1. Gehlavij Mohammadi 2014

2.  Basic definition  Graphical models for multivariate time series  Theory from TSC graph to causality graph  Degrees of causality  Experiments

3. Where,

5.  Time series chain graph  Granger causality

6. Time series chain graph

7. TSC-graph for a Vector autoregressive process

8. Granger causality graph

10.  As an example for theory 2.1, we consider the five-dimensional VAR(2)-process with parameters

11.  Corresponding TSC-graph for the VAR process

12.  Corresponding causality graph

14.  Weighted causality graph

15.  Methodology  Data  Finding intervals of analysis with regression tree  Fitting VAR model  Construct Tsc-graph  Obtain causality graph from Tsc-graph

16.  Basic example  Data (Japan(Nikkei2250, UK(FTSE100), USA(S & P500))  Finding intervals of analysis with regression tree

17.  Basic example  Finding intervals of analysis with regression tree

18.  Basic example  Fitting VAR model N225FTSESP500N225_1FTSE_1SP500_1N225_2FTSE_2SP500_2N225_3FTSE_3SP500_3N225011011100100 FTSE101011011111 SP500110011001101

19.  Basic example  Construct Tsc-graph

20.  Basic example  Obtain weighted causality graph from Tsc-graph

21.  Main example  Data (Brazil(BVSP), Mexico(MXX), India(BSESN), Indonesia(JKSE), Taiwan(TWII), Germany(GDAXI), Spain(IBEX), UK(FTSE), USA(GSPC), Japan(N225), China(HSCE) )

22.  Main example  Finding intervals of analysis with regression tree With respect to VLIC and Euro stock indices

23.  Main example  Finding intervals of analysis with regression tree

24.  Main example  Fitting VAR model  Construct Tsc-graph  Obtain causality graph from Tsc-graph

25.  Main example