C EXSM 10
C ..................................................................EXSM 20
C EXSM 30
C SUBROUTINE EXSMO EXSM 40
C EXSM 50
C PURPOSE EXSM 60
C TO FIND THE TRIPLE EXPONENTIAL SMOOTHED SERIES S OF THE EXSM 70
C GIVEN SERIES X. EXSM 80
C EXSM 90
C USAGE EXSM 100
C CALL EXSMO (X,NX,AL,A,B,C,S) EXSM 110
C EXSM 120
C DESCRIPTION OF PARAMETERS EXSM 130
C X - INPUT VECTOR OF LENGTH NX CONTAINING TIME SERIES EXSM 140
C DATA WHICH IS TO BE EXPONENTIALLY SMOOTHED. EXSM 150
C NX - THE NUMBER OF ELEMENTS IN X. EXSM 160
C AL - SMOOTHING CONSTANT, ALPHA. AL MUST BE GREATER THAN EXSM 170
C ZERO AND LESS THAN ONE. EXSM 180
C A,B,C - COEFFICIENTS OF THE PREDICTION EQUATION WHERE S IS EXSM 190
C PREDICTED T PERIODS HENCE BY EXSM 200
C A + B*T + C*T*T/2. EXSM 210
C AS INPUT-- IF A=B=C=0, PROGRAM WILL PROVIDE INITIAL EXSM 220
C VALUES. IF AT LEAST ONE OF A,B,C IS NOT ZERO, EXSM 230
C PROGRAM WILL TAKE GIVEN VALUES AS INITIAL VALUES. EXSM 240
C AS OUTPUT-- A,B,C CONTAIN LATEST, UPDATED COEFFI- EXSM 250
C CIENTS OF PREDICTION. EXSM 260
C S - OUTPUT VECTOR OF LENGTH NX CONTAINING TRIPLE EXSM 270
C EXPONENTIALLY SMOOTHED TIME SERIES. EXSM 280
C EXSM 290
C REMARKS EXSM 300
C NONE EXSM 310
C EXSM 320
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED EXSM 330
C NONE EXSM 340
C EXSM 350
C METHOD EXSM 360
C REFER TO R. G. BROWN, 'SMOOTHING, FORECASTING AND PREDICTIONEXSM 370
C OF DISCRETE TIME SERIES', PRENTICE-HALL, N.J., 1963, EXSM 380
C PP. 140 TO 144. EXSM 390
C EXSM 400
C ..................................................................EXSM 410
C EXSM 420
SUBROUTINE EXSMO (X,NX,AL,A,B,C,S) EXSM 430
DIMENSION X(1),S(1) EXSM 440
C EXSM 450
C IF A=B=C=0.0, GENERATE INITIAL VALUES OF A, B, AND C EXSM 460
C EXSM 470
IF(A) 140, 110, 140 EXSM 480
110 IF(B) 140, 120, 140 EXSM 490
120 IF(C) 140, 130, 140 EXSM 500
130 C=X(1)-2.0*X(2)+X(3) EXSM 510
B=X(2)-X(1)-1.5*C EXSM 520
A=X(1)-B-0.5*C EXSM 530
C EXSM 540
140 BE=1.0-AL EXSM 550
BECUB=BE*BE*BE EXSM 560
ALCUB=AL*AL*AL EXSM 570
C EXSM 580
C DO THE FOLLOWING FOR I=1 TO NX EXSM 590
C EXSM 600
DO 150 I=1,NX EXSM 610
C EXSM 620
C FIND S(I) FOR ONE PERIOD AHEAD EXSM 630
C EXSM 640
S(I)=A+B+0.5*C EXSM 650
C EXSM 660
C UPDATE COEFFICIENTS A, B, AND C EXSM 670
C EXSM 680
DIF=S(I)-X(I) EXSM 690
A=X(I)+BECUB*DIF EXSM 700
B=B+C-1.5*AL*AL*(2.0-AL)*DIF EXSM 710
150 C=C-ALCUB*DIF EXSM 720
RETURN EXSM 730
END EXSM 740