ANÁLISIS UNIVARIANTE Y EXTRACCIÓN
DE SEÑALES: ANÁLISIS DE UN CASO
Enrique M. Quilis
D.G. Análisis Macroeconómico
Ministerio de Economía y Hacienda
CONTENIDO
Fuente
Transformación logarítmica.
Estacionalidad: análisis exploratorio.
Diferenciación.
Modelización ARIMA: SCA.
Modelización ARIMA: TSW. Diagnóstico.
FUENTE
Matriculaciones de turismos.
Frecuencia: mensual.
Muestra: 1990:01 – 2010:03.
Niveles
Jan90 Jan95 Jan00 Jan05 Jan10
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8x 10
50 100 150 200 0.6 0.8 1 1.2 1.4 1.6
x 105 LEVELS
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 4
5 6 7 8 9x 10
4 MEAN-RANK PLOT
R
a
n
k
1 2 3 4 5 6 7 8 9 10 11 12 0.8
1 1.2 1.4
x 105 SEASONAL MEANS
2 4 6 8 10 12 14 16 18 20 0.8
1 1.2 1.4 1.6 1.8x 10
11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 0.5
0.55 0.6 0.65 0.7 0.75 0.8 0.85
MEAN-RANK PLOT: LOG-TRANSFORMED
R
a
n
BOX-COX: CRITERIO PREDICTIVO
-1 -0.5 0 0.5 1
0.94 0.96 0.98 1 1.02 1.04 1.06 1.08
1.1x 10
4 WITHIN SAMPLE RMSE
-1 -0.5 0 0.5 1
1.45 1.5 1.55 1.6 1.65
1.7x 10
1995
2000
2005
2010
11
11.5
12
Tim e
M A TT
0
2
4
6
-10
0
10
20
Periodogram
cycle/year
lo
g
(p
o
w
e
r)
0
12
24
36 40
-1
-0.5
0
0.5
1
S am ple autocorrelation coefficients
s
a
c
f
v
a
lu
e
s
0
12
24
36 40
-1
-0.5
0
0.5
1
Sam ple partial autocorrelation coefficients
1990 1992 1995 1997 2000 2002 2005 2007 10.5
11 11.5 12 12.5
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
11 11.5 12
1 2 3 4 5 6 7 8 9 10 11 12 11.2
ANÁLISIS FACTORIAL SUBSERIES ANUALES
0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10
STATIC FACTOR ANALYSIS: SCREE PLOT
Number E ig e n v a lu e
4 5 6 7 8 9 10 11 12 0 2 4 6 8 10 12
ORDERED EIGENVALUES: RECURSIVE COMPUTATION
Cross section dimension
HOME
1f
2f
1f
2f
All factors
JAN
0.8889
0.3586
0.7901
0.1286
0.9187
FEB
0.9244
0.3568
0.8546
0.1273
0.9819
MAR
0.9492
0.1881
0.9010
0.0354
0.9364
APR
0.9346
0.3012
0.8736
0.0907
0.9643
MAY
0.9663
0.1834
0.9337
0.0336
0.9674
JUN
0.9658
0.0042
0.9328
0.0000
0.9328
JUL
0.9691
-0.0727
0.9392
0.0053
0.9445
AUG
0.9361
-0.0557
0.8763
0.0031
0.8794
SEP
0.9427
-0.2546
0.8887
0.0648
0.9535
OCT
0.9207
-0.2804
0.8477
0.0786
0.9263
NOV
0.9401
-0.3069
0.8838
0.0942
0.9779
DEC
0.8601
-0.4425
0.7398
0.1958
0.9357
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
2010
-2
-1
0
1
2
3
Average
50 100 150 200 11
11.5 12 12.5
50 100 150 200 -0.6 -0.4 -0.2 0 0.2 0.4
50 100 150 200 -0.5
0 0.5 1
50 100 150 200 -0.6 -0.4 -0.2 0 0.2 0.4
50 100 150 200 -0.5
0 0.5
50 100 150 200 -0.5
0 0.5 1
d=1 D=1
50 100 150 200 -0.5
0 0.5 1
MOVING PERIODOGRAM
T
im
e
s
p
a
n
0 1 2 3 4 5 6
0 12 24 36 -0.6 -0.4 -0.2 0 0.2 0.4
Sample autocorrelation coefficients: d=1 D=1
lag s a c f v a lu e s
0 12 24 36
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
Sample partial autocorrelation coefficients: d=1 D=1
0
50
100
150
200
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0
12
24
36
-0.2
-0.1
0
0.1
0.2
Sample autocorrelation coefficients
lag
s
a
c
f
v
a
lu
e
s
0
12
24
3637
-0.2
-0.1
0
0.1
0.2
Sample partial autocorrelation coefficients
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0
1 2 3 4 5 6 7 8
Density kernel; h = 0.01565
Statistic
p-value
cv (5%)
1.0705
0.5855
5.9915
Jarque-Bera
Mean
t-Mean
Std. Dev
0.0024
0.5331
0.0664
0
50
100
150
200
250
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0
50
100
150
200
250
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Jan900 Jan95 Jan00 Jan05 Jan10 0.005
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
0
12
24
36
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
S am ple autocorrelation coefficients
Jan90 Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10
100
120
140
A DDITIVE OUTLIE RS
Jan90 Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10
50
100
150
TRANSITORY OUTLIERS
Jan90 Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10
60
80
100
120
LE VE L S HIFTS
Jan90 Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10
80
100
120
Jan90
Jan95
Jan00
Jan05
Jan10
11
11.5
12
Jan90
Jan95
Jan00
Jan05
Jan10
11.2
11.4
11.6
11.8
Jan90
Jan95
Jan00
Jan05
Jan10
-0.2
0
0.2
Jan90
Jan95
Jan00
Jan05
Jan10
Jan15
Jan90
Jan95
Jan90 Jan95 Jan00 Jan05 Jan10 0.6
0.8 1 1.2 1.4 1.6
x 105
70 80 90 100 110 120 130 140
80
90
100
110
120
130
0 1 2 3 4 5 6 15
20 25 30 35
Periodogram
lo
g
(p
o
w
e
SERIE
ORIGINAL
SAFIN
% dif
1990
1023013
1027674
0.46
1991
934104 937872.889
0.40
1992
1031148 1029047.33
-0.20
1993
792574 790020.589
-0.32
1994
956367
959308.72
0.31
1995
881511 879081.029
-0.28
1996
962905 961306.004
-0.17
1997
1074525 1073610.93
-0.09
1998
1264237 1260097.44
-0.33
1999
1500097 1496271.61
-0.26
2000
1469289 1476962.26
0.52
2001
1505263 1499628.71
-0.37
2002
1405275 1404884.51
-0.03
2003
1465077 1467846.14
0.19
2004
1615942 1614984.71
-0.06
2005
1649320 1657284.46
0.48
2006
1634608 1641748.96
0.44
2007
1614835 1615558.02
0.04
2008
1161176 1156574.94
-0.40
2009
952575 959292.274
0.71
2010
286410
289095.29
0.94
Mean
0.09
Jan06 Jan07 Jan08 Jan09 Jan10 0.6 0.8 1 1.2 1.4 1.6x 10
5
SAC
SAC+Denton
Jan06-1 Jan07 Jan08 Jan09 Jan10
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
