Gehlavij Mohammadi 2014. Basic definition Graphical models for multivariate time series Theory...

EXPLORING LINKAGES BETWEEN INTERNATIONAL

STOCK MARKETSUSING GRAPHICAL MODELS

FOR MULTIVARIATE TIME SERIES

Gehlavij Mohammadi

2014

CONTENTS Basic definition Graphical models for multivariate time

series Theory from TSC graph to causality

graph Degrees of causality Experiments

BASIC DEFINITION

Where,

BASIC DEFINITION

GRAPHICAL MODELS FOR MULTIVARIATE TIME SERIES Time series chain graph Granger causality

GRAPHICAL MODELS FOR MULTIVARIATE TIME SERIESTime series chain graph

GRAPHICAL MODELS FOR MULTIVARIATE TIME SERIESTSC-graph for a Vector autoregressive

process

GRAPHICAL MODELS FOR MULTIVARIATE TIME SERIESGranger causality graph

THEORY FROM TSC-GRAPH TO CAUSALITY GRAPH

THEORY FROM TSC-GRAPH TO CAUSALITY GRAPH As an example for theory 2.1, we

consider the five-dimensional VAR(2)-process with parameters

THEORY FROM TSC-GRAPH TO CAUSALITY GRAPH Corresponding TSC-graph for the VAR

process

THEORY FROM TSC-GRAPH TO CAUSALITY GRAPH Corresponding causality graph

DEGREES OF CAUSALITY

DEGREES OF CAUSALITY Weighted causality graph

EXPERIMENTS Methodology

Data Finding intervals of analysis with regression

treeFitting VAR model Construct Tsc-graphObtain causality graph from Tsc-graph

EXPERIMENTS Basic example

Data (Japan(Nikkei2250, UK(FTSE100), USA(S&P500))

Finding intervals of analysis with regression tree

EXPERIMENTS Basic example

Finding intervals of analysis with regression tree

EXPERIMENTS Basic example

Fitting VAR model  

N225 FTSE SP500 N225_1 FTSE_1SP500_

1N225_2 FTSE_2

SP500_2

N225_3 FTSE_3SP500_

3

N225 0 1 1 0 1 1 1 0 0 1 0 0

FTSE 1 0 1 0 1 1 0 1 1 1 1 1

SP500 1 1 0 0 1 1 0 0 1 1 0 1

EXPERIMENTS Basic example

Construct Tsc-graph

EXPERIMENTS Basic example

Obtain weighted causality graph from Tsc-graph

EXPERIMENTS 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) )

EXPERIMENTS Main example

Finding intervals of analysis with regression tree

With respect to VLIC and Euro stock indices

EXPERIMENTS Main example

Finding intervals of analysis with regression tree

EXPERIMENTS Main example

Fitting VAR model Construct Tsc-graphObtain causality graph from Tsc-graph

EXPERIMENTS Main example