Time series analysis

R98229029

陳漢卿

ENSO & ACW

0(ENSO)

-6

-12

-18

-24

-30

-36

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.

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.

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

全期分析• Mean~0• STD=1

兩段時間分析

1950 1955 1960 1965 1970 1975-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Mean=0.055

STD=1.004

1950-1977(PC1)

Mean=-0.0645

STD=0.9924

1978-2001(PC2)

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.

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.

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。

5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1PACF, nx=624

phi kk

time step lag

趨勢分析

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Y = -0.0001X + 0.0467一次回歸方程

趨勢分析

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

五次回歸方程

1950 1955 1960 1965 1970 1975-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Y = 0.0003X + 0.0100

Y = 0.0010X - 0.2042

一次回歸方程

1950 1955 1960 1965 1970 1975-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

二次回歸方程

突變點分析

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

mean d

iff

滑動平均 t-test

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

ARMA model

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

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。

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5OBS. DATA

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5ARMA PREDICT DATA

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。

ZSW & nino3.4 index 相關分析

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-3

-2

-1

0

1

2

3

ZSW & Eino3.4 Index

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000-3

-2

-1

0

1

2

3

• Correlation coefficients = 0.4686

1950 1955 1960 1965 1970 1975-3

-2

-1

0

1

2

3

1980 1985 1990 1995 2000-3

-2

-1

0

1

2

3

Correlation coefficients = 0.5246

Correlation coefficients = 0.4323

1950-1977(PC1)

1978-2001(PC2)