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Time series analysis

Time series analysis. R98229029 陳漢卿. ENSO & ACW. -36. -30. -24. -18. -12. -6. 0(ENSO). Data source.

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Time series analysis

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  1. Time series analysis R98229029 陳漢卿

  2. ENSO & ACW

  3. -36 -30 -24 -18 -12 -6 0(ENSO)

  4. Data source Time sequences of amplitudes associated with the dominant EOF modes of interannual zonal surface wind monthely anomalies for the 52-year record from 1950 through 2001 from NCEP/NCAR reanalysis. Displayed in units of standard deviation.

  5. Data preprocess • Isolate the 3.5- and 5.5-year period interannual signals from higher and lower- frequency signals by band-pass filtering using a period admittance window with half power points at 3-and 7-year period. • Monthly anomaly of ZSW was computed about long-term monthly means defining the mean cycle over the 52-years record.

  6. 全期分析 • Mean~0 • STD=1

  7. 兩段時間分析 1950-1977(PC1) Mean=0.055 STD=1.004 1978-2001(PC2) Mean=-0.0645 STD=0.9924

  8. 平均數差異統計檢定 • Use t-test of the null hypothesis in the PC1 and PC2.Assume that the mean of PC1 and PC2 are equal. The result of the test is returned in h = 0 indicates a failure to reject the null hypothesis at the 5% significance level. • That’s mean PC1 and PC2 have same mean.

  9. 變異數差異統計檢定 • Use f-test of the null hypothesis in the PC1 and PC2.Assume that the variance of PC1 and PC2 are equal. The result of the test is returned in H = 0 indicates a failure to reject the null hypothesis at the 5% significance level. • That’s mean PC1 and PC2 have same variance.

  10. 自相關分析 • ACF 指數衰減，PACF則是N>3後截斷 判斷應該為一適合AR(3) model的時間數列。

  11. 趨勢分析 一次回歸方程 Y = -0.0001X + 0.0467

  12. 趨勢分析 五次回歸方程

  13. 一次回歸方程 Y = 0.0003X + 0.0100 Y = 0.0010X - 0.2042

  14. 二次回歸方程

  15. 突變點分析 滑動平均t-test

  16. ARMA model • 利用ARMA model (p,q)=(10,9)時有最小的AIC=-10.0326 • 得到的ARMA model Φ(B)*X(t)=θ(B)*ε(t) • Φ(B)=1 - 4.439 B^1 + 8.809 B^2 - 10.31 B^3 + 7.207 B^4 - 1.407 B^5 - 3.461 B^6 + 4.816 B^7 - 3.013 B^8 +0.8462 B^9 - 0.0514 B^10 θ(B)= 1 - 0.3478 B^1 - 1.121 B^2 + 1.244 B^3 - 0.6484 B^4 - 0.5076 B^5 + 0.9255 B^6 - 1.078 B^7 - 0.1464 B^8 + 0.6975 B^9

  17. ARMA model 此model模擬的擬合性算相當不錯，但是會有一些高頻訊號出現。

  18. ARMA model 此model模擬的擬合性算相當不錯，但是會有一些高頻訊號出現。

  19. ZSW & nino3.4 index相關分析

  20. ZSW & Eino3.4 Index • Correlation coefficients = 0.4686

  21. Correlation coefficients = 0.5246 1950-1977(PC1) Correlation coefficients = 0.4323 1978-2001(PC2)

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