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小王爱学习 · 2022年01月21日

为什么df=3?为什么用卡方分布?

NO.PZ2020011101000016

问题如下:

Suppose you observed sample autocorrelations ρ^1=0.24,ρ^2=0.04\widehat\rho_1 = 0.24, \widehat\rho_2 = -0.04, and ρ^3=0.08\widehat\rho_3 = 0.08 in a time series with 100 observations. Would a Ljung-Box Q statistic reject its null hypothesis using a test with a size of 5%? Would the test reject the null using a size of 10% or 1%?

选项:

解释:

The test statistic is

QLB=Ti=1h(T+2T1)ρ^i2Q_{LB}=T\sum_{i=1}^h(\frac{T+2}{T-1})\widehat\rho_i^2

=100(102/99)(0.24)2+100(102/98)(0.04)2+100(102/97)(0.08)2=100*(102/99)(0.24)^2+100*(102/98)(-0.04)^2+100*(102/97)(0.08)^2

=5.93+0.16+0.67=6.77=5.93+0.16+0.67=6.77

The critical values for tests sizes of 10%, 5%, and 1% are 6.25, 7.81, and 11.34, respectively. (CHISQ.INV(1-α\alpha, 3) in Excel, where α\alpha is the test size). The null is only be rejected using a size of 10%

df=3是因为有三个p吗?

1 个答案

DD仔_品职助教 · 2022年01月21日

嗨,从没放弃的小努力你好:


同学你好,

因为这个是LBQ test,所以要用卡方分布来查找critical value。

是的,因为给出的autocorrelation有三个,所以自由度=3。

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NO.PZ2020011101000016问题如下 Suppose you observesample autocorrelations ρ^1=0.24,ρ^2=−0.04\wihat\rho_1 = 0.24, \wihat\rho_2 = -0.04ρ​1​=0.24,ρ​2​=−0.04, anρ^3=0.08\wihat\rho_3 = 0.08ρ​3​=0.08 in a time series with 100 observations. Woula Ljung-Box Q statistic rejeits null hypothesis using a test with a size of 5%? Woulthe test rejethe null using a size of 10% or 1%? The test statistic is QLB=T∑i=1h(T+2T−i)ρ^i2Q_{LB}=T\sum_{i=1}^h(\frac{T+2}{T-i})\wihat\rho_i^2QLB​=T∑i=1h​(T−iT+2​)ρ​i2​=100∗(102/99)(0.24)2+100∗(102/98)(−0.04)2+100∗(102/97)(0.08)2=100*(102/99)(0.24)^2+100*(102/98)(-0.04)^2+100*(102/97)(0.08)^2=100∗(102/99)(0.24)2+100∗(102/98)(−0.04)2+100∗(102/97)(0.08)2=5.93+0.16+0.67=6.77=5.93+0.16+0.67=6.77=5.93+0.16+0.67=6.77The criticvalues for tests sizes of 10%, 5%, an1% are 6.25, 7.81, an11.34, respectively. (CHISQ.INV(1-α\alphaα, 3) in Excel, where α\alphis the test size). The null is only rejecteusing a size of 10% 1、“卡方分布表自由度用3,ρ的数量”这里的意思是指,e1和e2,e1和e3,e1和e4,一共三个p,所以是4个e,所以自由度是3?2、这题的假设检验Ha至少有一个p不等于0,拒绝域为什么不是在两边?之前学的检验 H0:方差1=方差2 Ha方差1不等于方差2用(n-1)*样本方差/假设估计的方差,这个拒绝域我怎么记得是在两边?

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