outliers and conditional
TRANSCRIPT
-
8/9/2019 Outliers and Conditional
1/47
Working Paper 01-07
Statistics and Econometrics Series 04
February 2001
Departamento de Estadstica y Econometra
Universidad Carlos III de Madrid
Calle Madrid, 126
28903 Getafe (Spain)
Fax (34) 91 624-98-49
OUTLIERS AND CONDITIONAL AUTOREGRESSIVE HETEROSCEDASTICITY
IN TIME SERIES
M. Angeles Carnero, Daniel Pea and Esther Ruiz*
Abstract
This paper reviews the literature on GARCH-type models proposed to represent the dynamic
evolution of conditional variances. Effects of level outliers on the diagnostic and estimation of
GARCH models are also studied. Both outliers and conditional heteroscedasticity can generate
time series with excess kurtosis and autocorrelated squared observations. Consequently, bothphenomena can be confused. However, since outliers are generated by unexpected events and the
conditional variances are predictable, it is important to identify which one is producing the
observed features in the data. We compare two alternative procedures for dealing with the
simultaneous presence of outliers and conditional heteroscedasticity in time series. The first one
is to clean the series of outliers before fitting a GARCH model. The second is to estimate first the
GARCH model and then to clean of outliers by using the residuals adjusted by its conditional
variance. It is shown that both approaches may result in different estimated conditional variances.
Keywords: GARCH; EGARCH; CHARMA; Stochastic Volatility; Asymmetry; autocorrelation
of squares; kurtosis; robust procedures.
*Department of Statistics and Econometrics; Universidad Carlos III de Madrid, Getafe (Madrid),
Carnero: e-mail: [email protected]; Pea: e-mail: [email protected]; Ruiz: e-
-
8/9/2019 Outliers and Conditional
2/47
-
8/9/2019 Outliers and Conditional
3/47
-
8/9/2019 Outliers and Conditional
4/47
-
8/9/2019 Outliers and Conditional
5/47
-
8/9/2019 Outliers and Conditional
6/47
-
8/9/2019 Outliers and Conditional
7/47
-
8/9/2019 Outliers and Conditional
8/47
-
8/9/2019 Outliers and Conditional
9/47
-
8/9/2019 Outliers and Conditional
10/47
-
8/9/2019 Outliers and Conditional
11/47
-
8/9/2019 Outliers and Conditional
12/47
-
8/9/2019 Outliers and Conditional
13/47
-
8/9/2019 Outliers and Conditional
14/47
-
8/9/2019 Outliers and Conditional
15/47
-
8/9/2019 Outliers and Conditional
16/47
-
8/9/2019 Outliers and Conditional
17/47
-
8/9/2019 Outliers and Conditional
18/47
-
8/9/2019 Outliers and Conditional
19/47
-
8/9/2019 Outliers and Conditional
20/47
-
8/9/2019 Outliers and Conditional
21/47
-
8/9/2019 Outliers and Conditional
22/47
-
8/9/2019 Outliers and Conditional
23/47
-
8/9/2019 Outliers and Conditional
24/47
-
8/9/2019 Outliers and Conditional
25/47
-
8/9/2019 Outliers and Conditional
26/47
-
8/9/2019 Outliers and Conditional
27/47
-
8/9/2019 Outliers and Conditional
28/47
-
8/9/2019 Outliers and Conditional
29/47
-
8/9/2019 Outliers and Conditional
30/47
-
8/9/2019 Outliers and Conditional
31/47
-
8/9/2019 Outliers and Conditional
32/47
-
8/9/2019 Outliers and Conditional
33/47
0 1000 2000 30008
6
4
2
0
2
4
6
S&P 500
0 500 1000 1500 20006
4
2
0
2
4
US Dollar/Japanese Yen exchange rate
10 5 0 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7Normal and estimated density
densityestimationnormal
6 4 2 0 2 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7Normal and estimated density
densityestimationnormal
5 10 15 200.2
0
0.2
0.4
ACF of the series
5 10 15 200.2
0
0.2
0.4
ACF of the series
5 10 15 200.2
0
0.2
0.4
ACF of the squared observations
5 10 15 200.2
0
0.2
0.4
ACF of the squared observations
5 10 15 200.2
0
0.2
0.4
ACF of the absolute values
5 10 15 200.2
0
0.2
0.4
ACF of the absolute values
-
8/9/2019 Outliers and Conditional
34/47
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
20
25
30
First order autocorrelation of squares
kurtosis
+=0.99
+=0.95
+=0.95
+=0.99
+=0.99
ARCH
GARCH
Data
GARCHt10
GARCHt7
-
8/9/2019 Outliers and Conditional
35/47
0 200 400 600 800 1000 1200 1400 1600 1800 20000
0.5
1
1.5
2
2.5USJA
originalno marginal aono condic. ao
0 200 400 600 800 1000 1200 14001
1.5
2
2.5
3
3.5
4BOMBAY
originalno marginal aono condic. ao
-
8/9/2019 Outliers and Conditional
36/47
0 100 200 300 400 500
5
0
5
Normal ARCH(1) with =0.15
0 100 200 300 400 500
5
0
5
Normal ARCH(1) with =0.4
0 100 200 300 400 500
5
0
5
Normal GARCH(1,1) with =0.1
0 100 200 300 400 500
5
0
5
Normal GARCH(1,1) with =0.2
0 100 200 300 400 500
5
0
5
ARCH(1)t7
0 100 200 300 400 500
5
0
5
GARCH(1,1)t7
yt1
t2
GARCH
AVGARCH
EGARCH
0
-
8/9/2019 Outliers and Conditional
37/47
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
5
10
15
20
25
First order autocorrelation of squares
Kurtosis
=0.99=0.95
+=0.99
+=0.95
GARCH
EGARCH
Data
-
8/9/2019 Outliers and Conditional
38/47
0 0.2 0.40
0.1
0.2
0.3
0.4
=0.1
corrected
0 0.1 0.20
0.05
0.1
0.15
0.2
=0.1
0.6 0.8 10.5
0.6
0.7
0.8
0.9
=0.8
0 0.2 0.40
0.5
1
3consecutiveLO
0 0.2 0.40
0.2
0.4
0.6
0 0.5 10
0.5
1
0 0.5 10
0.5
1
3isolatedLO
original0 0.2 0.4
0
0.1
0.2
0.3
0.4
original0 0.5 1
0
0.5
1
original
32
9
38
3
8
33
83
17
92
8
14
86
85
15
56
44
68
32
-
8/9/2019 Outliers and Conditional
39/47
-
8/9/2019 Outliers and Conditional
40/47
-
8/9/2019 Outliers and Conditional
41/47
-
8/9/2019 Outliers and Conditional
42/47
-
8/9/2019 Outliers and Conditional
43/47
-
8/9/2019 Outliers and Conditional
44/47
-
8/9/2019 Outliers and Conditional
45/47
-
8/9/2019 Outliers and Conditional
46/47
-
8/9/2019 Outliers and Conditional
47/47