time series analysis projects - chalmersrootzen/timeseries/timeseries... · financial time series...
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Time series analysis projects Deliang, Emil & Toni
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Non-Financial Time Series
• Type: US GDP 1952-‐2014 in USD • Source: US. Bureau of Economic Analysis • Frequency: annual • Seasonally adjusted data • Units: Bilions of USD
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Non-Financial Time Series
• U.S. GDP growth from 1953-‐2014
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Non-financial Time Series
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Non-financial Time Series
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Non-financial Time Series
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Non-financial Time Series
Coefficients:
MA(1) -‐0.7638
Standard Error 0.1009
T-‐staSsSc -‐7.5699
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Non-financial Time Series
Min Max Mean Std. Devia4on N
-‐0.065 0.044 0.001 0.023 60
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Non-financial Time Series
Shapiro-‐Wilk Test
W=0.9805 p-‐value=0.4385
Lilliefors Test
D=0.0666 p-‐value=0.7187
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Non-financial Time Series
Difference-‐Sign Test
p-‐value=0.0785
Rank Test
p-‐value=0.3974
Ljung-‐Box Test
=0.8255 p-‐value=0.3636
Turning Point Test
p-‐value=0.3041
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Spectral analysis of non-financial time series
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Kernel smoothing
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Modified kernel
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Smoothing with kernel of kernel
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Financial Time Series
Data descrip4on • S&P 500 Index (2/1-‐2014 to 22/4-‐2015) • Source: Bloomberg LP • Frequency: daily closing prices • Type: prices (USD) and returns
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Financial Time Series
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Financial Time Series
Stylized facts • Heavy tails • Persistence of vol. • Asymmetry
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Financial Time Series
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Financial Time Series
Test for ARCH effects give significant results at the 5% significance level. The BIC gives ARCH(1) as best model. Proceed to test for GARCH and EGARCH models.
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Financial Time Series
• TesSng for GARCH(p, q) gives GARCH(1,1) as the best model using BIC (AIC gives the same).
• Ficng an EGRACH(1,1) gives an even lower BIC staSsSc.
These are our candidate models.
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Financial Time Series Parameter Value Standard Error T-‐sta4s4c
Constant 0.0648532 0.0333538 1.9444
GARCH(1) 0.700665 0.106673 6.56837
ARCH(1) 0.187322 0.0645716 2.901
GARCH(1,1)
Parameter Value Standard Error T-‐sta4s4c
Constant -‐0.0653356 0.0139735 -‐4.67567
GARCH(1) 0.904116 0.0147242 61.4036
ARCH(1) 0.0561225 0.0580531 0.966745
Leverage(1) -‐0.369402 0.0395309 -‐9.34463
EGARCH(1,1)
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Financial Time Series
Residuals GARCH(1,1)
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Financial Time Series
Residuals EGARCH(1,1)
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Thank you for your aRen4on!