为什么df=3？为什么用卡方分布？

NO.PZ2020011101000016

问题如下：

Suppose you observed sample autocorrelations $\widehat\rho_1 = 0.24, \widehat\rho_2 = -0.04$ , and $\widehat\rho_3 = 0.08$ 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%?

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解释：

The test statistic is

$Q_{LB}=T\sum_{i=1}^h(\frac{T+2}{T-1})\widehat\rho_i^2$

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

$=5.93+0.16+0.67=6.77$

The critical values for tests sizes of 10%, 5%, and 1% are 6.25, 7.81, and 11.34, respectively. (CHISQ.INV(1- $\alpha$ , 3) in Excel, where $\alpha$ 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？

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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 = -0.04ρ1=0.24,ρ2=−0.04, anρ^3=0.08\wihat\rho_3 = 0.08ρ3=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)ρi2=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？

2024-08-13 09:09 2 · 回答

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 = -0.04ρ1=0.24,ρ2=−0.04, anρ^3=0.08\wihat\rho_3 = 0.08ρ3=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)ρi2=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、为什么有三个autocorrelation，自由度就是3？自由度就是可以自由变动的变量个数？2、这里的p都是指残差的p吧？是估计值和真实值之间的残差？

2024-05-07 21:32 3 · 回答

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 = -0.04ρ1=0.24,ρ2=−0.04, anρ^3=0.08\wihat\rho_3 = 0.08ρ3=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)ρi2=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% 为什么是3，题干是3个P，没说有四个X 变量。怎么分析得出是3呢？

2024-01-29 10:07 1 · 回答

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2024-01-09 17:15 1 · 回答

为什么df=3？为什么用卡方分布？

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