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第四章 進階迴歸分析 PowerPoint PPT Presentation


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第四章 進階迴歸分析. 常見涉及誤差變異之問題 若誤差項不符合變異數相同的假說,則可能產生異值變異 (heteroskedasticity )的問題 若誤差項不符合獨立的假設,則可能產生自我相關 (autocorrelation) 的問題,即誤差項與前期的誤差相關 如何發現上述問題? 最快的方法是觀察殘差圖,再以統計檢定確定 如何修正? 對異值變異採用 WLS 法,對自我相關資料採用 AR(1) 模式. 殘差圖. 以殘差或 t 化殘差為縱軸的分散圖,或殘差的分佈圖,稱為 殘差圖 。.

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第四章 進階迴歸分析

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6565985

  • (heteroskedasticity

  • (autocorrelation)

  • WLSAR(1)


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t

t-( Student residual) MSE ei -3 3

  • :

    • t , ,

    • Y X


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()

:

95%


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1. X

fig1

2. X

fig2

3. X,

fig3

4.

()

fig4

5.

fig5


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ei = 0

fig1

fig2


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fig3

fig4


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fig5


Gls ols

GLS OLS

  • Yt = 0+ 1X 1t +.+ kX kt +t

    t ~ NID( 0, 2)

Cov(i, j)

Var(i)

  • (generalized least square method), GLS


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  • ij =0, for i j

  • ii2 =2

  • (ordirnary least square method), OLS


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  • (Heteroskedasticity)

  • x x

    • White test

    • Breusch-Pagan/Godfrey test

    • Goldfeld-Quandt test


White test

White test

    • X X

    • (R2)

  • White nR2 q q=(k-1)(k+2)/2


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White test :

White test :

SAS tip

Analysis Regression Linear

Statistics Diagnostics Heteroscedasticity test


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  • WLS

  • Yt = 0+ 1X 1t +t , var(t)= Zt2

    ZtXtXt

  • Zt1/Zt


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:

i(WLS)

:

Normal Equation: (XWX) bw = XWY

: bw = (XWX)-1 XWY

: {bw} = (XWX)-1 XWY


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:

1.

2.

wt

3. wt WLS

4.

SAS tip

wt relative weight


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(OLS )

(WLS , X-2 )


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  • ij 0, for i j


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(autocorrelation)

X(salec)Y

R2=0.999

()


Lag s

Lag s

  • (autocorrelation)

    • s


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  • MSE

  • s.e.{bk}

  • t-testF-testconfidence interval


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  • first-order autocorrelation t t-1

  • 1 = cor(t , t-1 ) for all t

  • 1.

    2. Durbin-Watson

    (t t-1 et et-1 )


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-- Durbin-Watson Test

Durbin-Watson

1 D 2(1-r1)0D4

2SAS regression / linear Time series/

Reg. w. Autoregressive error D-W

3 n, p, dL, dU,


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H0 1= 0 H11> 0

  • D < dL, H0

  • D > dU, H0

  • dL, <D < dU,()

1>0 1=0 1<0

0 dL dU 2 4-dU 4-dL 4


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H0 1= 0H11<0

  • (4-D) < dL, H0

  • (4-D) > dU, H0

  • dL, < (4-D) < dU,()

r1 >0 0< D < 2 r1 < 0 2< D < 4

r1 =1-hat


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X(salec)

Y (salei)

X-Y


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SAS/EG / regression/ linear

(dL=1.2. dU=1.36)

D=3.05 > 4-dL, R2


First order autocorrelative reg model

First-order autocorrelative reg. model

AR(1) errors model, AR(1) model.

AR(1) Model :

Yt = 0 + 1 xt + t , t= 1,2,, n

t = t-1 + ut , ||<1, ut ~NID(0,2)

SAS tip

Analyze Time series Reg. w Autoregressive Errors


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: 1=0

2

3t = 1t-1 + 2t-2 + ut ,

AR(2) model


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X(saleC)

Y (salei)

Time series / Reg. w Autoregressive Errors


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AR(1)

yt = 8.974 + 5.643 xt + t , t = -0.542t-1


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