NOB= Dickey=Fuller Engle-Granger., P. ( ). NVAR=Engle-Granger/Dickey-Fuller. 1( ), 6. CONSTANT/NOCONST (C) Dickey-Fuller. NOCONST NVAR=1. TREND/NOTREN

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1 CDF(BIVNORM or CHISQ or DICKEYF or F or NORMAL or T or WTDCHI, DF=CHISQ T, DF1=F, DF2=F, NLAGS= Dickey-Fuller, NOB=, NVAR=, RHO=BIVNORM, EIGVAL=WTDCHI, LOWTAIL or UPTAIL or TWOTAIL, CONSTANT, TREND, TSQ, INVERSE, PRINT) [ ]; or [ ]; (INVERSE ) or x y [ ]; (BIVNORM ) : CDF (P - ),,.. : CDF.,,. INVERSE,..,., REGOPT(PVPRINT). : BIVNORM/CHISQ/DICKEYF/F/NORMAL/T/WTDCHI, 2, 2 (χ 2 ), (DICKEY-FULLER), F,, t, 2. DF=χ 2 t, Dickey-Fuller (Dickey-Fuller NOB= ). DF1=F DF2=F RHO=2 EIGVAL= χ 2 NLAGS= Dickey=Fuller. P. ( ). NOB=,. 36

2 NOB= Dickey=Fuller Engle-Granger., P. ( ). NVAR=Engle-Granger/Dickey-Fuller. 1( ), 6. CONSTANT/NOCONST (C) Dickey-Fuller. NOCONST NVAR=1. TREND/NOTREND (1,2,...,T) Dickey-Fuller. TSQ/NOTSQ 2 (1,4,9,...) Dickey-Fuller. LOWTAIL/TWOTAIL/UPTAIL. TWOTAIL ( t), UPTAIL χ 2 F, LOWTAIL 2 Dickey-Fuller. TWOTAIL 2. INVERSE/NOINVERSE (, ).,. INVERSE 2. PRINT/NOPRINT. PRINT. : PRINT,. 2, ( 4 6 ). TSP. : CDF(CHISQ,DF=5) HAUS; -- CHISQ(5) Test Statistic: , Upper tail area: AR(1) : or REGOPT(PVPRINT) DHALT; 3. CDF(INV).05; -- NORMAL Critical Value: , Two-tailed area: READ PX; ; CDF(INV,NORM) PX CRIT; PRINT PX,CRIT; 37

3 5. F CDF(INV,F,DF1=3,DF2=10).05; -- F(3,10) Critical Value: , Upper tailed area: CDF(BIVNORM,RHO=.5,PRINT) -1-2 PBIV; -- BIVNORM Test Statistic: , , Lower tail area: (UNIT(MAXLAG=0,NOWS) Y; ) DY = Y-Y(-1); OLSQ DY TIME C Y(-1) ; 8., P- (UNIT(MAXLAG=3,NOWS,FINITE) Y; ) DY = Y-Y(-1); SMPL 5,50 ; OLSQ DY TIME C Y(-1) DY(-1)-DY(-3); 9. (COINT(NOUNIT,MAXLAG=0,ALLORD) Y1-Y4; ) OLSQ Y1 C TIME Y2 Y3 Y4; EGTEST; OLSQ Y2 C TIME Y1 Y3 Y4; EGTEST; OLSQ Y3 C TIME Y1 Y2 Y4; EGTEST; OLSQ Y4 C TIME Y1 Y2 Y3; EGTEST; PROC EGTEST; DU OLSQ SMPL 1,50; ENDPROC; 10. Durbin-Watson, 10 2 : SMPL 1,10; OLSQ Y C X1; SET PI=4*ATAN(1); SET F=PI/(2*@NOB); TREND I; EIGB=4*SIN(I*F)**2; SELECT I<=(@NOB-@NCOEF);?dL CDF(WTDCHI,EIG=EIGB).879;?5%(n=10,k'=1) dl SELECT (@NCOEF<=I) & (I<=(@NOB-1));?dU MMAKE du ;?5%,2.5%,1%(n=10,k'=1) du CDF(WTDCHI,EIG=EIGB,PRINT) du; 11. Durbin-Watson P- (REGOPT ) 38

4 SMPL 1,10; READ Y X1; ; REGOPT(DWPVAL=EXACT); OLSQ Y C X1; MMAKE MAT XPXI=(X'X)"; TREND OBS; SELECT OBS>1; DC=0; DX1=X1-X1(-1); MMAKE DX DC DX1; MMAKE BVEC 2-1; MFORM(BAND,NROW=@NOB) DDP=BVEC; MAT DMDP=DDP-DX*XPXI*DX';? DMD'=D*D'-DX*(X'X)"(DX)'? (A=D'D MA ) MAT ED = EIGVAL(DMDP); : BIVNORM: ACM Algorithm 462. Inverse x y. CHISQ: DCDFLIB Abramovitz-Stegun , DiDinato and Morris (1993). Inverse (x p ). F T : ACM Algorithm 322, DF1 DF2 (DF1+DF2 > 500 DF1 >1), ACM Algorithm 346. Inverse. NORMAL: ACM Algorithm 304, E < Inverse Applied Statistics Algorithm AS241, from StatLib. DICKEYF: MacKinnon(1994) 3 4. Cheung and Lai (1995) [Augumented Dickey-Fuller] MacKnnon (1991)[Engle-Granger]., ( ). P.01,.05,.10,. WTDCHI: w t ( EIGVAL ), c i χ 2 (1), d ( ), WTDCHI : Prob [ P (w i Λ c i ) <d] = Prob [ P ((w i d) Λ c i ) < 0]. Durbin-Watson, (, Vuong(1989) ) P-. Pan 90, Imhoff. 1D-12,... : Algorithm AS 241, Applied Statistics 37, (1988) Royal Statistical Society. Cheung, Yin-Wong, and Lai, Kon S., Lag Order and critical Values of the Augumented Dickey-Fuller test", Journal of the Business and Economics Statistics, July 1995, pp Collected Algorithms from ACM, New York,

5 DCDFLIB. by Barry W. Brown, downloaded v1.1, 4/1998. DiDinato, A.R. and Morris, Alfred H. Jr., Computation of the IncompleteGamma Function Ratios and Their Inverse", ACM Transactions on Mathematical Software 18, 1993, pp Engle, R.F., and Granger, C.W.J., Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, 55 (1987), pp Imhoff, P.J., Computing the Distribution of Quadratic Forms in Normal Variables," Biometrika 48, 1961, pp Judge, George G., Hill, R. Carter, Griffiths, William E., Lütkepohl, Helmut, and Lee, Tsoung-Chao, Introduction to the Theory and Practice of Econometrics, second edition, Wiley, New York, 1988, pp MacKinnon, James G., Critical Values for Cointegration Tests," in Long-Run Economic Relationships: readings in Cointegration, eds. R.F. Engle and C.W.J.Granger, New York: Oxford University Press, 1991, pp MacKinnon, James G., Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Test," Journal of Business and Economic Statistics, April 1994, pp Pan, Jie-Jian, Distribution of Noncircular Correlation Coefficients," Selected Transactions in Mathematical Statistics and Probability, 1968, pp Statlib, Vuong, Quang H., Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses," Econometrica, 57, 1989, pp

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