Arima

TIME SERIES REGRESSION MODELS WITH ARIMA ERRORS, MISSING VALUES AND OUTLIERS.
BETA VERSION (*)

BY

VICTOR GOMEZ & AGUSTIN MARAVALL

with the programming assistance of G. CAPORELLO

(*) Copyright : V. GOMEZ, A. MARAVALL (1994,1996)

SERIES TITLE=evtramoSINCE LONGER FORECAST FUNCTION IS REQUIRED
BY SEATS, NPRED CHANGED TO (24)

IF IEAST NOT = 0, IDUR SHOULD BE > 0
IDUR CHANGED TO: 6

ORIGINAL SERIES

NUMBER OF OBSERVATIONS: 130

YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

19912.780 3.280 3.480 3.770 3.900 3.800 3.540 3.370 3.280 3.480 3.750 4.430
1992 6.000 5.890 6.030 6.110 5.990 5.830 5.720 6.230 6.230 5.960 5.840 5.640
1993 5.170 4.850 4.400 4.130 4.010 3.960 4.090 3.700 4.020 4.440 4.700 4.810
19945.090 5.140 5.480 5.600 5.680 5.670 5.500 5.430 5.220 4.970 4.920 4.960
1995 5.430 6.110 6.150 6.310 6.490 6.660 6.640 6.680 6.590 6.620 6.270 6.230
1996 5.340 5.050 5.000 4.690 4.420 4.120 4.040 4.330 4.040 3.650 3.320 3.240
19971.760 0.500 0.210 -0.170 -0.310 -0.160 -0.270 -0.720 0.530 0.610 0.690 0.420
1998 1.050 1.670 1.590 1.860 1.990 1.850 1.970 1.950 0.680 0.550 0.520 0.360
1999 0.960 1.380 1.900 2.180 2.340 2.450 2.390 2.310 2.270 2.380 2.500 2.640
20001.940 1.550 1.070 0.770 0.640 0.460 0.330 0.540 0.780 0.800 0.900 1.140
2001 1.470 1.770 2.040 2.320 2.920 3.300 3.750 3.800 4.260 5.070

DATES OF EASTER DURING THE REQUESTED TIME SPAN

YEAR MONTH DAY

1991 MARCH 31
1992 APRIL 19
1993 APRIL 11
1994 APRIL 31995 APRIL 16
1996 APRIL 7
1997 MARCH 30
1998 APRIL 12
1999 APRIL 4
2000 APRIL 23
2001 APRIL 15
2002 MARCH 31
2003 APRIL 20

SEATS CANNOT BE RUN WITH AIO=0
AIO CHANGED TO 2

MODEL PARAMETERS
----------------
MQ= 12 IMEAN= 1 LAM= -1 D= 1 BD= 1
P= 0BP= 0 Q= 1 BQ= 1 IREG= 3
ITRAD= 2 IEAST= 1 IDUR= 6 M= 36 QM= 24
INCON= 0 NBACK= 0 NPRED= 24 INTERP= 2 INIT= 0
IFILT= 2 IDENSC= 1 IROOT= 2 INIC= 3 ICONCE= 1
ICDET= 1 IATIP= 1 IMVX= 0 IDIF= 3 PG= 0
AIO= 2 INT1= 1 INT2= 130 RSA= 0 SEATS= 2
VA= 3.50TOL= 0.100E-03 PC= 0.143E+00
NOADMISS= 1 BIAS= 1 SMTR= 0
THTR= -0.400 RMOD= 0.500 MAXBIAS= 0.500

TH = -0.10

BTH = -0.10

NUMBER OF INITIAL OBS. = 13

LAM CHANGED TO 1: SERIES HAS NEGATIVE OR ZERO VALUES

TRADING DAY CORRECTION IS NOT SIGNIFICANT:
ITRAD CHANGED TO 0

EASTER CORRECTION IS NOT SIGNIFICANT:
IEAST CHANGED TO0

MEAN IS NOT SIGNIFICANT:
IMEAN CHANGED TO 0

AUTOMATIC MODEL IDENTIFICATION BEGINS

MODEL FINALLY CHOSEN:

(1,1,0)(0,0,1)

WITHOUT MEAN

WITHOUT TRADING DAY CORRECTION

WITHOUT EASTER CORRECTION

OUTLIERS

13 LS ( 1 1992)
61 LS ( 1 1996)

METHOD OF ESTIMATION: EXACT MAXIMUM LIKELIHOOD

PARAMETER ESTIMATE STD...