Time Series Analysisrootzen/timeseries/timeseries... · 2016. 4. 25. · Time Series Analysis...
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Non Financial TS Financial TS Time Series Analysis V. Fermanelli, M. Longfils April 19, 2016 V. Fermanelli, M. Longfils Time Series Analysis
Transcript of Time Series Analysisrootzen/timeseries/timeseries... · 2016. 4. 25. · Time Series Analysis...
Non Financial TSFinancial TS
Time Series Analysis
V. Fermanelli, M. Longfils
April 19, 2016
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Data
1920 1922 1925 1927 1930 1932 1935 1937 194030
35
40
45
50
55
60
65
70
Figure: Mean monthly air temperature (◦F) Notthingam Castle1920-1939.
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Apply a 13 term MA to smooth the data and compute the stableseasonal component:
1920 1922 1925 1927 1930 1932 1935 1937 1940−10
−5
0
5
10
15Stable Seasonal Component
Te
mp
era
ture
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Apply a 13 term Henderson filter to the deseasonalised data toestimate the trend:
7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09
x 105
30
35
40
45
50
55
60
65
70Monthly temperature
Data
13−Term Henderson Filter
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Re-estimate the seasonal component on the detrended data andremove it from them:
1920 1922 1925 1927 1930 1932 1935 1937 194040
42
44
46
48
50
52
54
56Deseasonalized Series
Tem
pera
ture
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
0 5 10 15 20 25 30 35 40−0.2
0
0.2
0.4
0.6
0.8
Lag
Sam
ple
Auto
corr
ela
tion
ACF
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
0 5 10 15 20 25 30 35 40−0.2
0
0.2
0.4
0.6
0.8
Lag
Sam
ple
Part
ial A
uto
corr
ela
tions
PACF
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
AR(13)
0 100 200 300−4
−2
0
2
4Standardized Residuals
−4 −2 0 2 4−10
−5
0
5
10
Standard Normal Quantiles
Qu
an
tile
s o
f In
pu
t S
am
ple
QQ Plot of Sample Data versus Standard Normal
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le A
uto
co
rre
latio
n
Sample Autocorrelation Function
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le P
art
ial A
uto
co
rre
latio
ns Sample Partial Autocorrelation Function
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
AR(13) with only non-zero coefficients at lags (1,2,10,12)
0 100 200 300−5
0
5Standardized Residuals
−4 −2 0 2 4−10
0
10
Standard Normal QuantilesQuantile
s o
f In
put S
am
pleQQ Plot of Sample Data versus Standard Normal
0 5 10 15 20−0.5
0
0.5
1
Lag
Sam
ple
Auto
corr
ela
tion Sample Autocorrelation Function
0 5 10 15 20−0.5
0
0.5
1
Lag
Sam
ple
Part
ial A
uto
corr
ela
tions
Sample Partial Autocorrelation Function
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
MA(12)
0 100 200 300−4
−2
0
2
4Standardized Residuals
−4 −2 0 2 4−10
−5
0
5
10
Standard Normal Quantiles
Qu
an
tile
s o
f In
pu
t S
am
ple
QQ Plot of Sample Data versus Standard Normal
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le A
uto
co
rre
latio
n
Sample Autocorrelation Function
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le P
art
ial A
uto
co
rre
latio
ns Sample Partial Autocorrelation Function
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
MA(12) with only non-zero coefficients at lags (1,2,3,6,9,12)
0 100 200 300−4
−2
0
2
4Standardized Residuals
−4 −2 0 2 4−10
−5
0
5
10
Standard Normal Quantiles
Qu
an
tile
s o
f In
pu
t S
am
ple
QQ Plot of Sample Data versus Standard Normal
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le A
uto
co
rre
latio
n
Sample Autocorrelation Function
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le P
art
ial A
uto
co
rre
latio
ns Sample Partial Autocorrelation Function
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Model AIC BIC
AR(13) 1071.5 1116.8AR(13) reduced 1057 1070.9
MA(12) 1061.7 1110.4MA(12) reduced 1051.2 1075.6
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
1920 1922 1925 1927 1930 1932 1935 1937 194040
42
44
46
48
50
52
54
56
data
Forecast
Forecast Interval
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Periodogram (using Hamming window)
0 0.2 0.4 0.6 0.8 1−20
−10
0
10
20
30
40
50
Normalized Frequency (×π rad/sample)
Po
we
r/fr
eq
ue
ncy (
dB
/ra
d/s
am
ple
)
Periodogram Power Spectral Density Estimate
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Financial TS:
2009 2010 2011 2012 2013 2014 2015 2016 20171
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3x 10
4
Figure: Hang Seng Bank opening price from January 2009 to April 2016.
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
0 5 10 15 20 25 30 35 40−0.2
0
0.2
0.4
0.6
0.8
Lag
Sam
ple
Auto
corr
ela
tion
ACF of the Data
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
0 5 10 15 20 25 30 35 40−0.2
0
0.2
0.4
0.6
0.8
Lag
Sam
ple
Part
ial A
uto
corr
ela
tions
PACF of the Data
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
2009 2010 2011 2012 2013 2014 2015 2016 2017−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08Log Return
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
ACF and PACF of LogReturn; Ljung-Box Q-test rejects thehypotesis of zero autocorrelation up to lag 15 -> conditional meanmodel may be needed
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le A
uto
co
rre
latio
nSample Autocorrelation Function
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le P
art
ial A
uto
co
rre
latio
ns Sample Partial Autocorrelation Function
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
ACF and PACF of centered squares of LogReturn; ACF and PACFsignificant (Engle ARCH test) -> GARCH model
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le A
uto
co
rre
latio
nSample Autocorrelation Function
0 5 10 15 20−0.5
0
0.5
1
Lag
Sa
mp
le P
art
ial A
uto
co
rre
latio
ns Sample Partial Autocorrelation Function
V. Fermanelli, M. Longfils Time Series Analysis
Non Financial TSFinancial TS
Model AIC BIC
GARCH(1,1) 5897.6 5914.1GARCH(2,2) 5948.2 5975.7GARCH(3,3) 5979.7 6018.3EGARCH(1,1) 5872.5 5889EGARCH(2,2) 5858 5885.5
V. Fermanelli, M. Longfils Time Series Analysis
