Time series analysis projects Deliang,  Emil  &  Toni  

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    

Non-Financial Time Series

• U.S.  GDP  growth  from  1953-­‐2014  

Non-financial Time Series

Non-financial Time Series

Non-financial Time Series

Non-financial Time Series

Coefficients:  

MA(1)   -­‐0.7638  

Standard  Error   0.1009  

T-­‐staSsSc   -­‐7.5699  

Non-financial Time Series

Min   Max   Mean   Std.  Devia4on   N  

-­‐0.065   0.044   0.001   0.023   60  

Non-financial Time Series

Shapiro-­‐Wilk  Test  

W=0.9805   p-­‐value=0.4385  

Lilliefors  Test  

D=0.0666   p-­‐value=0.7187  

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  

Spectral analysis of non-financial time series

Kernel smoothing

Modified kernel

Smoothing with kernel of kernel

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  

Financial Time Series

Financial Time Series

Stylized  facts    • Heavy  tails  • Persistence  of  vol.  • Asymmetry    

Financial Time Series

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.    

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.    

 

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)  

Financial Time Series

Residuals  GARCH(1,1)          

Financial Time Series

Residuals  EGARCH(1,1)  

       

Thank  you  for  your  aRen4on!