR 模型
向量自回归介绍:
当我们对变量是否真是外生变量的情况不自信时,传递函数分析的自然扩展就是均等地对待每一个变量。在双变量情况下,我们可以令{yt}的时间路径受序列{zt}的当期或过去的实际值的影响,考虑如下简单的双变量体系
式(5.17)和(5.18)并非是诱导型方程,因为yt对zt有一个同时期的影响,而zt对yt也有一个同时期的影响。所幸的是,可将方程转化为更实用的形式,使用矩阵性代数,我们可将系统写成紧凑形式:
其中
也等价于:
在实际的应用估计中,我们并不能够直接估计出结构性VAR方程,因为在VAR过程中所固有的反馈,直接进行估计的话,则zt与误差项?yt相关,yt与误差项?zt相关,但是标准估计要求回归变量与误差项不相关。