Taiwan Fuures Exchange, TAIFEX TAIFEX Taiwan Sock Index Fuures 00 4 expiraion eec S&P 500 ( ). Kawaller, Koch and Koch 987 S&P

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1 004 May, 0 pp99-8 leehero00@yahoo.com.w ( ) ADF ( ) Granger ( ) (VAR) (SSM) : Sudy o an invesigaion o he relaionship among Taiwan s Spo, Fuures and Opions prices -The Applicaion o Sae Space Model Absrac This paper Sudy o an invesigaion o he relaionship among Taiwan s uures, spo and opions prices Daily daa o hese series are colleced rom December 4,00 o Augus 3, 003 The research procedure includes ideniicaion o saionaliy o a ime series or each variable using Augmened Dickey-uller es (ADF) causaliy es using Granger s mehodology esimaion o vecor auoregressive model (VAR) and Sae Space Model (SSM) The resuls show ha many o he variables under invesigaion are inerrelaed o each oher In order o obain beer research resuls and predicion accuracy i is imporan o markes Keywords Granger es Impulse response analysis Forecas error variance Vecor auoregressive es Sae space model

2 Taiwan Fuures Exchange, TAIFEX TAIFEX Taiwan Sock Index Fuures 00 4 expiraion eec S&P 500 ( ). Kawaller, Koch and Koch 987 S&P ~

3 . Soll and Whaley 987 S&P ~ Soll and Whaley 99 S&P ~989 6 Boosrapping 4. Edwards 998 S&P ~987 F-saisic 5. Lee Chun I 999 MMI NSE S&P500 sock index uures ~99 7 U 0 ( ) SIMEX ~997 0 ECM. 87 NIKKEI ~ ~997 6 GARCH GMM SIMEX TAIFEX Ljung-Box GARCH. TAIFEX SIMEX SIMEX ~ GARCH - 0 -

4 ~ GJR SIMEX TAIFEX 500 GARCH SIMEX TAIFEX TSE ~ GARCH / / - 0 -

5 ( ) R S, ( p = s, p P S, s, ) R S, P S, P S, - - ( ) R F, ( p = F, p P F, F, ) R F, : P F, P F, - - ( ) R C, ( p = C, p P C, C, ) R C, : P C, P C,

6 Engle & Granger(987) (inegraion) X d (inverible) ARMA(Auoregressive Moving Average) d I(d) I(0) I() I(0) X=0 I() X=0 (uni roo es)

7 ADF(Augmened Dickey-Fuller) DF (whie noise) Dickey-Fuller(98) Said & Dickey(984) X- ARMA DF X m + ρ X + ε i= = β X () X m + ρ X + ε i= = α + βx () X m + ρ X + ε i= = α + γt + βx (3) DF Dickey-Fuller(98) Granger Granger Granger Granger(980) ( ) X X X = { X =,,3..., } j = { =,,3..., } j = { X = 0,,,..., } j = { = 0,,,..., } j ( ) δ ( x X, ) < δ ( x X ) y (cause)x x δ (mean square error o orecasing) ( ) δ ( x X, ) < δ ( x X ) y (conemporaneous) x

8 004 ( ) δ ( x X, ) < δ ( x X ) δ ( y X, ) < δ ( y ) y (cause)x x (cause) y (eedback eecs) ( ) δ ( x X, ) = δ ( x X, ) = δ ( x X ) δ ( x X, ) = δ ( y X, ) = δ ( y ) x y (independen) ( ) δ ( x X, ) < δ ( x X ) δ ( y X, ) > δ ( y ) y (cause)x x y (unidirecional cause and eec relaionship) y x (VAR) Sims(980) (VAR) (prior) (srucural model) (VAR) VAR Sim(980) VAR n = α + A µ (3-6-) i= i + i ' E ( µ ) = 0 E ( µ µ ) = 0 E ( µ iµ s ) = 0 (3-6-) (n ) (joinly covariance saionary ) (linearly sochasic process) µ (n ) (orecas error) (shock, innovaion or impulse) Ai (n ) m E ( µ iµ s ) = 0 ' E ( µ µ ) =

9 ( ) (3-6-) (variance decomposiion) Sims (3-6-) Wold (Wold decomposiion heorem) (moving average) : = m m α + Aj j+ ε A j j = α + ε j= j= ( I A L ) m A L... Am L = α + ε = α ( I A L m m A L... Am L ) + ε ( I A L A L... Am L ) L lag operaor i= 0 = α ' + ciεµ ( 3-6-) α ' (n x ) c i (n x n) c 0 = I ( ) (3-6-) ( µ ) (conemporaneously uncorrelaed) µ µ ( ) VAR D i (innovaion) (3-6-) k (k-sep-ahead error) : Eˆ µ µ µ D W (3-6-3) k = c0 + c ck k + = D0W + DW (VAR) (MA) ARMA Vecor ARMA (Sae Space Model) k k

10 004 (SSM) (VAR) (MA) Granger & Newbold (990) (g x ) I X (s x ) E( I) X X = β + γ Z V ( g ) ( g s) ( s ) ( g u) ( u ) ( g ) X = τ X δ W µ ( s ) ( s s) + ( s ) + ( g ) ( ) + Ψ ( s m) ( m (3-7-) ) (3-7-) Z W V U X X (3-7-) (Sae Vecor) X Z V (3-7-) X Akaike(974) (ARMA) ARMA s-r Akaike ARMA(p q) Φ ( B ) = Θ ( B ) ε Φ... Φ p p = ε + Φ ε Φ p (3-7-3) (3-7-3) B ( B = - ) ε ; Φ( B) = Θ( B), Φ (0) = Θ(0) = I (3-7-3) = Φ ( B) Θ( B) ε = s= 0 ψ ε s s (3-7-4) ψ (3-7-4) s (Impulse response marix) : = s= i ψ ε s + i s = + i + ψ i ε + (3-7-5) (3-7-6)

11 (3-6-4) + p = Φ + p Φ p + ε + p + Θε + p Θ qε + p q (3-7-7) p>q ε ε 0( + I =0 I>0 ) i = p +p (3-7-6) P =.. Φ p Φ 0... p Φ 0... p Φ + p I ψ. +.. ψ p ε + µ + Z + = FZ + Gε + (3-7-8) Z (sx) F (sxs) (Transiion Marix) G (sxr) (Inpu Marix) (Impulse Response Marix) ε + r Σ 0 Akaike(976) Z Granger Newbold(986). (VAR) AIC K AIC(Akaike s Inormaion Crierion) = nin( p ) pr (3-7-9) AIC p + p r n. (Sae Vecor) p = (,,..., k ) = (, +,..., + k ) (Canonical correlaion) Χ

12 (.96) 4. (.96) E-Views ( ) ADF(Augmened Dickey Fuller) ( ) Granger ( ) (VAR) (SSM) ADF H 0 3 SPR FPR CPR (4 ) Mackinnon Criical Value ADF Tes ( ) Saisic 0% 5% % SPR * FPR * CPR * * 5% - 0 -

13 3 SPR FPR CPR 5% H 0 Granger VAR Vecor Auoregressive Granger VAR 6 AIC Akaike Inormaion Crierion VAR ADF VAR AIC, VAR AIC Lag AIC * * VAR (Impulse Response analysis) (Variance Decomposiion). SPR SPR. SPR CPR SPR CPR 3. FPR SPR FPR 4. FPR FPR 5. CPR CPR - -

14 004. (00%) (0%). (88.48%) (.5%) (0%) 3. (99.35%) (0.64%) ( %) SSM SAS ( Sae Space Model, SSM) Granger & Newbold(986) (VAR) AIC(Akaike Inormaion Crierion) K (Canonical Correlaions Analysis) (Sae Vecor) > F AR G MA R S (T;T), R F (T;T), R C (T;T), R S (T+;T), R F (T+;T),R C (T+;T) 4-6- AIC χ R S (T;T), R F (T;T), R C (T;T), R S (T+;T) * *0.398 R S (T;T), R F (T;T), R C (T;T), R S (T+;T), R F (T+;T) R S (T;T), R F (T;T), R C (T;T), R S (T+;T), R F (T+;T),R C (T+;T) R S (T;T), R F (T;T), R C (T;T), R S (T+;T), R F (T+;T),R C (T+;T), R S (T+;T) R S (T;T), R F (T;T), R C (T;T), R S (T+;T), R F (T+;T),R C (T+;T), R F (T+;T) R S (T;T), R F (T;T), R C (T;T), R S (T+;T), R F (T+;T),R C (T+;T), R C (T+;T) * - -

15 (Transiion Marix) (Inpu Marix) T T (.96 ) (.96 ) T 4-6- Sae Vecor RS (T ; T) RF (T;T) RC (T;T) RS (T+;T) RF (T+;T) RC (T+; T) Esimae o Transiion Marix Inpu Marix or Innovaion SSM Model - 3 -

16 SSM Model Parameer Esimae Sandard Error T-Value G(5,) G(5,) G(6,3) F(5,) F(5,) F(5,3) F(5,5) F(5,6) (Transiion Marix) ( Iupu Marix) (Innovaion) R R R R R R S, + F, + C, + S, + F, + C, R R R RS RF RC S, F, C,, +, +, ε ε F ε R S, + = R S, + ε S, + (4-6-4) R F, + = R F, + + ε F, + (4-6-5) S,+, + C,

17 R C, + =R C, + + ε c, + (4-6-6) R F, + = x R S, x R F, x R S, x R F, x R C, x ε S, x ε F, + (4-6-7) R C, + = x R S, x R F, x ε c, + (4-6-8) ( ) + (4-6-4) ( ) + (4-6-5) ( ) + (4-6-6) ( ) + (4-6-7)

18 004 ( ) + (4-6-8) R S, R F, R C, R S, + R F, + R C, + ε S, + ε F, + ε c, + R S, +/ + R F, +/ R C, +/ Aksu&Gunay(995) (Error cross-corelaion maraix) R S, R S, R F, R C, ( ) (<.000 ) (0.0790) R F, <.000 R C, (0.0790) ( ) (0.0866) ( ) - 6 -

19 Granger VAR Granger SSM SSM - 7 -

20 004.. GARCH Model Nikkei pp GARCH SIMEX TAIFEX TSE / 4 pp pp Edwards, F. R., Does uures rading increase sock marke volailiy? Financial Analyss Journal, 988, pp Kawaller, I. G., P. D. Koch, and T. W. Koch, The Temporal Price Relaionship Beween S&P 500 Fuures and he S&P 500 Index, Journal o Finance, 987, pp Lee, Chun I, The inluence o inormaion arrival on marke Microsrucure : Evidence rom hree relaed markes, The Financial Review, Feb. 999, Vol. 34, Iss., pp Soll, H. R. and R. E. Whaley, Program rading and expiraion-day eecs, Financial Analyss Journal, 987(March-April), pp Soll, H. R. and R. E. Whaley, Expiraion-day eecs: wha has changed? Financial Analyss Journal, 99(January-February), pp

4/09 4/15 4/21 4/25 5/07 5/13 5/19 5/23 5/29 6/04 6/10 6/16 6/20 6/26 7/02 7/08 第 2 期湖南人文科技学院大学生学报 2 由表 1 可知, 白银期货价格序列与现货价格

4/09 4/15 4/21 4/25 5/07 5/13 5/19 5/23 5/29 6/04 6/10 6/16 6/20 6/26 7/02 7/08 第 2 期湖南人文科技学院大学生学报 2 由表 1 可知, 白银期货价格序列与现货价格第 2 期湖南人文科技学院大学生学报 No.2 2015 年 3 月 Journal of College Sudens of Hunan Universiy of Huaniies, Science and Technology Mar.2015 白银期货与现货价格引导关系研究麦琼辉, 吴丽萍, 黄姿 ( 湖南人文科技学