????~ARIMA??????

1
????

• ??? ?? ???
• ??????????
• ??????????

2
??

• ????
• ????
• ????

3
????

• ???? Regression Model
• ?????? Time Series

4
????

• ??????????,???????????????????????
• ????????????????????????????????????
• ????
• ? ???????????????

5
????
6
??????

• ?????? Simple Linear Regression
• ?????? Multiple Linear Regression
• ?????? GLM (function relation)

7
??????

• 1.??(description)?????????????? (???????)
• 2.??(control)????????????,?????,?????(????)
• 3.??(prediction)???????????(??????)

8
??????????(??????)

• ????????????????????,??10???????????

9
(No Transcript)
10
????????????(??????)

• ?????????????????(serun cholesterol)??????????????
  ?,??10?20?30???????????

11
(No Transcript)
12
??????

• ??????????????????????
• ???????????????????????????????????????
• ????,??,?????????,??GNP,?????????????..??

13
????????

• ??????????(Forecasting)
• ?????????,???????(Trend Components)???????(Seasona
  l Components)
• ????????????????,???????????????????,???????????

14
??????????

• ??????(stationary)
• ??????????????
• ????????????(differencing)
• ?????????????????????????????????????

15

• ????????? (???)
• ??????
• ???????????????????????,?????????????????

16

• ?????????(parametric modeling)?ARIMA
  (autoregressive integrated moving average)
  ??????????? ARMA ??
• ARMA?????????????
• AR(autoregressive)
• MA(moving average)
• ???ARMA????????????,?????????????????

17

• ????????????????????????????????????????????(concu
  rrent)????(lead-lag)?????
• ?????????Box ?Jenkins
• ?????????? Box ? Tiao (1982) ? Tiao ? Tsay
  (1983)?

18

• ?????????????????????????????,??
• ARCH models,
• threshold AR model,
• co-integration,
• reduced rank models,
• scalar component models,
• state-space models?
• ???????????????
• Box?1980??????????,?????????????????????,??????

19
????Box-Jenkins??

• ????? ???????(?????????)

20

• ????????????????????(??)(1957????1961???)

21

• ?????????????????(1949??? ?1960????)

22

• ?????Magnavox???????????(??)(1976??? ?1983????)

23

• ????????????????(??/?)(1969????1991???)
• ????
• ????

24

• ?????????
• ???
• ????

25

• ?????????????????????????
• ???????
• ???????????

26
??????

• ???(Stationary)
• ????(Drifting)
• ???(Trend)
• ???(Seasonality)
• ?????(Exogenous effect)

27
????

• ????????????????????,??????????????????????
• ????(???)
• 1.??(Prediction)
• a.??(Short term)
• b.??(Long term)
• c.????(????) (Historical Pattern)
• 2.???????(Effect of exogenous changes)
• a.????(Oil Crisis)
• b.????(Economic Recessions)
• 3.??????
• a.??(Temperature)
• b.??(Employment)
• c.??(Population)
• d.?????(Housing starts)

28

• ???????????,??????
• 1.??????????????
• 2.??????????
• 3.???????????????
• 4.????????????
• 5.??????????????

29
????????

• ?????(Prediction and Forecasting)
• ??????(Policy Impact Analysis)
• ????-?????(Signal Extraction-Seasonal Adjustment)
• ????(Process Control)
• ??????(Description of a Stochastic System)

30
????????

• ????
• a.????(Model Identification)
• b.???????????(Efficient Estimation)
• c.?????(Model Checking) -???????a. ???
• d.????(Statistical Inference)

31
??????

• ????????????????(memory)
• ?????????????????????????????

32
??????

• ?? ??????(memory
  function),? ???????? ? ??????
• ??????? ?, ?????????
  ?????????????

33
MA model AR model

• Udny Yule ??????????????????
• ?????? (Moving Average Model, MA)
• ?????? (Autoregressive Model, AR)

34
MA model

• ????????, MA(1)
• ?? ?????(white noise)
• ?? at ??????????(shock effect or memory function)
• q???????,MA(q)

35
AR model

• ????????,AR(1)
• ??????? Zt-1 ????,Zt ????
• p???????,AR(p)

36
ARMA model

• ????????????????
• ?? p????????,AR(p)
• ??q????????,MA(q)
• ????????????,ARMA(p,q)

37
???????

• Homogeneous Nonstationary Models
• ??????????????????
• ???

38

• ????????????????
• ??????(first difference)?
• ????????????,??????????
• ???????????,??????

39
?????B

• ???????????????
• ??
• AR(p)
• MA(q)

40
ARIMA(p,d,q)

• ??
• ???
• ??

41
????

• ??????ACF ??MA(q)

42

• ??MA(2) ?ACF
• AUTOCORRELATIONS
•  
•  
• 1- 12 -.78 .42 -.16 -.04 .18 -.24 .18
  -.06 .04 -.11 .20 -.26
• ST.E. .14 .21 .23 .23 .23 .23 .24
  .24 .24 .24 .24 .24
• Q 32.5 42.0 43.4 43.4 45.4 48.8 50.7
  50.9 51.0 51.8 54.5 59.0
•  
•  
• -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2
  0.4 0.6 0.8 1.0
• -----------------------------
  -----------
• I
• 1 -0.78 XXXXXXXXXXXXXXXXXXXI
• 2 0.42 IXXXXXXXXXX
• 3 -0.16 XXXXI
  
• 4 -0.04 XI
  
• 5 0.18 IXXXXX
  
• 6 -0.24 XXXXXXI
  
• 7 0.18 IXXXX
  

43

• ???????PACF ??AR(p)

44

• ??AR(2) , ?PACF
• PARTIAL AUTOCORRELATIONS
•  
• 1- 12 .86 -.34 -.06 .02 -.18 .01 .10
  -.21 -.05 .05 .06 .03
• ST.E. .10 .10 .10 .10 .10 .10 .10
  .10 .10 .10 .10 .10
•  
• 13- 24 .07 .10 -.07 -.02 .13 -.08 .02
  -.15 -.10 -.03 -.05 -.03
• ST.E. .10 .10 .10 .10 .10 .10 .10
  .10 .10 .10 .10 .10
•  
• -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2
  0.4 0.6 0.8 1.0
• -----------------------------
  -----------
• I
• 1 0.86
  IXXXXXXXXXXXXXXXXXXXX
• 2 -0.34 XXXXXXXXI
• 3 -0.06 XI
• 4 0.02 I
• 5 -0.18 XXXXI
• 6 0.01 I
• 7 0.10 IXX

45
ARIMA(p,d,q) ??????????????
46

• ????????EACF ??????ARMA(p,q)
• ????j?????EAFC? ????
  ??j????????,??

47

• Tsay and Tiao (1984)?????p??ARMA(p,q)?
• ??????(0,x)?????,??
• SIMPLIFIED EXTENDED ACF TABLE (5 LEVEL)
•  
• (Q--gt) 0 1 2 3 4 5 6 7 8 9 10 11 12
• -----------------------------------------------
• (P 0) X O O O O O O O O O O O O
• (P 1) X X O O O O O O O O O O O
• (P 2) X O O O O O O O O O O O O
• (P 3) X O O O O O O O O O O O O
• (P 4) X O O O O O O O O O O O O
• (P 5) X O X O O O O O O O O O O
• (P 6) O X O O O O O O O O O O O

48

• ARMA(0,1)MA(1)
• (Q--gt) 0 1 2 3 4 5 6 7 8 9 10 11 12
• -----------------------------------------------
• (P 0) X O O O O O O O O O O O O
• (P 1) X O O O O O O O O O O O O
• (P 2) X X X O O O O O O O O O O
• (P 3) O O O O O O O O O O O O O
• (P 4) O O O X O O O O O O O O O
• (P 5) X O O O O O O O O O O O O
• (P 6) X O O O O O O O O O O O O

• ARMA(2,0)AR(2)
• (Q--gt) 0 1 2 3 4 5 6 7 8 9 10 11 12
• -----------------------------------------------
• (P 0) X X X O O O O O O O O O O
• (P 1) X X O O O O O O O O O O O
• (P 2) O O O O O O O O O O O O O
• (P 3) X O O O O O O O O O O O O
• (P 4) O X X O O O O O O O O O O
• (P 5) O X X O O O O O O O O O O
• (P 6) X O X O O O O O O O O O O

49

• ARMA(1,1)
• (Q--gt) 0 1 2 3 4 5 6 7 8 9 10 11 12
• -----------------------------------------------
• (P 0) X X X O O O O O O O O O O
• (P 1) X O O O O O O O O O O O O
• (P 2) X O O O O O O O O O O O O
• (P 3) X O O O O O O O O O O O O
• (P 4) X O O O O O O O O O O O O
• (P 5) X O O O O O O O O O O O O
• (P 6) X X O O O O O O O O O O O

50
????????????(ARMA ?????)

• ????????????????????????,????????????
• ?????,????????????????
• ????????????????????????,???????????????,????????
  ???????
• ?????1985?1??1996?2????????????(????)??,??122??
• ????????????????

51

• ????

52

• ACF
• AUTOCORRELATIONS
  
• 1- 12 .38 .31 .26 .13 .12 .05 .01
  .08 .23 .25 .29 .24
• ST.E. .09 .10 .11 .11 .12 .12 .12
  .12 .12 .12 .13 .13
• Q 17.9 30.1 38.4 40.5 42.4 42.7 42.7
  43.6 50.7 59.0 70.4 78.0
• 
  
• 13- 24 .26 .14 .09 .02 -.06 -.08 .01
  -.03 -.07 .10 .03 .14
• ST.E. .13 .14 .14 .14 .14 .14 .14
  .14 .14 .14 .14 .14
• Q 87.3 90.0 91.2 91.3 91.7 92.6 92.6
  92.7 93.5 94.9 95.1 98.0
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .38 IXXXXXXXX
  
• 2 .31 IXXXXXXX
  
• 3 .26 IXXXXX
  
• 4 .13 IXXX
  
• 5 .12 IXXX
  
• 6 .05 IX
  

53

• PACF
• PARTIAL AUTOCORRELATIONS
  
• 1- 12 .38 .20 .11 -.04 .02 -.03 -.03
  .09 .24 .14 .11 -.00
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• 13- 24 .07 -.09 -.03 -.05 -.06 -.09 .05
  -.07 -.16 .08 -.03 .10
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .38 IXXXXXXXX
  
• 2 .20 IXXXX
  
• 3 .11 IXXX
  
• 4 -.04 XI
  
• 5 .02 IX
  
• 6 -.03 XI
  
• 7 -.03 XI
  
• 8 .09 IXX
  

54

• EACF
• THE EXTENDED ACF TABLE
  
• 
  
• (Q--gt) 0 1 2 3 4 5 6 7
  8 9 10 11 12
• --------------------------------------------------
  ----------------------
• 
  
• (P 0) .38 .31 .26 .13 .12 .05 .01 .08
  .23 .25 .29 .24 .26
• 
  
• (P 1) -.48 .04 .09 -.08 .05 .02 -.05 -.01
  .13 -.03 .05 -.05 .15
• 
  
• (P 2) -.42 .16 .12 -.00 .04 .01 -.06 .02
  .16 .05 -.02 -.00 .14
• 
  
• (P 3) .30 -.03 .10 .01 .01 .02 -.05 -.02
  .19 .04 -.03 .01 .11
• 
  
• (P 4) .38 .05 .00 .15 .00 .01 -.06 -.05
  .19 -.04 -.03 .01 .14
• 
  
• (P 5) .43 -.17 -.02 -.02 -.06 -.01 -.08 -.14
  .11 -.06 .13 -.07 .16
• 
  
• (P 6) -.47 .11 -.03 -.03 -.04 -.14 -.12 .02
  .14 -.10 .09 .01 .15

55

• ?SCA??????ACF, PACF,EACF?????????ARMA(1,1)?MA(3)
• ARMA(1,1) ???(1)
• MA(3)???(2)

56

• ??(1)??????
• ???(1)????????????????????????
•  
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
• 
  
• 1 CNST CNST 1 0
  NONE 2.6376 1.5066 1.75
• 2 TH LNTEA MA 1 1
  NONE .4759 .1628 2.92
• 3 PH LNTEA AR 1 1
  NONE .7890 .1205 6.55
•  
• 
  
• ?????(CNST)???,?????????(1)???,???????????????????
  ???????
•  
•  
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
• 
  
• 1 TH1 LNTEA MA 1 1
  NONE .6798 .0702 9.69

??1
57

• ??1?????0.9998???1,????????LNTEA??????????????????
  ?(1)????,?????????????????????????
•  
•  
•  
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
• 
  
• 1 TH1 LNTEA MA 1 1
  NONE .6841 .0681 10.04
• 
  
• EFFECTIVE NUMBER OF OBSERVATIONS . .
  121
• R-SQUARE . . . . . . . . . . . . . .
  .162
• RESIDUAL STANDARD ERROR. . . . . . .
  .309958E00
• ??????(1)

58

• ??(1)????????ACF?PACF?EACF 
• ??ACF
• AUTOCORRELATIONS
  
• 1- 12 .02 .07 .04 -.09 -.06 -.13 -.21
  -.11 .12 .07 .13 .12
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .10 .10 .10 .10 .10
• Q .0 .6 .7 1.8 2.3 4.5 10.2
  11.7 13.6 14.3 16.6 18.5
• 
  
• 13- 24 .22 .08 .04 -.04 -.11 -.11 .03
  -.08 -.16 .09 -.02 .11
• ST.E. .10 .11 .11 .11 .11 .11 .11
  .11 .11 .11 .11 .11
• Q 25.3 26.2 26.5 26.7 28.6 30.5 30.6
  31.5 35.1 36.3 36.4 38.4
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .02 I
  
• 2 .07 IXX
  
• 3 .04 IX
  
• 4 -.09 XXI
  
• 5 -.06 XXI
  

59

• ??PACF
• PARTIAL AUTOCORRELATIONS
  
• 
  
• 1- 12 .02 .07 .04 -.10 -.07 -.12 -.20
  -.11 .15 .09 .09 .06
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• 13- 24 .19 .05 .03 .02 -.01 -.06 .12
  .02 -.17 -.00 -.08 -.00
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .02 I
  
• 2 .07 IXX
  
• 3 .04 IX
  
• 4 -.10 XXI
  
• 5 -.07 XXI
  
• 6 -.12 XXXI
  

60

• ??EACF
• THE EXTENDED ACF TABLE
  
• 
  
• (Q--gt) 0 1 2 3 4 5 6 7
  8 9 10 11 12
• --------------------------------------------------
  ----------------------
• 
  
• (P 0) .02 .07 .04 -.09 -.06 -.13 -.21 -.11
  .12 .07 .13 .12 .22
• 
  
• (P 1) -.18 .04 .03 -.07 .02 -.00 -.12 -.16
  .14 -.03 .04 -.04 .15
• 
  
• (P 2) -.41 .38 -.00 -.07 .03 .03 -.06 -.11
  .16 .04 -.05 -.01 .15
• 
  
• (P 3) .36 .41 .04 -.07 .01 .01 -.05 -.06
  .19 .03 -.01 -.00 .10
• 
  
• (P 4) -.46 -.23 -.18 .31 .03 .01 -.07 -.09
  .17 -.02 -.01 .02 .15
• 
  
• (P 5) -.39 .03 -.13 .19 .20 -.00 -.12 .02
  .13 -.12 .12 -.13 .14
• 
  
• (P 6) -.42 -.04 -.15 .01 .25 -.15 -.13 .02
  .16 -.03 .04 -.02 .15

61

• ??(2) ??????
•   ???(2)????????????????????????
•  
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
• 
  
• 1 CNST CNST 1 0
  NONE 12.4850 .0458 272.72
• 2 TH1 LNTEA MA 1 1
  NONE -.2878 .0902 -3.19
• 3 TH2 LNTEA MA 1 2
  NONE -.2656 .0979 -2.71
• 4 TH3 LNTEA MA 1 3
  NONE -.2149 .0963 -2.23
• 
  
• 
  
• EFFECTIVE NUMBER OF OBSERVATIONS . .
  122
• R-SQUARE . . . . . . . . . . . . . .
  .183
• RESIDUAL STANDARD ERROR. . . . . . .
  .305928E00
• ??????(2)

62

• ??(2)???
• ??ACF
• AUTOCORRELATIONS
  
• 1- 12 .01 .03 .05 .10 .12 -.01 -.09
  -.02 .19 .11 .13 .07
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .10 .10 .10
• Q .0 .1 .4 1.8 3.6 3.6 4.7
  4.8 9.5 11.3 13.5 14.2
•  
• 13- 24 .18 .05 .07 -.01 -.08 -.05 .08
  -.00 -.13 .08 -.02 .13
• ST.E. .10 .10 .10 .10 .10 .10 .10
  .10 .10 .11 .11 .11
• Q 18.8 19.2 19.8 19.9 20.8 21.2 22.1
  22.1 24.6 25.7 25.7 28.3
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .01 I
  
• 2 .03 IX
  
• 3 .05 IX
  
• 4 .10 IXXX
  
• 5 .12 IXXX
  

63

• ??PACF
• PARTIAL AUTOCORRELATIONS
  
• 1- 12 .01 .03 .05 .10 .12 -.02 -.11
  -.05 .18 .13 .16 .09
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• 13- 24 .15 -.03 -.00 -.04 -.10 -.10 .07
  -.00 -.16 .01 -.09 .03
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .01 I
  
• 2 .03 IX
  
• 3 .05 IX
  
• 4 .10 IXXX
  
• 5 .12 IXXX
  
• 6 -.02 I
  
• 7 -.11 XXXI
  
• 8 -.05 XI
  

64

• ??EACF
• THE EXTENDED ACF TABLE
  
• 
  
• (Q--gt) 0 1 2 3 4 5 6 7
  8 9 10 11 12
• --------------------------------------------------
  ----------------------
• 
  
• (P 0) .01 .03 .05 .10 .12 -.01 -.09 -.02
  .19 .11 .13 .07 .18
• 
  
• (P 1) -.24 .01 -.01 .03 .10 -.01 -.11 -.01
  .16 -.05 .03 -.04 .16
• 
  
• (P 2) -.42 -.32 -.03 .03 .00 .05 -.03 .05
  .20 .02 -.00 -.02 .12
• 
  
• (P 3) -.36 -.31 .05 .03 -.03 .04 -.05 .02
  .21 -.02 -.04 -.06 .12
• 
  
• (P 4) -.48 .24 -.12 -.03 .03 .05 -.06 -.03
  .17 .06 .11 .06 .13
• 
  
• (P 5) .04 .27 -.08 -.24 -.01 .06 -.06 -.08
  .13 -.08 .10 -.07 .15
• 
  
• (P 6) -.03 .37 -.13 .08 -.07 .07 -.06 -.03
  .17 .01 .01 -.01 .18

65

• ??????
• ????
• ??(1)?1???,??(2)?3???
• ????(1)
• ??????
• ??(1)?0.3100,??(2)?0.3059
• ????(2)
• ??(2)???ACF, PACF, EACF???(1) ??(clean)
• ????????????????????????,?????????????????????????
  ???(2)

66

• ???(2) ????
• ?1995?4?(t112)??????,?????1995?4??1996?2?(t1121
  22)
• --------------------------------------------------
  ------------
• 1 FORECASTS, BEGINNING AT 112 to 122
  
• --------------------------------------------------
  ------------
• ?? ??? ???? ??? ????
• TIME FORECAST STD. ERROR ACTUAL IF KNOWN
  FORE. ERROR
• 
  
• 113 12.2889 .3059 12.6318
  0.3429
• 114 12.4862 .3059 12.2484
  -0.2378
• 115 12.5347 .3059 12.6112
  0.0765
• 116 12.5176 .3059 12.3796
  -0.1380
• 117 12.4145 .3059 12.3803
  -0.0342
• 118 12.4550 .3059 12.1077
  -0.3473
• 119 12.3463 .3059 12.0396
  -0.3067
• 120 12.2972 .3059 12.0243
  -0.2729
• 121 12.2504 .3059 10.9886
  -1.2618
• 122 11.9835 .3059 12.0275
  0.0440

67

• ?????1996?2?????12?????????????,???????
• --------------------------------------------------
  ---
• 12 FORECASTS, BEGINNING AT 122
  
• --------------------------------------------------
  ---
• ?? ??? ???? ???
• TIME FORECAST STD. ERROR ACTUAL IF KNOWN
  
• 
  
• 123 12.1039 .3059
  
• 124 12.2255 .3183
  
• 125 12.4944 .3285
  
• 126 12.4850 .3351
  
• 127 12.4850 .3351
  
• 128 12.4850 .3351
  
• 129 12.4850 .3351
  
• 130 12.4850 .3351
  
• 131 12.4850 .3351
  
• 132 12.4850 .3351
  
• 133 12.4850 .3351
  

68
(No Transcript)
69
???????

• ????????????????
• ??????? ????

70

• ?????????????????(1949??? ?1960????)

71

• ?????Magnavox???????????(??)(1976??? ?1983????)

72

• Seasonal ARIMA???

73
???????????(???ARIMA?????)

• ????
• ??1961?????1996?????????????????????,??142??

74

• ??
• ?????????????,???4????,?12????????
• ????????????,???????????????

75
ACF

• 1- 12 .98 .95 .92 .90 .87 .85 .82
  .80 .78 .75 .73 .70
• ST.E. .08 .14 .18 .21 .24 .26 .28
  .30 .31 .32 .34 .35
• Q 138 270 395 515 629 738 841
  938 1031 1118 1201 1278
• 
  
• 13- 24 .68 .65 .63 .60 .58 .56 .53
  .51 .48 .46 .44 .41
• ST.E. .36 .37 .37 .38 .39 .39 .40
  .40 .41 .41 .42 .42
• Q 1351 1420 1484 1543 1598 1650 1697
  1740 1780 1816 1849 1878
• 
  
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 .98
  IXXXXXXXXXXXXXXXXXXXXXXX
• 2 .95
  IXXXXXXXXXXXXXXXXXXXXXXX
• 3 .92
  IXXXXXXXXXXXXXXXXXXXXXX
• 4 .90
  IXXXXXXXXXXXXXXXXXXXXX
• 5 .87
  IXXXXXXXXXXXXXXXXXXXXX
• 6 .85
  IXXXXXXXXXXXXXXXXXXXX

• ACF???????????,????????????,????????????

76
????ACF

• 1- 12 -.02 -.16 .06 .57 .02 -.12 -.01 .51
  .01 -.09 .04 .43
• ST.E. .08 .08 .09 .09 .11 .11 .11
  .11 .13 .13 .13 .13
• Q .1 3.6 4.0 51.2 51.3 53.5 53.5
  92.5 92.5 93.9 94.1 123
• 
  
• 13- 24 .10 -.07 -.01 .40 .06 -.04 .02
  .26 .04 .02 .03 .20
• ST.E. .14 .14 .14 .14 .15 .15 .15
  .15 .15 .15 .15 .15
• Q 124 125 125 151 151 151 151
  163 163 163 163 170
• 
  
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 -.02 I
  
• 2 -.16 XXXXI
  
• 3 .06 IX
  
• 4 .57
  IXXXXXXXXXXXXX
• 5 .02 IX
  
• 6 -.12 XXXI
  
• 7 -.01 I
  

• ACF??????4,8,12,16,20???????????
• ????????????
• ??4???????,?

77
?ACF

• 1- 12 -.16 -.00 .18 -.49 .07 .01 -.15 .05
  -.16 .00 .14 -.08
• ST.E. .09 .09 .09 .09 .11 .11 .11
  .11 .11 .11 .11 .11
• Q 3.7 3.7 8.1 42.4 43.2 43.2 46.5
  46.9 50.5 50.5 53.5 54.3
• 
  
• 13- 24 .19 -.02 -.10 .14 -.06 -.04 .01
  -.07 -.06 .02 .03 .05
• ST.E. .11 .12 .12 .12 .12 .12 .12
  .12 .12 .12 .12 .12
• Q 60.1 60.2 61.6 64.9 65.5 65.8 65.8
  66.7 67.3 67.3 67.5 67.9
• 
  
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 -.16 XXXXI
  
• 2 .00 I
  
• 3 .18 IXXXX
  
• 4 -.49 XXXXXXXXXXXI
  
• 5 .07 IXX
  
• 6 .01 I
  
• 7 -.15 XXXXI
  

• ACF?????????????????????
• ????????????
• ??????,???????

78
????

• PARAMETER VARIABLE NUM./ VALUE STD
  T
• LABEL NAME DENOM. ERROR
  VALUE
• 
  
• 1 CNST CNST 694.2029 387.6253
  1.79
• 2 T1 PRD MA .1748 .0845
  2.07
• 3 T4 PRD MA .6511 .0671
  9.70
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
• 
  
• 1 T1 PRD MA 1 1
  NONE .1477 .0846 1.75
• 2 T4 PRD MA 2 4
  NONE .6256 .0710 8.82
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
• 
  
• 1 T4 PRD MA 1 4
  NONE .6237 .0702 8.88

79

• ????

80
????????

• ACF
• AUTOCORRELATIONS
  
• 
  
• 1- 12 -.16 -.02 .07 -.06 -.05 -.01 -.09
  .02 -.13 -.04 .08 -.01
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• Q 3.7 3.7 4.5 5.0 5.4 5.4 6.6
  6.7 9.1 9.2 10.2 10.2
• 
  
• 13- 24 .13 -.07 -.06 .13 -.04 -.07 .01
  -.02 -.07 .01 .06 -.00
• ST.E. .09 .09 .09 .09 .09 .09 .10
  .10 .10 .10 .10 .10
• Q 12.9 13.7 14.2 17.0 17.2 18.0 18.0
  18.1 18.9 19.0 19.6 19.6
• 
  
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 -.16 XXXXI
  
• 2 -.02 I
  
• 3 .07 IXX
  
• 4 -.06 XXI
  

• PACF
• PARTIAL AUTOCORRELATIONS
  
• 
  
• 1- 12 -.16 -.04 .07 -.04 -.07 -.04 -.10
  -.01 -.14 -.08 .04 .01
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• 13- 24 .13 -.07 -.10 .08 .01 -.07 -.06
  .00 -.06 -.00 .06 -.03
• ST.E. .09 .09 .09 .09 .09 .09 .09
  .09 .09 .09 .09 .09
• 
  
• 
  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• ------------------------------
  ----------
• I
  
• 1 -.16 XXXXI
  
• 2 -.04 XI
  
• 3 .07 IXX
  
• 4 -.04 XI
  
• 5 -.07 XXI
  
• 6 -.04 XI
  

81

• EACF
• THE EXTENDED ACF TABLE
  
• (Q--gt) 0 1 2 3 4 5 6 7
  8 9 10 11 12
• --------------------------------------------------
  ----------------------
• 
  
• (P 0) -.16 -.02 .07 -.06 -.05 -.01 -.09 .02
  -.13 -.04 .08 -.01 .13
• 
  
• (P 1) -.25 -.04 .04 -.06 -.04 .00 -.09 -.01
  -.11 -.06 .08 .01 .11
• 
  
• (P 2) .46 .13 -.05 -.07 -.02 .02 -.01 .01
  -.12 -.07 .07 .01 .11
• 
  
• (P 3) .45 .21 -.24 .00 -.05 .01 .01 -.01
  -.12 -.04 .07 -.06 .10
• 
  
• (P 4) -.44 .25 -.26 -.03 -.05 .02 .01 -.02
  -.08 -.07 -.03 .01 .11
• 
  
• (P 5) -.43 -.42 .01 .01 -.19 -.01 -.01 -.03
  -.04 -.04 -.03 .00 .12
• 
  
• (P 6) -.35 -.40 .17 -.01 -.04 .09 -.06 -.03
  -.01 .01 -.00 -.05 .08
• 
  

82
??

• ?1993????(t132)??????
• ??1994?????1996????(t133142)
• -------------------------------------------------
  
• 1 FORECASTS, BEGINNING AT 132 to 142
  
• -------------------------------------------------
  
• ?? ??? ???? ??? ????
• TIME FORECAST STD. ERROR ACTUAL IF KNOWN
  FORE. ERROR
• 133 .14363E07 .15832E05 .14156E07
  -0.207E05
• 134 .14278E07 .15832E05 .14273E07
  -0.005E05
• 135 .14905E07 .15832E05 .15030E07
  0.125E05
• 136 .15253E07 .15832E05 .15405E07
  0.152E05
• 137 .15258E07 .15832E05 .15137E07
  -0.121E05
• 138 .15258E07 .15832E05 .15289E07
  0.031E05
• 139 .15968E07 .15832E05 .16065E07
  0.097E05
• 140 .16346E07 .15832E05 .16489E07
  0.143E05
• 141 .16297E07 .15832E05 .16147E07
  -0.150E05

83

• ??????1996????(t142)????12???????????,?????
•  
• -------------------------------------------------
  
• 12 FORECASTS, BEGINNING AT 142
  
• -------------------------------------------------
  
• ?? ??? ???? ???
• TIME FORECAST STD. ERROR ACTUAL IF KNOWN
  
• 
  
• 143 .17037E07 .15832E05
  
• 144 .17372E07 .22389E05
  
• 145 .17123E07 .27421E05
  
• 146 .17272E07 .31663E05
  
• 147 .17987E07 .38436E05
  
• 148 .18321E07 .44182E05
  
• 149 .18073E07 .49263E05
  
• 150 .18221E07 .53866E05
  
• 151 .18936E07 .60592E05
  
• 152 .19271E07 .66643E05
  
• 153 .19022E07 .72188E05
  

84
(No Transcript)
85
??????????????

• ????????(Dynamic Regression Models)???????????????
  ?
• ???????????? ?????,??????????? ???,???????
  ? ??????(Transfer Function)?

86
??????

• ??
• ??????
• ??
• ?????? ??
• C???
• ???????????(unidirectional)

87
???????
88
????????????

• ?????????????????????????????(SACF)??????????????
  ?,??????????????????(cross correlation
  function,???CCF)??????

89

• ??Xt?Yt?????k??????????(cross-correlation)?,
• ??
• ,

90

• ???????????????????
• 1. ????????
• 2. ???????????s?r?b
• 3. ?????
• 4. ??????ARMA??
• 5. ??1.-4.???,????????

91
????????????????(???????)

• ????
• ??????????????,??????????
• ?????????????,????????,??????????
• ?????????,??????????????,????????????????
• ????????????????--????,??????,????????????????????
  ?????

92

• ????
• ?????????1971?????1996????????????,???????????????
  (??)??????,??103 ??
• ???????????????????????
• ????
• ????????? IMP,?????????,?????? ?
• ??????????? GNP ?

93

• ????IMP
• ??????GNP

94
?????Nt?ARIMA model

• ???????LNIMP
• ACF AUTOCORRELATIONS
• 1- 12 .96 .92 .88 .85 .80 .77 .73
  .70 .66 .63 .60 .57
• ST.E. .10 .17 .21 .24 .27 .29 .31
  .33 .34 .35 .36 .37
• Q 97.2 188 271 349 421 486 546
  601 651 697 738 777
•   13- 24 .54 .52 .50 .48 .45 .42 .40
  .37 .35 .32 .30 .28
• ST.E. .38 .39 .40 .40 .41 .41 .42
  .42 .42 .43 .43 .43
• Q 812 845 877 905 931 954 974
  992 1008 1022 1034 1044
•   
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• --------------------------------
  --------
• I
• 1 .96
  IXXXXXXXXXXXXXXXXXXXXXXX
• 2 .92
  IXXXXXXXXXXXXXXXXXXXXXX
• 3 .88
  IXXXXXXXXXXXXXXXXXXXXX
• 4 .85
  IXXXXXXXXXXXXXXXXXXXX
• 5 .80
  IXXXXXXXXXXXXXXXXXXX
• 6 .77
  IXXXXXXXXXXXXXXXXXX
• 7 .73
  IXXXXXXXXXXXXXXXXX

• Die out
• ??
• (1-B)LNIMP

95

• ACF of (1-B)LNIMP
• AUTOCORRELATIONS
•  
• 1- 12 -.14 .24 -.21 .32 -.30 .11 -.20
  .27 -.12 .11 -.07 .18
• ST.E. .10 .10 .11 .11 .12 .13 .13
  .13 .14 .14 .14 .14
• Q 2.0 8.0 12.6 23.5 33.4 34.8 39.4
  47.7 49.3 50.8 51.4 55.4
•  
• 13- 24 -.20 .02 -.19 .19 -.10 .12 -.18
  .20 -.20 .08 -.15 .19
• ST.E. .14 .14 .14 .15 .15 .15 .15
  .15 .15 .16 .16 .16
• Q 60.0 60.0 64.5 69.1 70.4 72.3 76.3
  81.6 86.7 87.6 90.8 95.8
•  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• --------------------------------
  --------
• I
• 1 -.14 XXXI
• 2 .24 IXXXXX
• 3 -.21 XXXXXI
• 4 .32 IXXXXXXX
• 5 -.30 XXXXXXXI

• Significant at lag 2,4,8
• ????????
• (1-B)(1-B4)LNIMP

96

• ACF of (1-B)(1-B4)LNIMP
• AUTOCORRELATIONS
•  
• 1- 12 .19 .07 -.03 -.48 -.21 -.12 -.10
  .01 .14 .06 .12 -.06
• ST.E. .10 .10 .11 .11 .13 .13 .13
  .13 .13 .13 .13 .13
• Q 3.6 4.2 4.3 28.3 33.1 34.5 35.6
  35.6 37.8 38.2 39.8 40.2
•  
• 13- 24 -.12 -.02 -.04 .04 .12 .05 -.04
  .01 -.11 -.02 -.06 -.06
• ST.E. .13 .14 .14 .14 .14 .14 .14
  .14 .14 .14 .14 .14
• Q 41.9 41.9 42.1 42.3 43.9 44.1 44.4
  44.4 45.9 45.9 46.4 46.8
•  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• --------------------------------
  --------
• I
• 1 .19 IXXXXX
• 2 .07 IXX
• 3 -.03 XI
• 4 -.48 XXXXXXXXXXXI
• 5 -.21 XXXXXI

• ????????????? ?ACF??

97
????

• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
•  
• 1 C CNST 1 0
  NONE -.0028 .0022 -1.27
• 2 T1 LNIMP MA 1 1
  NONE -.0765 .1010 -.76
• 3 T4 LNIMP MA 2 4
  NONE .8236 .0515 15.98
• ????
•  
• PARAMETER VARIABLE NUM./ FACTOR ORDER
  CONS- VALUE STD T
• LABEL NAME DENOM.
  TRAINT ERROR VALUE
•  
• 1 T4 LNIMP MA 1 4
  NONE .8114 .0529 15.33

98
????

• ACF
• AUTOCORRELATIONS
• 1- 12 .10 .12 -.01 -.06 -.16 -.06 -.09
  -.08 .01 -.01 .03 -.08
• ST.E. .10 .10 .10 .10 .10 .11 .11
  .11 .11 .11 .11 .11
• Q 1.0 2.4 2.4 2.8 5.4 5.7 6.6
  7.3 7.3 7.3 7.4 8.2
•  
• 13- 24 -.09 .03 -.07 .00 .02 .07 -.12
  .01 -.09 -.00 -.06 .00
• ST.E. .11 .11 .11 .11 .11 .11 .11
  .11 .11 .11 .11 .11
• Q 9.2 9.3 9.9 9.9 10.0 10.6 12.4
  12.4 13.3 13.3 13.8 13.8
•  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• --------------------------------
  --------
• I
• 1 .10 IXX
• 2 .12 IXXX
• 3 -.01 I
• 4 -.06 XI
• 5 -.16 XXXXI
• 6 -.06 XI

• PACF
• PARTIAL AUTOCORRELATIONS
•  
•  
• 1- 12 .10 .11 -.04 -.07 -.14 -.02 -.05
  -.07 .02 -.03 .01 -.12
• ST.E. .10 .10 .10 .10 .10 .10 .10
  .10 .10 .10 .10 .10
•  
• 13- 24 -.12 .07 -.08 -.01 -.00 .04 -.15
  -.04 -.07 .01 -.06 -.04
• ST.E. .10 .10 .10 .10 .10 .10 .10
  .10 .10 .10 .10 .10
•  
•  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• --------------------------------
  --------
• I
• 1 .10 IXX
• 2 .11 IXXX
• 3 -.04 XI
• 4 -.07 XXI
• 5 -.14 XXXXI

99

• EACF
• THE EXTENDED ACF TABLE
• (Q--gt) 0 1 2 3 4 5 6 7
  8 9 10 11 12
• -------------------------------------------------
  -----------------------
•  
• (P 0) .10 .12 -.01 -.06 -.16 -.06 -.09 -.08
  .01 -.01 .03 -.08 -.09
•  
• (P 1) -.50 .12 -.03 -.00 -.13 .06 -.02 -.09
  -.03 .00 -.00 -.06 -.10
•  
• (P 2) .29 .42 -.04 .00 -.12 .06 -.02 -.09
  -.02 -.01 -.00 -.04 -.08
•  
• (P 3) -.40 -.01 .46 -.01 -.15 -.05 -.06 -.08
  -.02 .00 .02 -.02 -.08
•  
• (P 4) -.38 -.03 .37 -.07 -.11 .06 .02 -.06
  .03 -.01 .04 -.02 -.08
•  
• (P 5) -.12 -.34 -.44 .09 .05 .10 .02 .00
  .01 .03 -.03 .01 -.04
•  
• (P 6) -.30 -.07 -.45 .25 -.01 .12 -.08 .02
  -.00 .03 -.00 -.02 -.03
•  

• White noise
• ????

100

• ???????????????????,?????????
• ?????????????,?
• ??

101

• ?????????

102
?????????CCF

• CROSS CORRELATION BETWEEN RMTF2(T) AND
  RM1(T-L)
•  
•   1- 12 .07 -.10 -.14 -.17 -.18 -.02 -.02
  .00 -.03 .00 .06 -.04
• ST.E. .10 .11 .11 .11 .11 .11 .11
  .11 .11 .11 .11 .11
•  
•  
• CROSS CORRELATION BETWEEN RM1(T) AND
  RMTF2(T-L)
•  
•  
• 1- 12 -.16 -.09 .02 -.03 -.04 .05 -.07
  -.01 -.03 -.06 -.01 -.04
• ST.E. .10 .11 .11 .11 .11 .11 .11
  .11 .11 .11 .11 .11
•  
• -1.0 -.8 -.6 -.4 -.2 .0 .2 .4
  .6 .8 1.0
• --------------------------------
  --------
• -12 -.04 XI
• -11 -.01 I
• -10 -.06 XXI
• -9 -.03 XI
• -8 -.01