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8. 시계열 자료 분석기법의 1 장의 1 절부터 6 절에 대한 내용을 요약하고 , 예제 및 표에 대한 문제를 Excel 을 이용하여 풀어서 제출하라 . PowerPoint PPT Presentation


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8. 시계열 자료 분석기법의 1 장의 1 절부터 6 절에 대한 내용을 요약하고 , 예제 및 표에 대한 문제를 Excel 을 이용하여 풀어서 제출하라. 환경공학과 20041469 임건섭. 1. 시계열 자료 분석 - 1.1 예측.

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8. 시계열 자료 분석기법의 1 장의 1 절부터 6 절에 대한 내용을 요약하고 , 예제 및 표에 대한 문제를 Excel 을 이용하여 풀어서 제출하라 .

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8 1 1 6 excel

8. 1 1 6 , Excel .

20041469


1 1 1

1. - 1.1

, . , . , , .

() ( ) .


8 1 1 6 excel

1.2

. , , . , , , , , .

. .


8 1 1 6 excel

  • (, stationary) , (, non-stationary) . .

    < 1.2-1> < 1.2-2> .


8 1 1 6 excel

< 1.2-1>


8 1 1 6 excel

< 1.2-2>


8 1 1 6 excel

1.3

. , 1 , 2 .

, .

, , . , (t) n . .


8 1 1 6 excel

  • , . n m , .


8 1 1 6 excel

  • n . ,

    .

    , , ( ) , .


8 1 1 6 excel

,

, .

, m , ,


8 1 1 6 excel

. .

1) Mean Error : ()

2) Mean Absolute Error : ()

3) Mean Squared Error : ( )

4) Standard Deviation of Errors : ( )

5) Percentage Error : ( )


8 1 1 6 excel

6) Mean percentage Error : ( )

7) Mean Absolute Percentage Error :

( )

8) Theil's U-Statistic (Theil U )

, ( )

( )

9) Durbin-Watson Statistic (Durbin-Watson )


1 4 smoothing method

1.4 (Smoothing Method)

(Smoothing Method) .

, (Random) .

, Smoothing (Moving Average) (Exponential Smoothing) .


1 4 1

1.4.1

. .

1) (Average)

. , .

, .


8 1 1 6 excel

(T+1)

. (T+1)

. (T+2) ,

.


8 1 1 6 excel

  • (Trend) (Seasonality) . (Stable) . , , .


8 1 1 6 excel

2) (Simple Moving Average)

, .

(T) (N) , (moving average) . , . N , < 1.4.1-2> (T+1, T+2, T+3) , .


8 1 1 6 excel

< 1.4.1-2>


8 1 1 6 excel

, .

(N)

(a) MA(1) (T) (T+1) .

(b) MA(4) , 4 , . , 4 4 .

(c) . .


8 1 1 6 excel

3) (Linear Moving Average Method)

.

, (linear moving average method) .

. N N MA(NxN) .

MA(3) t=3 . MA(3x3) 3 (4, 6, 8) , [MA(3) - MA(3x3)] .


8 1 1 6 excel

, .

,

: MA(3) + (MA(3)-MA(3*3)) (1.4.1-1)

: (Trend) (1.4.1-2)

(T+m)

(1.4.1-3)

. (T+1) .


8 1 1 6 excel

1.5

(1.4-1) , (1.4-2) . (1.4-2) 2/(N-1) .

, N (N+1)/2 . , N N N-(N+1)/2=(N-1)/2 .

(N-1)/2 ( ) (N-1)/2 , (1.4-2) .


1 5 1 the component of time series data

1.5.1 (The Component of Time Series Data)

  • .

    1) (Trend)

    . (Long-run) , , . , (Exponentially)


8 1 1 6 excel

2) (Cyclical Movement)

(Ups and Downs) . , GNP(), , , , , ,

3) (Seasonal Fluctuation)

. , (1 ), (1 ), (1 )

(1, 1, 1 ) (Cycle) .


8 1 1 6 excel

( )

. (Error/Randomness) , , , .

,

(1.5.1-1)

. , , , , , .


8 1 1 6 excel

  • .

    (1) (N) N () . (N) 12, 4, 7 N , .

    (2) ( ) (1) .

    (3) , ( ) .

    (4) (2) (3) ( )

    (5) , , ( ).


1 5 2

1.5.2

  • (Log-run) (Trend) . , (Linear) . < 1.5-2> .


8 1 1 6 excel

< 1.5.2-1>


8 1 1 6 excel

< 1.5.2-1>(a) . ,

. < 1.5.2-1>(b)

. (Non-linear),

.


8 1 1 6 excel

< 1.5.2-1> (c) (d)

.

< 1.5.2-1> (e) , .

.

a b .


8 1 1 6 excel

(1)

t

. ( ,t) n b a . , < 1.5.2-1> ( ) a b , a=3.823.7 b=166.0

.


8 1 1 6 excel

< 1.5.2-1> (:)


8 1 1 6 excel

  • (scatter plot) < 1.5.2-2> .

< 1.5.2-2>


8 1 1 6 excel

(2)

( ) < 1.5-2> (b), (c), (d)

, (Logarithm) .


8 1 1 6 excel

Scatter Plot . , (Differencing), (Autocorrelation) .

, (Constant) . , 2 .


8 1 1 6 excel

,

2 2 . , ( ) 1 , .

(Detrending) , (Stationary Time-series) .


1 5 3

1.5.3

  • (Cyclical Fluctuation) , .


1 5 4

1.5.4

  • (Seasonal Variation) 1 . 1, 1, 1 , . . , , . , . .


1 6 box jenkins

1.6 Box-Jenkins

ARIMA(Auto Regressive Integrated Moving Average) Box-Jenkis . Box-Jenkins , ,

(1) (model identification)

(2) (testing)

(3) (forecasting)

.


1 6 1 box jenkins

1.6.1 Box-Jenkins

, Box-Jenkins . ,

(1)

(2)

(3)

(1) (Autoregressive Model)

( ) . ,

(1.6.1-1)

, (t) ( ) (t-1) , 2 (t-2) .


8 1 1 6 excel

  • p (1.6.1-1) p AR(p) . , , AR(1)

    (1.6.1-2)

    . .

    ,

    .


8 1 1 6 excel

(2) (Moving Average Model)

(1.6.1-3)

(6-3) q , MA(q) . , (t-1) 1 ,

(1.6.1-4)

.


8 1 1 6 excel

(3) (Autoregressive Moving Average Model)

, . AR MA . ,

(1.6.1-5)

.


8 1 1 6 excel

ARMA(p,q) . ARMA

(1.6.1-6)

ARMA(1,1) .

ARMA AR MA , AR MA ARMA . , , AR(1) ARMA(1,0) MA(1) ARMA(0,1) .


8 1 1 6 excel

( ) , (1.6.1-2) (), AR(1)

(1.6.1-7)

. (1.6.1-7)

(1.6.1-8)

., (1.6.1-4) MA(1) ,

(1.6.1-9)

. , 0 .


1 6 2

1.6.2

  • AR, MA, ARMA . (order) . , (identification) . , , (autocorrelation : AC) (partial autocorrelation : PAC) .


8 1 1 6 excel

  • Box-Jenkins (AC) (PAC) (AR), (MA), (ARMA) .

    O MA

    AC PAC , AC .

    O AR

    PAC , AC PAC .

    O ARMA

    AC PAC .


1 6 3 ma ar arma ac pac

1.6.3 MA, AR, ARMA AC PAC

  • (MA, AR, ARMA) .


8 1 1 6 excel

1) MA

MA(1),

(AC) . , (lag) 1

(1.6.3-1)

. 2 0

(1.6.3-2)

.


8 1 1 6 excel

  • , MA(1) 1 AC 2 AC 0 PAC . < 1.6.3-1> MA(1) AC PAC .


8 1 1 6 excel

< 1.6.3-1> MA(1) AC PAC


8 1 1 6 excel

MA(2) . , MA(2)

, 1

(1.6.3-3)

, 2

(1.6.3-4)

, 3 0.


8 1 1 6 excel

  • , MA(2)

    AC PAC < 1.6.3-2> .

< 1.6.3-2> MA(2) AC PAC


8 1 1 6 excel

(backward operator) "B" . , B

(1.6.3-5)

MA(1)

(1.6.3-6)

, MA(2)

(1.6.3-7)

. .


8 1 1 6 excel

2) AR

, AR(1) (AC) .

(1.6.3-8)

AC k .

< 1.6.3-3> AR(1) AC PAC .


8 1 1 6 excel

< 1.6.3-3> AR(1) AC PAC


8 1 1 6 excel

AR(2)

(1.6.3-9)

, < 1.6-3> AR(2) AC, PAC . , AR PAC PAC , AC () .


8 1 1 6 excel

< 1.6.3-4> AR(2) AC PAC


8 1 1 6 excel

3) ARMA

AR MA ARMA (AC) (PAC) . AC, PAC AR , MA ARMA . ARMA(1,1) ACPAC < 1.6.3-5> .


8 1 1 6 excel

< 1.6.3-5> ARMA(1,1) AC PAC


1 6 4

1.6.4

. , . (differencing) .

, { } 1 (first difference)

, 1

2 . , 2

.

2 , 2 , .


1 6 5

1.6.5

1.6.3 MA AR ARMA AC PAC , AC PAC . , ACPAC AC PAC .

AC PAC .

o

o

o

, . (SAS, SPSS, RATS, Minitab ) .


8 1 1 6 excel

, , AIC(Akaike Information Criterion) SBC(Schwartz Bayesian Criterion) . , ARMA(p,q)

, AIC( SBC) (p,q) . , ( ) .


8 1 1 6 excel

  • Box-Pierce

    . (autocorrelation of residuals) Box-Pierce(Portmanteu) Q (lag) . , Q

    , T ( ), (lag) , m 1 m . ,

    Q M 6, 12, 18 .


8 1 1 6 excel

  • 2 . , . , 3 .

    , 2 3 0.856 , 2 3 1 . , 3 .


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