TSP-Programm zu Abschnitt 6.1.: Zeitreihenanalyse

Transcription

1 TSP-Programm zu Abschnitt 6.1.: Zeitreihenanalyse this copy licensed for use by: TSP/GiveWin update 4/07#50AGT TSP Version 5.0 ( 4/17/07) TSP/GiveWin 4MB Copyright (C) 2007 TSP International ALL RIGHTS RESERVED 01/07/09 2:30 PM In case of questions or problems, see your local TSP consultant or send a description of the problem and the associated TSP output to: TSP International P.O. Box Palo Alto, CA USA PROGRAM COMMAND *************************************************************** 1 options crt; 2 2?Laden der Daten: 2 freq q;?quartalsdaten 3 smpl 1972:4 2005:4;?Stichprobe über die Quartale 1972Q4 bis 2005Q4 4 4 read (FILE= Office.xls );?Lese eine Excel-Datei ein 5 5?Ansehen der Daten 5?print ne; 5 5?Logarithmierte Werte (Daten in Levels) 5 lne = log(ne); 6 6 smpl 1973:1 2005:4; 7 dlne = lne - lne(-1); 8 8?deskriptive Statistik 8 msd dlne; 9 1

2 9?Diagramm 9 plot lne; 10 bjident(ndiff=1,nlag=12,nlagp=12)lne; 11 11?stop; 11 11?Augmented Dickey-Fuller in Levels 11 smpl 1975:3 2005:4; 12 olsq dlne lne(-1) dlne(-1) dlne(-2) dlne(-3) dlne(-4) dlne(-5) dlne(-6) dlne(-7) dlne(-8) dlne(-9) dlne(-10) c; 13 cdf(dickeyf)@t(1); 14?Kritische Werte: 1% = ? 5% = ? 10% = smpl 1973:2 2005:4; 15 olsq dlne lne(-1) dlne(-1) c; 16 cdf(dickeyf)@t(1); 17 17?Kritische Werte: 1% = ? 5% = ? 10% = resid1 18 bjident(ndiff=0,nlag=24,nlagp=24)resid1; 19 19?Augmented Dickey-Fuller in Differenzen 19 smpl 1973:2 2005:4; 20 ddlne = dlne - dlne(-1); 21 smpl 1975:4 2005:4; 22 olsq ddlne dlne(-1) ddlne(-1) ddlne(-2) ddlne(-3) ddlne(-4) ddlne(-5) ddlne(-6) ddlne(-7) ddlne(-8) ddlne(-9) ddlne(-10) c; 23 cdf(dickeyf)@t(1); 24?Kritische Werte: 1% = ? 5% = ? 10% = smpl 1973:2 2005:4; 25 olsq ddlne dlne(-1) c; 26 cdf(dickeyf)@t(1); 27?Kritische Werte: 1% = ? 5% = ? 10% = resid2 2

3 28 bjident(ndiff=0,nlag=24,nlagp=24)resid2; 29 29?stop; smpl 1973:2 2005:4; 30 olsq dlne dlne(-1) c; resid3 32 bjident(ndiff=0,nlag=24,nlagp=24)resid3; 33 33?stop; smpl 1973:2 2005:4; 34 bjest(cumplot, nback=5, nar=1, nma=2, ndiff=1,root)dlne; smpl 1974:1 2005:4; 36 resid4 37 bjident(ndiff=0,nlag=24,nlagp=24)resid4; 38 EXECUTION ******************************************************************************* 3

4 Current sample: 1972:4 to 2005:4 Current sample: 1973:1 to 2005:4 Number of Observations: 132 Univariate statistics ===================== Mean Std Dev Minimum Maximum DLNE Sum Variance Skewness Kurtosis DLNE ====================== Box-Jenkins procedures Procedure BJIDENT ====================== OPTIONS FOR THIS ROUTINE ======================== BARTLETT = TRUE ESACF = FALSE IAC = FALSE NAR = 0 NDIFF = 1 NLAG = 12 NLAGP = 12 NMA = 0 NSDIFF = 0 NSPAN = 4 PACMETH = BURG PLOT = TRUE PLOTAC = TRUE PLTRAW = FALSE PREVIEW = TRUE PRINT = FALSE SILENT = FALSE Series: (1-B) LNE Mean = Std. Error = E E-01 4

5 Autocorrelations ================ Series: LNE Mean = Std. Error = Lags Autocorrelations Standard Errors E Q-statistics Autocorrelations Standard Errors Q-statistics E+04 Autocorrelations Standard Errors Q-statistics 0.112E E+04 Series: (1-B) LNE Mean = E-02 Std. Error = E-01 Lags Autocorrelations E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations 0.805E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E-01 Standard Errors E E-01 Q-statistics

6 Partial Autocorrelations ======================== Series: LNE Standard Error of Autocorrelations = E-01 Lags Partial Autocorrs E E E-01 Partial Autocorrs E E E E Partial Autocorrs E E-01 Series: (1-B) LNE Standard Error of Autocorrelations = E-01 Lags Partial Autocorrs E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E-01 Autocorrelation Function of: LNE R R R R R R R R R R R R

7 Partial Autocorrelation Function of: LNE R R R R R R R R R R R R Autocorrelation Function of: (1-B) LNE R R R R R R R R R R R R

8 Partial Autocorrelation Function of: (1-B) LNE R R R R R R R R R R R R Current sample: 1975:3 to 2005:4 8

9 Dependent variable: DLNE Current sample: 1975:3 to 2005:4 Number of observations: 122 Equation 1 ============ Method of estimation = Ordinary Least Squares Mean of dep. var. = E-02 Std. dev. of dep. var. = Sum of squared residuals = Variance of residuals = E-03 Std. error of regression = R-squared = Adjusted R-squared = LM het. test = [.343] Durbin-Watson = [.119,.850] Durbin s h alt. = [.342] Jarque-Bera test = [.000] Ramsey s RESET2 = [.248] F (zero slopes) = [.186] Schwarz B.I.C. = Log likelihood = Estimated Standard Variable Coefficient Error t-statistic P-value LNE(-1) E [.646] DLNE(-1) [.003] DLNE(-2) [.636] DLNE(-3) [.883] DLNE(-4) [.905] DLNE(-5) [.756] DLNE(-6) [.587] DLNE(-7) [.605] DLNE(-8) [.510] DLNE(-9) [.123] DLNE(-10) [.759] C [.619] DICKEY-FULLER(CT,ASY.,0) Test Statistic: , Lower tail area: Current sample: 1973:2 to 2005:4 9

10 Equation 2 ============ Method of estimation = Ordinary Least Squares Dependent variable: DLNE Current sample: 1973:2 to 2005:4 Number of observations: 131 Mean of dep. var. = E-02 Std. dev. of dep. var. = Sum of squared residuals = Variance of residuals = E-03 Std. error of regression = R-squared = Adjusted R-squared = LM het. test = [.265] Durbin-Watson = [.486,.628] Durbin s h = [.438] Durbin s h alt. = [.592] Jarque-Bera test = [.000] Ramsey s RESET2 = [.030] F (zero slopes) = [.002] Schwarz B.I.C. = Log likelihood = Estimated Standard Variable Coefficient Error t-statistic P-value LNE(-1) E [.985] DLNE(-1) [.001] C E [.978] DICKEY-FULLER(CT,ASY.,0) Test Statistic: E-01, Lower tail area: ====================== Box-Jenkins procedures Procedure BJIDENT ====================== 10

11 OPTIONS FOR THIS ROUTINE ======================== BARTLETT = TRUE ESACF = FALSE IAC = FALSE NAR = 0 NDIFF = 0 NLAG = 24 NLAGP = 24 NMA = 0 NSDIFF = 0 NSPAN = 4 PACMETH = BURG PLOT = TRUE PLOTAC = TRUE PLTRAW = FALSE PREVIEW = TRUE PRINT = FALSE SILENT = FALSE Autocorrelations ================ Series: RESID1 Mean = E-10 Std. Error = E-01 Lags Autocorrelations E E E E E-01 Standard Errors E E E E E-01 Q-statistics 0.238E Autocorrelations 0.502E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations 0.258E E E E-02 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E-01 Standard Errors E E E E-01 Q-statistics

12 Partial Autocorrelations ======================== Series: RESID1 Standard Error of Autocorrelations = E-01 Lags Partial Autocorrs E E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E E E-01 Autocorrelation Function of: RESID1 1 + R R R R R R R R R R R R R R R R R R R R R R R R

13 Partial Autocorrelation Function of: RESID1 1 + R R R R R R R R R R R R R R R R R R R R R R R R Current sample: 1973:2 to 2005:4 Current sample: 1975:4 to 2005:4 13

14 Dependent variable: DDLNE Current sample: 1975:4 to 2005:4 Number of observations: 121 Equation 3 ============ Method of estimation = Ordinary Least Squares Mean of dep. var. = E-04 Std. dev. of dep. var. = Sum of squared residuals = Variance of residuals = E-03 Std. error of regression = R-squared = Adjusted R-squared = LM het. test = [.309] Durbin-Watson = [.129,.863] Durbin s h alt. = [.780] Jarque-Bera test = [.000] Ramsey s RESET2 = [.031] F (zero slopes) = [.000] Schwarz B.I.C. = Log likelihood = Estimated Standard Variable Coefficient Error t-statistic P-value DLNE(-1) [.005] DDLNE(-1) [.477] DDLNE(-2) [.662] DDLNE(-3) [.548] DDLNE(-4) [.563] DDLNE(-5) [.687] DDLNE(-6) [.912] DDLNE(-7) [.843] DDLNE(-8) [.723] DDLNE(-9) [.353] DDLNE(-10) [.308] C E E [.404] DICKEY-FULLER(CT,ASY.,0) Test Statistic: , Lower tail area: Current sample: 1973:2 to 2005:4 14

15 Equation 4 ============ Method of estimation = Ordinary Least Squares Dependent variable: DDLNE Current sample: 1973:2 to 2005:4 Number of observations: 131 Mean of dep. var. = E-03 Std. dev. of dep. var. = Sum of squared residuals = Variance of residuals = E-03 Std. error of regression = R-squared = Adjusted R-squared = LM het. test = [.259] Durbin-Watson = [.523,.593] Jarque-Bera test = [.000] Ramsey s RESET2 = [.030] F (zero slopes) = [.000] Schwarz B.I.C. = Log likelihood = Estimated Standard Variable Coefficient Error t-statistic P-value DLNE(-1) [.000] C E E [.343] DICKEY-FULLER(CT,ASY.,0) Test Statistic: , Lower tail area: ====================== Box-Jenkins procedures Procedure BJIDENT ====================== 15

16 OPTIONS FOR THIS ROUTINE ======================== BARTLETT = TRUE ESACF = FALSE IAC = FALSE NAR = 0 NDIFF = 0 NLAG = 24 NLAGP = 24 NMA = 0 NSDIFF = 0 NSPAN = 4 PACMETH = BURG PLOT = TRUE PLOTAC = TRUE PLTRAW = FALSE PREVIEW = TRUE PRINT = FALSE SILENT = FALSE Autocorrelations ================ Series: RESID2 Mean = E-10 Std. Error = E-01 Lags Autocorrelations E E E E E-01 Standard Errors E E E E E-01 Q-statistics 0.242E Autocorrelations 0.504E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations 0.261E E E E-02 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E-01 Standard Errors E E E E-01 Q-statistics

17 Partial Autocorrelations ======================== Series: RESID2 Standard Error of Autocorrelations = E-01 Lags Partial Autocorrs E E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E E E-01 Autocorrelation Function of: RESID2 1 + R R R R R R R R R R R R R R R R R R R R R R R R

18 Partial Autocorrelation Function of: RESID2 1 + R R R R R R R R R R R R R R R R R R R R R R R R Current sample: 1973:2 to 2005:4 18

19 Equation 5 ============ Method of estimation = Ordinary Least Squares Dependent variable: DLNE Current sample: 1973:2 to 2005:4 Number of observations: 131 Mean of dep. var. = E-02 Std. dev. of dep. var. = Sum of squared residuals = Variance of residuals = E-03 Std. error of regression = R-squared = Adjusted R-squared = LM het. test = [.265] Durbin-Watson = [.523,.593] Durbin s h = [.577] Durbin s h alt. = [.594] Jarque-Bera test = [.000] Ramsey s RESET2 = [.030] F (zero slopes) = [.000] Schwarz B.I.C. = Log likelihood = Estimated Standard Variable Coefficient Error t-statistic P-value DLNE(-1) [.000] C E E [.343] ====================== Box-Jenkins procedures Procedure BJIDENT ====================== 19

20 OPTIONS FOR THIS ROUTINE ======================== BARTLETT = TRUE ESACF = FALSE IAC = FALSE NAR = 0 NDIFF = 0 NLAG = 24 NLAGP = 24 NMA = 0 NSDIFF = 0 NSPAN = 4 PACMETH = BURG PLOT = TRUE PLOTAC = TRUE PLTRAW = FALSE PREVIEW = TRUE PRINT = FALSE SILENT = FALSE Autocorrelations ================ Series: RESID3 Mean = E-10 Std. Error = E-01 Lags Autocorrelations E E E E E-01 Standard Errors E E E E E-01 Q-statistics 0.242E Autocorrelations 0.504E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations 0.261E E E E-02 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E-01 Standard Errors E E E E-01 Q-statistics

21 Partial Autocorrelations ======================== Series: RESID3 Standard Error of Autocorrelations = E-01 Lags Partial Autocorrs E E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E E E E-01 Partial Autocorrs E E E E-01 Partial Autocorrs E E E E-01 Autocorrelation Function of: RESID3 1 + R R R R R R R R R R R R R R R R R R R R R R R R

22 Partial Autocorrelation Function of: RESID3 1 + R R R R R R R R R R R R R R R R R R R R R R R R Current sample: 1973:2 to 2005:4 ====================== Box-Jenkins procedures Procedure BJEST ====================== 22

23 Working space used: 2195 STARTING VALUES PHI1 THETA1 THETA2 VALUE F= FNEW= ISQZ= 0 STEP= 1. CRIT= F= FNEW= ISQZ= 0 STEP= 1. CRIT= F= FNEW= ISQZ= 2 STEP=.063 CRIT= F= FNEW= ISQZ= 2 STEP=.063 CRIT= F= FNEW= ISQZ= 2 STEP=.063 CRIT= F= FNEW= ISQZ= 2 STEP=.063 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 2 STEP=.063 CRIT= F= FNEW= ISQZ= 1 STEP=.250 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 3 STEP=.016 CRIT= F= FNEW= ISQZ= 5 STEP=.977E-03 CRIT= F= FNEW= ISQZ= 5 STEP=.977E-03 CRIT= F= FNEW= ISQZ= 5 STEP=.977E-03 CRIT= F= FNEW= ISQZ= 6 STEP=.244E-03 CRIT= F= FNEW= ISQZ= 7 STEP=.610E-04 CRIT= PHI1 THETA1 THETA2 ESTIMATE CHANGES CONVERGENCE NOT ACHIEVED AFTER 20 ITERATIONS 392 FUNCTION EVALUATIONS. 23

24 Results of Box-Jenkins Estimation ================================= Dependent variable: DLNE Current sample: 1973:2 to 2005:4 Number of observations: 130 Statistics Based on Differenced Series ====================================== Mean of dep. var. = E-04 Adjusted R-squared = Std. dev. of dep. var. = LM het. test = [.048] Sum of squared residuals = Durbin-Watson = Variance of residuals = E-03 Schwarz B.I.C. = Std. error of regression = Log likelihood = R-squared = Standard Parameter Estimate Error t-statistic P-value PHI [.000] THETA [.000] THETA [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) 1 2 Real Imag Modulus Roots of the Polynomial THETA(Z) 24

25 Autocorrelations of the Residuals Autocorr Q-stat P-value Autocorr Q-stat P-value Autocorr Q-stat P-value Autocorr Q-stat P-value Autocorr Q-stat P-value

26 Normalized Cumulative Periodogram of Residuals Expected CP plotted with (.) Actual CP plotted with (*) Band (+) marks the 10% Kolmogorov-Smirnov limits Period * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * + 26

27 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Current sample: 1974:1 to 2005:4 27

28 ====================== Box-Jenkins procedures Procedure BJIDENT ====================== OPTIONS FOR THIS ROUTINE ======================== BARTLETT = TRUE ESACF = FALSE IAC = FALSE NAR = 0 NDIFF = 0 NLAG = 24 NLAGP = 24 NMA = 0 NSDIFF = 0 NSPAN = 4 PACMETH = BURG PLOT = TRUE PLOTAC = TRUE PLTRAW = FALSE PREVIEW = TRUE PRINT = FALSE SILENT = FALSE Autocorrelations ================ Series: RESID4 Mean = E-03 Std. Error = E-01 Lags Autocorrelations E E-01 Standard Errors E E E E E-01 Q-statistics 0.180E Autocorrelations E E E E-03 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E-01 Standard Errors E E E E E-01 Q-statistics Autocorrelations E E E E-01 Standard Errors E E E E-01 Q-statistics

29 Partial Autocorrelations ======================== Series: RESID4 Standard Error of Autocorrelations = E-01 Lags Partial Autocorrs E Partial Autocorrs E E E E-01 Partial Autocorrs E E E-01 Partial Autocorrs E E E-02 Partial Autocorrs E E E E-01 Autocorrelation Function of: RESID4 1 + R R R R R R R R R R R R R R R R R R R R R R R R

30 Partial Autocorrelation Function of: RESID4 1 + R R R R R R R R R R R R R R R R R R R R R R R R ******************************************************************************* END OF OUTPUT. MEMORY USAGE: ITEM: DATA ARRAY TOTAL MEMORY UNITS: (4-BYTE WORDS) (MEGABYTES) MEMORY ALLOCATED : MEMORY ACTUALLY REQUIRED : CURRENT VARIABLE STORAGE :

31 Grafik 1: Plot 31

32 Grafik 2: Bjident 2 32

33 Grafik 3: Bjest 3 33