data ACF; do h=0 to 30; rho_h = .99**h*(sin((h/6+.49446)*3.1415926))/.99985; output; end; proc plot; plot rho_h*h/vpos=20; data graph; Y1=0; Y2=0; do t = -100 to 100; Y = 1.7147*Y1-0.9801*Y2 + normal(7655097); if t>0 then output; Y2=Y1; Y1=Y; end; proc plot; plot Y*t/vpos=20; proc arima; i var=y; run; Plot of RHO_H*H. Legend: A = 1 obs, B = 2 obs, etc. RHO_H ‚ 1 ˆ A ‚ A A ‚ A A A ‚ A A ‚ A ‚ A A A ‚ A ‚ ‚ 0 ˆ A A A A A ‚ ‚ ‚ A ‚ A A A A ‚ ‚ A ‚ A A A A A ‚ A A -1 ˆ Šƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒ 0 5 10 15 20 25 30 H Plot of Y*T. Legend: A = 1 obs, B = 2 obs, etc. Y ‚ ‚ 20 ˆ ‚ ‚ ‚ AA 10 ˆ BA A B A ‚ A A AA A A B ‚ A A AB AA A BA A AA A ‚ A A A A A A AA A A 0 ˆ A A A A A A A A A A ‚ A A A A A A A A ‚ A A A A A A A A A A A ‚ AA AA AA A A A AA -10 ˆ A AB A AA A B AB AA A ‚ AA ‚ ‚ -20 ˆ ‚ Šƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒ 0 20 40 60 80 100 T ARIMA Procedure Name of variable = Y. Mean of working series = -0.85084 Standard deviation = 6.78199 Number of observations = 100 Autocorrelations Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 0 45.995388 1.00000 | |********************| 1 39.368344 0.85592 | . |***************** | 2 22.607375 0.49151 | . |********** | 3 0.925607 0.02012 | . | . | 4 -19.913949 -0.43296 | *********| . | 5 -34.831744 -0.75729 | ***************| . | 6 -39.895391 -0.86738 | *****************| . | 7 -34.002037 -0.73925 | ***************| . | 8 -19.123282 -0.41577 | . ********| . | 9 0.060351 0.00131 | . | . | 10 18.192569 0.39553 | . |******** . | 11 30.246702 0.65760 | . |************* | 12 33.021759 0.71794 | . |************** | 13 25.843568 0.56187 | . |***********. | 14 11.183510 0.24314 | . |***** . | 15 -6.423055 -0.13965 | . ***| . | 16 -21.735434 -0.47256 | . *********| . | 17 -30.324914 -0.65930 | *************| . | 18 -29.763189 -0.64709 | .*************| . | 19 -20.451622 -0.44465 | . *********| . | 20 -5.463455 -0.11878 | . **| . | 21 10.880729 0.23656 | . |***** . | 22 24.220901 0.52659 | . |*********** . | 23 31.056876 0.67522 | . |**************. | 24 29.324355 0.63755 | . |************* . | "." marks two standard errors