MATLAB Application of Matlab in Analysing and Modeling Financial Time Sequences

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1 CN / TP ISSN X COMPUTER ENGINEERING & SCIENCE Vol126,No17, X(2004) MATLAB Ξ Application of Matlab in Analysing and Modeling Financial Time Sequences 1 2, LI Xing2xu 1, CUI Jian2fu 2 ( 1., ;2., ) ( 1. Yunnan University of Finance and Economics, Kunming ; 2. Department of Statistics, Yunnan University, Kunming , China) MATLAB, MATLAB Abstract MATLAB is an outstanding mathematical computing tool. In this paper, we expatiate how to analyze and model financial time sequences with MATLAB. ;MATLAB ; ;ARMA ; GARCH Key words financial time sequence ;MATLAB ; technical analysis ; ARMA ; GARCH O245 A 1 MATLAB MathWorks MATLAB,,, MATLAB GARCH,MATLAB, ARMAX GARCH, ;, Eviews TSP,,, MAT2, 2 LAB, GARCH Ξ ; (2000A0003M) ( ),,,, ;, ;Tel (0871) ; E2mail com Address School of Statistics and Information, Yunnan University of Finance and Economics, Kunming, Yunnan ,P. R. China 100

2 ,, 3 MATLAB 2. 1 ( MACD) MACD (DIF) (DEA),DIF,DEA DIF MACD, DIF DEA, ;DIF DEA, 2 IBM DIF macdts = macd(tsobj, series - name) ; tsobj,series - name ; IBM 10/ 01/ 95212/ 31/ 95 ; macd - ibm = macd(part - ibm) ; plot (macd - ibm) ; 1 rsi - ibm = rsindex(part - ibm) ; plot (rsi - ibm) ; 3 IBM 3, { y ( t) } 1 t, 1 IBM, 2. 2 ( William s %R) 3. 1 William s %R , %0 %, (Autocorrelation Function, ACF) William s %R - 20 %, Cov[ y ( t), y ( t - k) ] k =, ;William s %R - 80 % [ V ( y ( t) ) V ( y ( t - k) ) ] 1/ 2,,, wpctrts = willpctr (tsobj, nperiods) ; nperiods(, 14) ; IBM William s %R wpctr - ibm = willpctr (part - ibm) ; plot (wpctr - ibm) ;datetick(x,mm/ dd/ yy ) ; ( RSI) RSI, rsits = rsindex(tsobj, nperiods,parametername, Parameter2 Value) ; nperiods ; IBM RSI ; y (1), y (2),, y ( T),, [ACF,Lags,Bounds] = autocorr (Series,nLags,M,nSTDs) Series,nLags( ) ACF,M( ) Lags > M, ACF 0, nstds( ) ACF ACF,Lags,Bounds ACF szzs. txt, 2000 szzs = ascii2fts(szzs. txt,1,3) ; part - szzs = szzs(01/ 04/ / 24/ 2000 ) ; closepri = fts2mtx (part - szzs. close) ; [ ACF,Lags, Bounds ] = autocorr ( closepri, ( length (closepri) - 1) ) ; autocorr (closepri, (length(closepri) - 1) ) ; Bounds = ( , ), ACF Lag 4 101

3 [ PartialACF, Lags, Bounds] = parcorr (Series, nlags, R, nstds) ; PartialACF ; parcorr (closepri, (length(closepri) - 1) ) ; ACF, 2000 PACF AR( na) MA( nc) ARMA( na, nc) 1, MATLAB ARMA ( na, nc) (Partial ACF, PACF) m = armax( data, orders) k AR( k) y ( data, orders = [ na nc ] t) = < k1, na nc ; na = 0, y ( t - 1) + + < kk y ( MA( nc),nc = 0 t - k) + t < kk, <, AR ( na) m kk, FPE Akaike Yule2Walker, 2000 ACF (4) PACF ( 5), closepri, ACF PACF logclose = log(closepri) ; subplot (2,1,1) ; autocorr (logclose) ; subplot (2, 1, 2) ; parcorr (logclose) ; 6 log (closepri) ACF, AR( na), 2,,ARIMA(2,0) M = armax(logclose,[2 0 ]) A ( q) = q q na [AR ( na) ] A ( q) y ( t) = e ( t), A ( q) = 1 + a 1 q a 2 q a na q - na, a i < 1, q, q - m =( y ( t) = C ( q) e ( t), C ( q) = 1 + c 1 q c nc q - nc, ARCH AR( na) MA ( nc), AR2 (Generalized ARCH, GARCH) (Bollerselv, MA( na, nc) A ( q) y ( t) = C ( q) e ( t) 6 closepri ACF PACF 3. 3 ARCH( q) ), q - m y ( t) = y ( t - m), e ( t) WN (0, 2 y ( t) = + t U t ),, U t, t, E { e ( t) }, ( U t ) = 0, V ( u t ) = 1, t = ( 0 + nc [MA ( nc) ] q i = 1 a i ( y ( t - i) - u) 2 ) 1/ 2,ARCH, 1986,1988) GARCH( p, q) 2 t = q i =1 a i p j =1 j 2 t - j t - i +

4 , p > 0 j 0,1 j p, y ( t) = t, 2 t e - 005, t t - 1, (3), GARCH,garchfit, GARCH (LLF) (innova2 ( Fat tions) ( sigma), garchplot Tails) (Volatility Clustering) garchplot (innovations, sigma) MATLAB GARCH 8, GARCH 2000,, plot (innovations. / sigma), (1), 9 returnmtx = price2ret (closepri) ; % Create the daily return vector returnmtx subplot (2,2,1) ; plot (returnmtx) ; title (The Daily Return ) ; subplot(2,2,2) ; autocorr ( returnmtx) ; title (ACF of Daily Re2 turn ) ; subplot (2,2,3) ; parcorr (returnmtx) ; title (PACF of the Daily Re2 turn ) ; subplot (2,2,4) ; autocorr (returnmtx.^2) ; title (ACF of the Square of Daily Return ) ; ,, ACF PACF, ACF 9, Q2 ARCH Q2 ARCH [ H,pValue, Stat, CriticalValue ] = lbqtest ( returnmtx2mean ( return2 mtx),[ ],0. 05) [ H,pValue,Stat,CriticalValue ] = archtest ( returnmtx2mean ( return2 mtx),[ ],0. 05) Q ARCH , ARCH Q2 H = 0, ; ARCH H = 1, ARCH (2) [coeff, errors, LLF, innovations, sigma, summary] = garchfit (re2 turnmtx) ; garchdisp (coeff, errors) [ H,pValue,Stat,CriticalValue ] = lbqtest ( (innovations. / sigma). ^ 2,[ ],0. 05) [ H, pvalue, Stat, CriticalValue ] = archtest (innovations. / sigma, [ ],0. 05) ; Q ARCH H = 0, GARCH(1,1) 4, MATLAB GARCH(1,1), 103

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