EC361-1.dvi

CÉ%Èã D\µ 2Ûû Í%Èû F 36:1 (2005), 1 28 JØàN Ñ!5,ñ%Èã =} ²=Ú`²A ÅCÉ ç%èçí 2 2Ûû Í%Èû F Ä= W\Í3lTú ÉœÈ: ØàN %ÈAÅ0 Ää 3A}}& JEL }éhu: C32, C51 :ût6: =}, ÅCÉ ç%èçí, C 100 21 U Úu: (02) 2351-9641 } œ 274; fö: (02) 2351-1826; E-mail: d89323002@ntu.edu.tw T6b>á3)DsPˆ±Çöí <c, U dy ÀUêe dcñt6b5u û -),.H[T6bFœÉí<c

b dj Stock and Watson (1998) íj Ñ!, ø_s í Ø àn ã _, 1@àk%ÈAÅ0íã Î7Y Stock and Watson (1998) ít Õ, Bb6ø bywô4 }Ѽ¹Ò b, ŒÞÒ b D Ò b, y} ú Ò b,lwøàn, Í(;W <N ªWã õ! éý, ØàN ã _xóçßíã ô^, 6i kåqø<%èàpftíã, Ä ªJTÑ V,ñ%Èã,íÇø ²Ï

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) 1. k,ñ%èã ø²u\ Æ È ÆDçXäFÉ í½õ <ã!.cªdñ\l\íyw, 6ª? $ D Vúk í i Ê VÖí}&Dã j 2, l¾_uw2 ½bíøá x; ÅqrÖ%È ã ÀP¹ ó í:j _ (simultaneous equations model) *9 ã _íiõêkñp7rö%è b, FJqk bí WÑD b5èíé[ Wà, W\Í3lT (J- 3lT) í, XÛ _¹ 51 j, w2l 24 ì2j 27 WÑj Í 7ó í_ª?ßþ_ïq (misspecification), 6%%_wì (identification),í Ø, ª7 àƒ,l! J š Õíã? k, röû 6SàÀ ¾CœüíÖ ¾_J*9}&Dã Wà, Ê =íû jþ, Š² (1998) Huang (1999) SàÀ ¾ïªÚā² _ (Markov switching model), 7 Chen and Lin (2000) =}D2 (2001) àö ¾ïªÚā²_ é_é úøcýb b J}&, ÖÍU_qì )óúñq, Oº[J7wFª?àí,ñ e * e«àíivõ, ít ª??Ý ^í}&j Stock and Watson (1998) y1ååð%èû (NBER) í ØàN (diffusion index) í 1, T øhíã j, Ö.Ûqló í_, ºE?k}«à,ñ bfúöí m NBER ít uø %È bí 8$3h#8āb, Í( AªXwì =ÛïíN Stock and Watson (1998) à$lj 2í3A}}& (principal component analysis), A ¾ e2¾ 3bÄäçTN b, Í(y à <N bø_àí(4ã _ D NBER íj óª, Stock and Watson í T éíœñîh Î 5Õ, Stock and Watson (1998, 2002) íj % _ çô.(,?ª vtü. ä0í e; WàBbªJ v à ed~ 3

CÉ%Èã D\µ 36:1 (2005) eªw_,ldã }& d3bj Stock and Watson (1998) íj Ñ!, ø_s í ØàN ã _, 1@àk%ÈAÅ0íã Î7Y Stock and Watson (1998) ít Õ, Bb6ø bywô4 }Ѽ¹Ò b, ŒÞÒ bd Ò b, y} ú Ò b,lwøàn, Í(;W < N ªWã T Î7\ŸVj íiõ, 6UBb)Jyªø ³. Òú%ÈAÅ0í à Bbíõ }&O½Êú%ÈAÅ0 VøBûíã, 1SàÌj;Ï "úïïìmd"úïïì0 V eã ô^, Åq 3b%Èã ÀPFt0í! óªœ Bb êû.uy Stock and Watson (1998) íj,løàn, CY. Ò },lwøàn, à <N FZííã _Ìã7íã ô ^ âkåqñ þ øj í@à, Ä duøÿhíþt, õ! 6TX VÊ,ñ%Èã,íÇø²Ï Î kõ, d íqñ) à- ùü Stock and Watson (1998) í,ldã j úñ dõ j ín; ûñã! íªœ (øñ!d 2. ØàN j BbílÜ Stock and Watson (1998) ís íã j ø u,l F%È bíää (factor) ²¾, ù u à <Ää²¾ªWã cq x it u i _%È bêvè t íhôm, / x it = λ i F t + ǫ it, i = 1,...,N, (1) w2 F t (r 1) Ñ.Ó bz íää²¾, λ i (r 1) H[ i _ bíä äš- (factor loading) ²¾, ǫ it ÑÏÏá ø N _%È bdää5èí 4

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) É[ã V, ¹ª)ƒ x t = F t + ǫ t, (2) w2 x t = (x 1t,x 2t,,x Nt ), = (λ 1,λ 2,,λ N ) Ñ N r íääš -ä³, ǫ t = (ǫ 1t,ǫ 2t,,ǫ Nt ) â (2) ªø, N _ bíwñ3bâ r _u Ää F t F²ì, 7 F t 6ÿu Stock and Watson (1998) F í Øà N, Ê(d2Bb6J 5 1 JcqÏÏ ǫ it Ñ i.i.d. G}º, wìbñ 0, æbñ σ 2, _2 í ø b F t í,lªâ Nƒb ) wj à-: íli F = (F 1,F 2,,F T ), F í N,lªâJ-ñ ƒbí ü 2 ): V NT (F, ) = 1 NT N i=1 T t=1 ( x it λ i F t) 2. (3) I ξ i = (x i1,x i2,,x it ) Ñ i _%È br hômf$aí²¾ # ì F 5-, λ i.ìå J-íø¼ K: 1 NT N i=1 T t=1 ( ) x it λ i F t F t = 0. (4) ] λ i Ñ F íƒb: λ i (F) = (F F) 1 F ξ i ø λ i (F) Hñ ƒb (3) ª) ƒ V NT (F, (F)) = 1 NT N i=1 (ξ i ξ i ξ i ( ) ) F F 1 F F ξi. (5) 1 (2003) 2 àøàn VwìCÉí =, ñwfì2íøàn d1.ó 5

CÉ%Èã D\µ 36:1 (2005) JqìØàN ä³ F Å Ä íì : F F/T = I,?U (5) ü í F, 6}U- (N) 1 N i=1 ( ξ i FF ξ i = trace [F 1 N ) ] N ξ i ξ i F. (6) FJ, F í N,l ˆF 6ÿuú@k N i=1 ξ i ξ i /N í r _Ô M (eigenvalue) íô²¾ (eigenvector) F$A5ä³, 7 ˆF í ø_w² ¾ÿuø_Ô²¾ ø ˆF Hp λ i (F) ¹)ƒ λ i í,l _j 6ÿ uøof2í3a}}& ç,l F 5(, Bbª à N ø_àí(4_, JZú Ôì b y T V h íã íl àš qí e, J y t+h úbá i=1 ç ØàN F t wr( F t 1,,F t p Tc, )ƒ y t+h = ˆα 0,h + ˆβ 0,h F t+ + ˆβ p,h F t p+ê t+h, t = p+1,...,t h, (7) w2 ˆα 0,h ˆβ j,h }H[c [bí,lm (,lmó h Z 7. ), ê t+h Ñ_{Ï, T H[š hômí_b y;w (7) í,l!, Bbª )š Õ T + h y íã MÑ ŷ T +h = ˆα 0,h + ˆβ 0,h F T + + ˆβ p,h F T p. (8),Híã j Dd.,í øj óªröiõ âk (2) ªJ ÖrÖ %È b, ØàN ÿ)j švö bèíé[j b ÚÖí m, uà ¾CœüíÖ ¾_FÌ dƒí 7lØà N 1.Û ó í_, Ä fn7:j _ª?ßÞí_Ï qdwì,í Ø âk3a}}&ud.,ø±í$lj,,løàn uøk'ñqí T, röú7p_,ñ ªÏW á T 7 (7) í( 4ã _qk,l, 6U øj Ëã í¹v4 6

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) M) <íu, dsàíj cìktüì e (balanced data),? ¹F eìxó í e È à e È. 7$AÝÌ e (unbalanced data), _,lÿœñµæ, 7âJ EM algorithm CwFj,l ÇÕ,,lØàN vbbcq: ÏÏ ǫ it Ñ i.i.d. G}º, /Ää ²¾ F t ÑÝÓœ b O Stock and Watson (1998) 6 p7éb eå ø< ÜíÏ K, _,lj F,l VíÄä ˆF ÊyøO ícq - (àorïï5èóé4) Exø_4 (consisitency); Ìzpª 5 Stock and Watson (1998, 3.2 ) 3. edõ j díõ }&JCÉ,ñ%È b eñ!, ªW%ÈAÅ0íã B bâ3ltå %È}l 2² FÛ5 b, OxÎ ÌhbW5 b, (,u²ï 81 _ b ;W3lT, ÄXÛ, _ 2íÒ, < bªj }Ñ 31 _¼¹Ò b, 32 _ŒÞÒ b, J 18 _ Ò b e È* 1988 2 B 2003 2, ø_ bî 61 e < e2, Å F), ÓgD e} A3lT) í Å %Ȳ$lÑ, Óg$l~Ñ, A Ä$l~Ñ DÞß $l~ñ ; À e A2ÛÁWí À $l~ñ ; Õü e A \ í ª $l~ñ ; e ACÉ >qfí Ò>q~Ñ BbÊ #, ØàN j íÿ¹êka ¾ e2¾ m, ]BbÊõ 26j¾Ö² b âk3a}}&1. bèí (4É[F à, FJ¹U b5èò~óé, Bb?ª?ø b vñp} &; Stock and Watson (1998)?S ó ít Ê etüjþ, úkx4í b, djìª0 (ratio to moving average) ªW c Ñ7ü\F eìxìg (stationary) 4, ç eñ ÄM (level) v, Bbl úb, yywà; ìí! ²ì u â Ï}ā²; ç eñª0 (ratio) v, òqªwà; ì(²ìu 7

CÉ%Èã D\µ 36:1 (2005) â Ï} Ìí bzpd btüj~ cë 1 F b%, Hā² (, Bb yøw Ä, JfnÄ bàp.ø_7 A,l, írï Bbíõ j }As øÿu Stock and Watson (1998) ít, òqâ 81 _%È b2,løàn, 7(y à ØàN ú%èa Å0 V h íã _ ã (2) D (7), Ää!ZDã _ª[ýà -: y t+h = α 0,h + x t = F t + ǫ t, p β i,h F t i + e t+h, t = p + 1,...,T h, (9) i=0 Bb 5Ñ ØàN.}Ò_ ø_2 _íøàn _b r F t ír( b p îâó«m7ä (Bayesian information criterion, BIC) F²ì âkbbíõ ½õu_íã?, ]ØàN í_b u;wù 2º_(4ã _5ß; (¹ BIC) V²ì, 7.uYWw F?j,ñ eí ªW7²ì 2 7Ñ7fn,l b Ö7 AAâ. í½æ, BbÌ ín _bñ 6, 7 ±ír( bñ 3,Hj uã F bv,lwu Ää, FJ <Ää1Ì } _ÒíÔ4 Ñ7zp ø8$, Bb;W 1988 2 B 2003 2 F e, ø _,ñ b}ú 6 _ØàN dà(4c, 1l w R 2 (?¹ ø_øàn F?j b, 5ªW) Bbø! kë 2 íç2, w2,ñ b5 åàë 1 F: 1 ƒ 31 Ѽ¹Ò b, 32 ƒ 63 ÑŒÞÒ b, 64 B 81 Ñ Ò b â <Ç2ªJ õ, ø_øàn? šrö b. í Wà 1 _Øà N? šœöœþò bí (O6j 7ø<¼¹Ò Ò 2 ÔW7k, JJ 2003 1 Ñ!, à ØàN.}Ò_ ã 2003 2 í%èaå0 ù v;w BIC ² íääbñ 3 (r( bñ 1) ÖÍ 3 _ÄäÊø 2É?j 41.7%,ñ eí, O uê BIC Ä- 7! í²ï 8

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) bí ), 2 _ØàN š7œö Ò }¼¹Ò bí, 3 _ØàN šœö¼¹ò bj ø< Ò bí (O s_n Ì šœþò bí ) Ñ7yÀU ³ _Òí bê%èã 2rÆíiH, Bbõ, 6SàÇøT : lø b }Ѽ¹Ò b ŒÞÒ bd Ò b, y},l úò b AíØàN, Í(;W <ÒØà N ªWã óúk (9), }Ò5-íÄä!ZDã _Ñ: y t+h = α 0,h + x j t = j F j t + ǫ j t, j = c,m,l, p c i=0 t = max pm βi,h c F t i c + i=0 pl βi,h m F t i m + i=0 β l i,h F l t i + e t+h, { p c,p m,p l} + 1,...,T h, (10) w2 bí, c [ý¼¹ò b,, m [ýœþò b, 7 l Ñ Ò b _ 5Ñ ØàN }Ò_ âk }Ò (_ín bó, Ñfn_Ø µæ, Ê,lvBbcor _Ò ín _bñ 3, 7 ±ír( bñ 2; _ín _bdr( be â BIC ²ì 7 }Ò5(y,lØàN íj, ªU ÒíØàN ùæ[û Òí, 6UBb)J. Òúã íõ. âk. \µ3b àíò.`ó, xò!zíã _ú\µû }& ѽb, 7 6u Stock and Watson (1998) Ÿáj FÌ TXí 4. õ }&Dªœ Ñ7 ¾ØàN íš Õã ô^, Bbø 2000 1 ƒ 2003 2 (u 14 ) í%èaå0\gñš Õí t Ê t È, CÉ% ÈAÅ Û Ùš, Ê 2000 AÅÇáî, 2001 Û½ «(1 9

CÉ%Èã D\µ 36:1 (2005) [ 1. hôõ-%èaå0íã! (ØàN.}Ò) ñ õòm º_M ã M ø ù ú û 2000 1 7.94 7.73 6.99 5.56 6.89 6.07 2 5.10 6.22 6.50 6.62 5.30 7.15 3 6.73 6.40 5.78 6.83 7.13 4.75 4 3.82 3.67 5.04 5.50 5.67 3.79 2001 1 0.61 1.94 3.59 4.28 4.57 4.53 2 3.26 1.40 2.72 4.75 5.15 5.68 3 4.42 3.10 0.11 2.39 3.50 6.19 4 1.58 0.90 0.23 0.31 4.00 4.95 2002 1 0.94 1.99 4.81 0.32 3.50 6.90 2 3.67 3.41 4.36 4.40 2.57 3.68 3 5.21 6.08 6.23 4.10 7.40 2.88 4 4.52 5.73 6.23 6.04 4.83 3.27 2003 1 3.53 5.35 4.98 5.39 5.90 2.34 2 0.08 2.82 3.59 4.41 2.82 3.08 Å: ÀPÑ % 2 3 ÛŠAÅ), 5(Ö)+Ñ AÅ, 2003 2 º Ä SARS P 8~ô7y ÛŠAÅ Bb²ì ø vètñã í t, Î7U _Ê,l bve?\óçíaâõ, yªj ð. _ÊC É%ÈAÅ0 Û½ víã? Bbø.}Ò_D }Ò_íã! }k[ 1 [ 2, [2 š Õã Dš qº_í! J[ 1 íù (ã ñ Ñ 2000 2 ) ÑW, Bb àš eƒ 2000 1, ã 2000 2 í%èaå0, Ñø íš Õã, ã MÑ 6.50%; J àš eƒ 1999 4, 2000 2 (2 íš Õã ) íã MÑ 6.62%; wìj ér Î 5Õ, Bb6 àš eƒ 2000 2, Jlv íš qº_m (6.22%), 1ø <! D3lTt0íõÒM (5.1%) J úî ªø e ØàN }Ò_ í,l!, ªJêÛ } ;W BIC F² í_2, ¼¹ÒíØàN.u_bCur( b œwfòñö, éý¼¹òíç Dr(N Êã vræ7óú½b 10

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) [ 2. hôõ-%èaå0íã! (ØàN }Ò) ñ õòm º_M ã M ø ù ú û 2000 1 7.94 7.22 5.54 5.76 6.72 5.39 2 5.10 6.38 6.22 6.89 5.21 7.49 3 6.73 5.50 6.81 6.19 5.47 4.00 4 3.82 3.99 5.43 4.76 4.64 5.02 2001 1 0.61 1.96 4.35 5.72 4.65 4.79 2 3.26 1.79 1.69 3.80 3.58 4.94 3 4.42 3.46 1.14 3.99 2.87 5.39 4 1.58 0.15 2.17 0.48 3.30 5.89 2002 1 0.94 1.75 1.94 0.38 8.35 5.86 2 3.67 4.85 2.50 6.12 5.04 5.97 3 5.21 4.66 5.22 3.66 5.52 6.38 4 4.52 4.67 4.79 5.47 3.30 8.02 2003 1 3.53 3.15 3.52 5.15 5.13 5.41 2 0.08 1.68 2.77 2.97 1.04 2.25 Å: ÀPÑ % íih, 7!u ØàN.}Ò_ FÌ )ƒí Ñ7 ô¹ù, Bb. ø íìí b,l!, Eû íè6ª J²BbØ Î7;WØàN Físã! 5Õ, Bb6øABc (AR) _íã! k[ 3, Åq_3b%Èã ÀPíã! k[ 4 B [ 6, JZóªœ [ 4 Ñ3lTFì t0íã!, eväñw\ Í3lTúí Å F)$lD%È8 h9ā ; [ 5 ÑCÉ%È û Í ( ÑC%Í), eväñwfì êwí CÉ%Èû ~ ; [ 6 Ñ2M%Èû Í ( Ñ2%Í) íã!, eväñ2%íì êw5 CÉ%Èã D 1998 B 2003 5 r7%è 3 _ œz3buyw Aí,ñ:j _ªWã, y;wùðç6í< c J c7)ƒ (íã! Ou ÀPtÓã ívõ., 3 ã 3 3lTt0ã ívõñ í 2 5 8 11 ~M, 2 ~MFt0íã! Ñ ø 4 Fdíã ; 5 ~MFt0í Ñç 1, J ér 7C%Ít0ã ívõñ í 1 4 7 11 ~M, 1 ~Mt0íã! Ñ ø 4 Fdíã, wìér 2%Íí 11

CÉ%Èã D\µ 36:1 (2005) [ 3. hôõ-%èaå0íã! (AR _) ñ õòm º_M ã M ø ù ú û 2000 1 7.94 6.15 4.89 4.17 5.59 5.48 2 5.10 6.19 6.50 5.81 4.55 5.27 3 6.73 6.39 6.45 6.97 5.44 5.19 4 3.82 2.15 3.32 2.89 3.85 2.98 2001 1 0.61 2.82 3.72 5.44 4.79 4.96 2 3.26 3.33 1.94 3.02 5.80 5.81 3 4.42 5.83 3.20 3.50 5.42 4.74 4 1.58 1.23 5.70 0.66 6.62 5.72 2002 1 0.94 6.34 2.46 1.49 5.72 4.70 2 3.67 3.00 6.85 2.46 4.38 3.84 3 5.21 3.24 1.71 3.83 3.77 3.51 4 4.52 3.38 1.41 0.10 1.18 1.27 2003 1 3.53 1.00 0.42 0.15 2.67 2.75 2 0.08 4.74 2.86 4.24 3.98 4.40 Å: ÀPÑ % íé6., [2Ñ N/A 6¹[ýÌvéã e âk2ûí%èf íã šnê0øÿ, wfœz ê0ít., ]Bb.ø5 pªœíúï â [íã båõv, ø íã! œß, ± íã ó úœï à *ø íã Võ, Ê t 2 œ í 2001 2003, Ø àn.}ò _ú 2001 í«n 1.Ü>, ø íã Éé ý/í«, 7Êw(í 2002 D 2003 M/ò,%ÈAÅ0 O Øà N }Ò _ø íã ºœ? ³ 2001 í«8, úw( í 2002 D 2003 6œÄüíã s_ö[û., O?ã 2001 3 íšaå AR _ÖÍú 2001 3 Q íã M, OÊÓ( Ûóç.ìíã, v7 7h (2001 4, 2002 3 4, D 2003 1 ), vº h (2002 2 ) D AR _ óª, C%ÍD2%Íø íã óúu, Oú 2001 í«ìbb tóã ívõñ í 4 7 10 12 ~M, YŸ Ñç 1 B 4 íã 12

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) ñ [ 4. hôõ-%èaå0íã! (3lT) õòm ã M ø ù ú û 2000 1 7.94 7.53 6.35 N/A N/A 2 5.10 5.51 5.88 5.33 N/A 3 6.73 6.67 6.90 6.73 6.29 4 3.82 5.97 6.32 6.64 6.10 2001 1 0.61 4.02 5.82 6.45 N/A 2 3.26 3.26 4.54 5.90 6.32 3 4.42 2.45 5.15 5.85 6.14 4 1.58 2.68 2.38 6.43 6.49 2002 1 0.94 0.52 0.79 3.59 N/A 2 3.67 1.53 1.08 0.92 3.43 3 5.21 4.06 3.86 3.72 3.16 4 4.52 3.17 3.34 3.89 3.80 2003 1 3.53 3.38 3.43 3.52 N/A 2 0.08 1.20 3.06 2.77 2.60 Å: 1. ÀPÑ % 2. evä: W\Í3lTúí Å F)$lD%È8 h9ā ñ [ 5. hôõ-%èaå0íã! (CÉ%Èû Í) õòm ã M ø ù ú û 2000 1 7.94 N/A N/A N/A N/A 2 5.10 6.12 N/A N/A N/A 3 6.73 6.61 6.77 N/A N/A 4 3.82 5.58 6.04 6.08 N/A 2001 1 0.61 N/A N/A N/A N/A 2 3.26 3.91 N/A N/A N/A 3 4.42 1.88 5.14 N/A N/A 4 1.58 0.16 4.48 6.53 N/A 2002 1 0.94 N/A N/A N/A N/A 2 3.67 1.97 N/A N/A N/A 3 5.21 4.74 4.33 N/A N/A 4 4.52 3.25 4.67 4.63 N/A 2003 1 3.53 4.08 N/A N/A N/A 2 0.08 2.06 2.97 N/A N/A Å: 1. ÀPÑ % 2. evä: CÉ%Èû ~ 13

CÉ%Èã D\µ 36:1 (2005) ñ [ 6. hôõ-%èaå0íã! (2M%Èû Í) õòm ã M ø ù ú û 2000 1 7.94 6.17 N/A N/A N/A 2 5.10 5.81 5.43 N/A N/A 3 6.73 6.93 7.03 6.34 N/A 4 3.82 5.93 6.34 6.57 6.26 2001 1 0.61 5.46 N/A N/A N/A 2 3.26 4.14 5.52 N/A N/A 3 4.42 1.72 4.33 5.79 N/A 4 1.58 0.96 4.42 6.06 6.14 2002 1 0.94 0.21 N/A N/A N/A 2 3.67 1.23 0.81 N/A N/A 3 5.21 4.01 3.95 3.96 N/A 4 4.52 3.48 4.59 4.83 4.8 2003 1 3.53 3.96 N/A N/A N/A 2 0.08 2.98 3.12 N/A N/A Å: 1. ÀPÑ % 2. evä: CÉ%Èã 1998 r7%è B 2003 r7%è v 4 v (ç«;) nã ŠAÅ Ñ7yüíªœ _íã!, BbSàúçXäJ õ, àíã ô^n : Ìj;Ï (root mean square error; RMSE) "úïï ÌM (mean absolute error; MAE) "úïïì0 (mean ratio of absolute error; MRAE), wt}à-: ( 1 RMSE = T ) T ) 1/2 2 (Ŷt Y t, t=1 MAE = 1 T MRAE = 1 T T Ŷt Y t, t=1 T Ŷ t Y t Y t t=1, (11) 14

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) w2 Ŷ t Ñú t íã M, Y t Ñ t íõòm Î 5Õ, Bb6;W ܃b Ŷ t Y t, ú _œz ØàN _ª Wã Ïæí ì âk<œzíã eýý/1. / (àc%íú íã É 3 e), Ñ7_àkFã íªœ, Bb²Ïxüš }ºí sign ìtñã ô^í ì KJBbkªœ/øÔì_ Ø àn _íã Ïæ, sign ìí$l¾ulêfã e2, _ í ܃bM køàn _í ܃bMí_b; Ê Ìcq- $ l¾xùá}º J sign ì Q Ìcq, [ýøàn _D _íã! Ì$l,íéOÏæ, 5 éýøàn _íã i kçø_ É sign ìíª 5 Diebold and Mariano (1995) ÊJ -í 쪜2, BbîSà 90% íéo ÄV²ì@äM [ 7 10 ÑØàN _}D AR _ 3lT C%Í 2%Ííø Bû íã ªœ! (C%ÍÌû íã ), w2 ØàN.}Ò_ DØàN }Ò_ íã ô^, J sign ìí! âk ÀPíã é., Ñ7Uã ô^n u íª œ!ä, BbYÎ ÀPíã Vlú@5ØàN íã ô^ Wà, C %Íþ_ù íã! (à[ 5), BbÿYWú@5þ_ØàN ã Vl ô^n [2rU[ýã ô^œ76; J[ 8 2íø ã ÑW, JJ RMSE N Ñ Ä, ØàN }Ò_ œß, O JJ MAE MRAE N Ñ Ä, 3lT5ã œ7 [ 7 í! éý, Fíã ô^ Ä éýøàn _ª AR _ Ñ7, w2 ØàN }Ò_ ÊøDú íã, ik Ø àn.}ò_, OÊwF ã,s6 Å â[ 8 í! Võ, 3lTíø ã DØàN _Ê. Ä-išc, OuØ àn _úùj,íã Ìik3lTíã, w2 ØàN } Ò_ íú ã, Ê Ä- ik3ltd ØàN.} Ò_ íã *[ 9 Võ, Î7ø ã 2í MRAE N 5Õ, Øà N _Ê Ä- œßíã ô^, 7 ØàN }Ò_ 15

CÉ%Èã D\µ 36:1 (2005) [ 7 ØàN _D AR _íã ªœ ã ã ô^n AR _.}Ò ØàN }Ò RMSE 2.91 2.74 2.23 ø MAE 2.58 2.25 1.65 MRAE 3.56 4.33 3.34 sign ì Q " RMSE 3.76 3.46 3.62 ù MAE 3.00 2.65 2.79 MRAE 4.93 5.07 3.99 sign ì " Q RMSE 5.08 3.89 3.84 ú MAE 3.99 2.91 2.82 MRAE 5.32 3.97 2.65 sign ì " " RMSE 4.88 4.75 4.71 û MAE 3.88 3.56 3.90 MRAE 5.59 4.54 3.88 sign ì " Q [ 8 ØàN _D3lTíã ªœ ã ã ô^n 3lT.}Ò ØàN }Ò RMSE 2.30 2.74 2.23 ø MAE 1.61 2.25 1.65 MRAE 1.93 4.33 3.34 sign ì Q Q RMSE 4.00 3.46 3.62 ù MAE 2.86 2.65 2.79 MRAE 4.09 5.07 3.99 sign ì Q Q RMSE 4.97 4.02 3.97 ú MAE 3.59 3.06 2.94 MRAE 4.63 4.26 2.84 sign ì " " RMSE 5.63 5.33 5.30 û MAE 4.07 3.87 4.30 MRAE 5.02 5.53 4.55 sign ì Q " 16

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) [ 9 ØàN _DC%Ííã ªœ ã ã ô^n C%Í.}Ò ØàN }Ò RMSE 3.12 2.71 2.11 ø MAE 2.17 2.16 1.45 MRAE 2.99 4.68 3.57 sign ì Q " RMSE 4.52 3.31 3.56 ù MAE 3.14 2.51 2.50 MRAE 6.42 8.55 6.02 sign ì Q Q RMSE 4.86 3.40 2.94 ú MAE 3.49 2.58 2.31 MRAE 1.92 1.36 1.19 sign ì Q Q [ 10 ØàN _D2%Ííã ªœ ã ã ô^n 2%Í ØàN.}Ò }Ò RMSE 3.21 2.74 2.23 ø MAE 2.37 2.25 1.65 MRAE 3.83 4.33 3.34 sign ì Q " RMSE 4.65 3.79 3.84 ù MAE 3.41 2.79 2.88 MRAE 5.03 6.28 4.53 sign ì " Q RMSE 5.35 4.13 3.67 ú MAE 3.76 3.04 2.63 MRAE 1.37 1.06 0.91 sign ì Q Q RMSE 4.68 3.84 4.81 û MAE 3.48 2.60 4.06 MRAE 1.86 1.47 1.94 sign ì Q Q Ê Ä- (Î7ù ã 2í RMSE N ) Ìik ØàN. }Ò_ *[ 10 Võ, ØàN _íã ô^ê Ä-?Ì 2%Ííã, w2 ØàN }Ò_ ÊøDú ã, ØàN.}Ò_, (6 Êû ã,[ûœß Î 5Õ, 17

CÉ%Èã D\µ 36:1 (2005) Jâ sign ìí! R, BbªêÛØàN _íã? éoí ik AR _ 7ÊD3lTíªœjÞ, ØàN _ø ù íã 3lTóœ1ÌéOÏæ, ñú û íã éoik3lt Õ, ØàN _íã? 6Êø íã,éoíikc%íd2 %Ííã J,í! u;wbb²ì5 t F)ƒí!; à t Z, ó Éí,lDã! Aͪ?Z Í7 õ }&íñíêkéýøàn _íã? D@àgM, 7.ub p j.íikwf_ B ku øì ßí ã _,.ân yödy pí}&d_ò, nª?)ƒ!, 7 dí ˇ 5.!D dyw Stock and Watson (1998) FT íøàn j, J. jv ZCÉ%ÈAÅ0íã _ ØàN ã _xe7ó :j _ ªñÑVÖ bíiõ, Oºñq,l, 6³_Ïqí½æ, FJuø x ñ4, /qkítíõ ã _ Bbíõ }&! éý, ØàN _íã! %%ikåqø<3b%èàpíã, Ä ØàN _ ªJTÑf$,ñã j 5ÕíÇø²Ï óœk Stock and Watson (1998) ŸVT íøàn j, dft í ØàN }Ò_.c6'ßíã [Û, 6TX7yîóíã }&!Z, Uû 6)J ³. Ò bêã 2íõ. V@ªø _ @àk %È ã, Jð wã ô^ dõ j íÿõuc?@àkì e, V ªø j ô.ƒýì e, 1/ vñp. ä0í e (à~ ed e) ªWã, à @ªªø Zªã ô^dã í¹v4 18

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JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) Ë 2 6 _ÄäF?j _,ñ bíªw R 2 1 R-Squared 0.5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Factor 1 1 R-Squared 0.5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Factor 2 23

CÉ%Èã D\µ 36:1 (2005) 1 R-Squared 0.5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Factor 3 1 R-Squared 0.5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Factor 4 24

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) 1 R-Squared 0.5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Factor 5 1 R-Squared 0.5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Factor 6 25

CÉ%Èã D\µ 36:1 (2005) 5d. (2003), BÅŸ =ò¼ë5 wì, %Èû, 3, W\Í% Èqãº}%Èû T Š², ô²ëd2 (1998), ā~õwìd%èaå0ã, %Èd, 26(4), 431 457 =}D2 (2001), 90 HCÉí =: ïªúā²_d³g š í@à, Ad þ}çõ, 13(5), 515 540 Chen, S.-W. and J.-L. Lin (2000), Modelling Business Cycles in Taiwan With Time-Varying Markov-Switching Models, Academia Economic Papers, 28(1), 17 42. Diebold, F. X. and R. S. Mariano (1995), Comparing Predictive Accuracy, Journal of Business and Economic Statistics, 13(3), 253 263. Huang, C.-H. (1999), Phases and Characteristics of Taiwan Business Cycles: A Markov Switching Analysis, Taiwan Economic Review, 27(2), 185 214. Stock, J. H. and M. W. Watson (1998), Diffusion Indexes, NBER Working Paper No. 6702. Stock, J. H. and M. W. Watson (2002), Macroeconomic Forecasting Using Diffusion Indexes, Journal of Business and Economic statistics, 20(2), 147 162. 26

JØàN Ñ!5,ñ%Èã (=}, 2 Ä=) MACROECONOMIC FORECASTING BASED ON DIFFUSION INDEXES Shih-Hsun Hsu Ph. D. Candidate Department of Economics National Taiwan University Chung-Ming Kuan Institute of Economics Academia Sinica Ya-Hui Lo Directorate-General of Budget Accounting and Statistics Executive Yuan Keywords: Diffusion index, Economic growth rate, Factor, Principal component analysis JEL Classification: C32, C51 Correspondence: Shih-Hsun Hsu, Department of Economics, National Taiwan University, Taipei 100, Taiwan. Tel: (02) 2351-9641 ext. 274; Fax: (02) 2351-1826; E-mail: d89323002@ntu.edu.tw. 27

CÉ%Èã D\µ 36:1 (2005) ABSTRACT In this paper, we construct a two-step model for forecasting Taiwan s economic growth rates based on the diffusion indexes method proposed by Stock and Watson (1998). In addition to Stock and Watson s original approach, we also classify the macroeconomic variables into three markets (namely, the commodity, monetary and labor markets) and compute their respective diffusion indexes. A forecasting model is then constructed using these market-specific indexes. Our results show that, based on various evaluation criteria, the diffusion-index-based forecasting models usually perform better than those reported by other forecasting agencies in Taiwan. Hence, the models proposed here are good alternatives in macroeconomic forecasting. 28