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胖胖 · 2023年10月29日

AR(2) and first differencing, Dickey fuller difference

What is the difference in the equation for AR(2) and first differencing? and also Dickey fuller test? I want to know how the equation is different from each other.


AR(2) comes after AR(1) and uses t-2 to explain t


Dicky fuller is used to test for covariance stationary


I understand that first differencing is used to correct for covariance stationary but could you explain the difference between the appearance of the equation for AR(2) vs first differencing?


They look very similar because first differencing subtracts y(t-1) on both sides of the equation

Original equation

yt= bo+b1y(t-1)


Dickey fuller becomes - subtract both sides by y(t-1)

y(t)- y(t-1) = bo+(b1-1)y(t-1)


Isn't first differencing the same as dickey fuller then?

1 个答案

星星_品职助教 · 2023年10月30日

同学你好,

1)AR(2)是在AR(1)后面加一项;即从Xt = b0 + b1Xt-1,变为Xt = b0 + b1Xt-1 + b2Xt-2;

2)first difference是将原对Xt做回归的AR模型,改成对一阶差分后的Yt做回归;即从Xt = b0 + b1Xt-1,变为Yt = c0 + c1Yt-1,其中Yt=Xt - Xt-1

3)DF test不是模型,是假设检验。是在原模型Xt = b0 + b1Xt-1 的两侧同时减Xt-1,模型并没有变化。目的是将系数从b1转化为b1-1。即从Xt = b0 + b1Xt-1,变为Xt -Xt-1= b0 + (b1-1)Xt-1。可见等式右侧的 (b1-1)Xt-1并不是一阶差分的形式。

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