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Shuangshuang · 2021年03月07日

问一道题:NO.PZ2020011101000016 [ FRM I ]

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%?

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%

这道题的临界值都是如何查询的呀,麻烦老师给下过程吧 谢谢
1 个答案

品职答疑小助手雍 · 2021年03月07日

嗨,努力学习的PZer你好:


卡方分布表自由度用3,ρ的数量

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努力的时光都是限量版,加油!

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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?

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 = -0.04ρ​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、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 = -0.04ρ​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% 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

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−1)ρ^i2Q_{LB}=T\sum_{i=1}^h(\frac{T+2}{T-1})\wihat\rho_i^2QLB​=T∑i=1h​(T−1T+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% T+2/T-1的分母部分,是怎么算的,为什么不是统一的T-1=100-1=99?

2024-01-09 17:15 1 · 回答

NO.PZ2020011101000016 =3是因为有三个p吗?

2022-01-21 15:11 1 · 回答