C AUTO 10
C ..................................................................AUTO 20
C AUTO 30
C SUBROUTINE AUTO AUTO 40
C AUTO 50
C PURPOSE AUTO 60
C TO FIND AUTOCOVARIANCES OF SERIES A FOR LAGS 0 TO L-1. AUTO 70
C AUTO 80
C USAGE AUTO 90
C CALL AUTO (A,N,L,R) AUTO 100
C AUTO 110
C DESCRIPTION OF PARAMETERS AUTO 120
C A - INPUT VECTOR OF LENGTH N CONTAINING THE TIME SERIES AUTO 130
C WHOSE AUTOCOVARIANCE IS DESIRED. AUTO 140
C N - LENGTH OF THE VECTOR A. AUTO 150
C L - AUTOCOVARIANCE IS CALCULATED FOR LAGS OF 0, 1, 2,...,AUTO 160
C L-1. AUTO 170
C R - OUTPUT VECTOR OF LENGTH L CONTAINING AUTOCOVARIANCES AUTO 180
C OF SERIES A. AUTO 190
C AUTO 200
C REMARKS AUTO 210
C THE LENGTH OF R IS DIFFERENT FROM THE LENGTH OF A. N MUST AUTO 220
C BE GREATER THAN L. IF NOT, R(1) IS SET TO ZERO AND RETURN AUTO 230
C IS MADE TO THE CALLING PROGRAM. AUTO 240
C AUTO 250
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED AUTO 260
C NONE AUTO 270
C AUTO 280
C METHOD AUTO 290
C DESCRIBED IN R.B. BLACKMAN AND J.W. TUKEY, 'THE MEASURMENT AUTO 300
C OF POWER SPECTRA', DOVER PUBLICATIONS INC., NEW YORK, 1959. AUTO 310
C AUTO 320
C ..................................................................AUTO 330
C AUTO 340
SUBROUTINE AUTO (A,N,L,R) AUTO 350
DIMENSION A(1),R(1) AUTO 360
C AUTO 370
C CALCULATE AVERAGE OF TIME SERIES A AUTO 380
C AUTO 390
AVER=0.0 AUTO 400
IF(N-L) 50,50,100 AUTO 410
50 R(1)=0.0 AUTO 420
RETURN AUTO 430
100 DO 110 I=1,N AUTO 440
110 AVER=AVER+A(I) AUTO 450
FN=N AUTO 460
AVER=AVER/FN AUTO 470
C AUTO 480
C CALCULATE AUTOCOVARIANCES AUTO 490
C AUTO 500
DO 130 J=1,L AUTO 510
NJ=N-J+1 AUTO 520
SUM=0.0 AUTO 530
DO 120 I=1,NJ AUTO 540
IJ=I+J-1 AUTO 550
120 SUM=SUM+(A(I)-AVER)*(A(IJ)-AVER) AUTO 560
FNJ=NJ AUTO 570
130 R(J)=SUM/FNJ AUTO 580
RETURN AUTO 590
END AUTO 600