MODELING THE DYNAMIC INTERDEPENDENCE OF MAJOR EUROPEAN STOC.pdf
연역적 회로가 작동하지 않는 멍청한 학생으로서 결과물을 얻기 위해서는
귀납적 행동의 축척을 위해 시간 투자가 필요할 뿐이다. ㅠㅠ
Multivariate VAR EGARCH 모델은 이미
Koutmos（1996）"Modeling the Dynamic interdependence of major stock markets"
이곳에서 다루어졌고, 몇개의 논문에서 모델을 이용한 분석이 이루어졌음에도
STATA,Eviews,RATS,TSP 등등의
계량 경제 전문 소프트에서조차 기본 기능으로 내재되어 있지 않다는 것에 의문을 느끼고 있다.
모델이 가진 본질적인 한계가 분석의 정확성을 훼손시키기 때문일까
아니면, 범용성을 가지지 못한 모델의 자기 정체성일까?
관련 포럼에서 code를 얻지 못했다면 난 어떠한 방향으로 논문을 작성했을지 모르겠다..
기초 계량경제학부터 시계열분석까지
"그러한 의미" 수준으로만 "읽었던" 탓인지 여러가지가 부족하다.
명확한 개념의 부족과 제한된 해석 수준으로는
기본 틀을 갖추어 나가기까지 많은 반복 작업이 필요했다.
그런 이유로, 관련 논문과 비슷한 결과를 얻기 위해
샘플을 나눠보고, 기간 설정을 바꾸어보고, 논문을 다시 읽어보고
반복과 반복과 반복.
그리고 대략적인 결과물을 얻어냈다.
code분석을 다시 해본 후, 정량적 분석은 잠시 일단락 될 듯 하다..
기본 분석 code는 아래와 같다.
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************************************
**FOUR DIMENSIONAL EGARCH PROGRAM
**WITH MEAN AND ASYMMETRIC VOLATILITY SPILLOVERS
**BY GREGORY KOUTMOS
**
**FAIRFIELD UNIVERSITY SCHOOL OF BUSINESS
**FAIRFIELD CT 06430
*** EMAIL: GKOUTMOS@FAIRFIELD.EDU
***NOTE: For more info on the multivariate EGARCH Model
***see Koutmos G. (1996) "Modeling the Dynamic Interdependence of
***Major European Stock Markets", Journal of Business Finance and Accounting,
***1996, Vol. 23, pp. 975-988.
**
**Revised 12/2009 by Tom Doan, Estima.
**
****************************************
cal(d) 2003:1:2
all 2007:06:29
open data period1.xls
data(format=xls, org=obs) / nasdaq idx xr
*
compute n=3
*
* Define the return series
*
dec vect[series] r(n)
compute start=2003:1:2, end=2007:06:29
set r(1) = 100*log(nasdaq/nasdaq{1})
set r(2) = 100*log(idx/idx{1})
set r(3) = 100*log(xr/xr{1})
*
* Template for mean equation. This is a VAR(2)
*
equation meaneq *
# constant r(1){1} r(1){2} r(2){1} r(2){2} r(3){1} r(3){2}
*
table
*
dec vect[series] u(n) ;* Residuals
dec vect[series] v(n) ;* Variances
dec vect[frml] e(n) ;* Model for mean
dec vect[frml] z(n) ;* EGARCH indexes
dec vect d(n) ;* Asymmetry coefficients in EGARCH
dec vect g(n) ;* Lagged variance coefficients in EGARCH
*
* Subdiagonal for correlation matrix
*
dec symm rr(n-1,n-1)
*
* Coefficient vectors for the VAR (b) and the EGARCH with spillover (a).
* The variance for equation i takes the form:
*
* log h(i) = a(i)(1)+sum_j a(i)(j+1) z(j){1} + g(i) log h(i){-1}
*
* z(i) = abs(u(i)/sqrt(h(i))) - sqrt(2/pi) + d(i)*u(i)/sqrt(h(i))
*
dec vect[vect] b(n)
dec vect[vect] a(n)
*
* Set up the formulas for the mean and for calculating the "z"
*
do i=1,n
frml(equation=meaneq,vector=b(i)) e(i)
frml z(i) = abs(u(&i){0})/sqrt(v(&i){0})-sqrt(2/%pi)+d(&i)*u(&i){0}/sqrt(v(&i){0})
end do i
*
dec symm sigma
*
* Do calculations at time <<t>> for the residuals (u), variances (v) and
* full covariance matrix (return value for function).
*
function EGARCHSpillover t
type symmetric EGARCHSpillover
type integer t
*
local integer i j
local real hlog
*
do i=1,n
compute hlog=a(i)(1)+g(i)*log(v(i)(t-1))
do j=1,n
compute hlog=hlog+a(i)(j+1)*z(j)(t-1)
end do j
compute v(i)(t) = exp(hlog)
compute u(i)(t) = r(i)(t)-e(i)(t)
end do i
dim EGARCHSpillover(n,n)
ewise EGARCHSpillover(i,j)=%if(i==j,v(i)(t),rr(i-1,j)*sqrt(v(i)(t)*v(j)(t)))
end EGARCHSpillover
*
* Log likelihood
*
frml Lt = sigma=EGARCHSpillover(t),%logdensity(sigma,%xt(u,t))
*
* Initial guess values from running regressions. The b's are the OLS
* estimates, a's, g's and d's are (except for the constant) standard
* guess values.
*
do i=1,n
linreg(equation=meaneq,noprint) r(i)
set u(i) = %if(%valid(%resids),%resids,0.0)
compute b(i) = %beta
compute a(i) = %zeros(n+1,1)
compute a(i)(1)=log(%seesq),a(i)(i+1)=.25
compute g(i)=.80,d(i)=0.0
set v(i) = %seesq
end do i
*
compute rr=%zeros(n-1,n-1)
*
nonlin b a d g rr
maximize(pmethod=simplex,piters=2,method=bfgs,trace,iters=200) Lt start+3 end
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결과물
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MAXIMIZE - Estimation by BFGS
NO CONVERGENCE IN 46 ITERATIONS
LAST CRITERION WAS 0.0000000
SUBITERATIONS LIMIT EXCEEDED. ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT.
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR.
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK
Daily(5) Data From 2003:01:07 To 2007:06:29
Usable Observations 1169
Function Value -3983.03609507
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. B(1)(1) 0.026006783 0.023529048 1.10531 0.26902728
2. B(1)(2) -0.028430619 0.030126867 -0.94370 0.34532475
3. B(1)(3) -0.010582568 0.029317822 -0.36096 0.71812917
4. B(1)(4) 0.083215149 0.022413095 3.71279 0.00020499
5. B(1)(5) -0.020585508 0.023642741 -0.87069 0.38392322
6. B(1)(6) 0.115966525 0.054327655 2.13458 0.03279563
7. B(1)(7) -0.068522058 0.055612423 -1.23214 0.21789836
8. B(2)(1) 0.131525988 0.032656036 4.02762 0.00005635
9. B(2)(2) -0.039888916 0.032295194 -1.23513 0.21678036
10. B(2)(3) 0.108129217 0.032911051 3.28550 0.00101802
11. B(2)(4) 0.136969553 0.035398639 3.86935 0.00010913
12. B(2)(5) -0.093608226 0.031328737 -2.98793 0.00280869
13. B(2)(6) -0.097266650 0.078838409 -1.23375 0.21729720
14. B(2)(7) -0.154587109 0.069489422 -2.22461 0.02610719
15. B(3)(1) 0.006660069 0.009197937 0.72408 0.46901485
16. B(3)(2) -0.042832064 0.012182270 -3.51593 0.00043821
17. B(3)(3) -0.009709606 0.011628094 -0.83501 0.40371058
18. B(3)(4) -0.007234165 0.009435563 -0.76669 0.44326503
19. B(3)(5) 0.002878325 0.009020124 0.31910 0.74965043
20. B(3)(6) -0.027146506 0.032451223 -0.83653 0.40285534
21. B(3)(7) -0.009892376 0.022498278 -0.43969 0.66015816
22. A(1)(1) -0.000113987 0.001345023 -0.08475 0.93246239
23. A(1)(2) 0.036815296 0.011305063 3.25653 0.00112782
24. A(1)(3) 0.023142526 0.011347961 2.03936 0.04141456
25. A(1)(4) -0.012299481 0.009218166 -1.33427 0.18211686
26. A(2)(1) 0.051407596 0.014012791 3.66862 0.00024386
27. A(2)(2) -0.004001650 0.040407963 -0.09903 0.92111349
28. A(2)(3) 0.254554708 0.044859992 5.67443 0.00000001
29. A(2)(4) -0.002990072 0.039019970 -0.07663 0.93891846
30. A(3)(1) -0.221001083 0.024998394 -8.84061 0.00000000
31. A(3)(2) 0.054891577 0.027059677 2.02854 0.04250539
32. A(3)(3) 0.035698531 0.039188210 0.91095 0.36232130
33. A(3)(4) 0.423803398 0.041719006 10.15852 0.00000000
34. D(1) -0.536471786 0.268431119 -1.99855 0.04565756
35. D(2) -0.593369199 0.131211076 -4.52225 0.00000612
36. D(3) 0.108272960 0.066727347 1.62262 0.10467120
37. G(1) 0.998435664 0.002304331 433.28661 0.00000000
38. G(2) 0.802303232 0.040048229 20.03343 0.00000000
39. G(3) 0.831733282 0.016086500 51.70381 0.00000000
40. RR(1,1) 0.280460824 0.029142596 9.62374 0.00000000
41. RR(2,1) -0.184668486 0.028372748 -6.50866 0.00000000
42. RR(2,2) -0.305142667 0.022703382 -13.44041 0.00000000
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