Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Exploring EME Asset Returns Conditional
Comovement
Nico Katzke
Equity Quantitative Analyst, Fairtree Capital
[email protected]
July 2015
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Table of contents
1
Introduction
Overview
Plots
Main Idea
2
Methodological Discussion
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
3
Data
4
Results
Statistics
Fitting Procedures
Graphs
Variables Used
Regression Outputs
5
6
Conclusion
Bonus!
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Introduction
In this paper, I explore the dynamics of comovement between
emerging market asset and currency returns series since 2000.
The main idea is to explore which events and / or factors
contributed to the increased comovement of returns.
For emerging market securities and currencies, there has been a
steady increase in comovement since 2000, characterized by several
events that drove return comovements higher.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Introduction
In this paper, I explore the dynamics of comovement between
emerging market asset and currency returns series since 2000.
The main idea is to explore which events and / or factors
contributed to the increased comovement of returns.
For emerging market securities and currencies, there has been a
steady increase in comovement since 2000, characterized by several
events that drove return comovements higher.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Introduction
In this paper, I explore the dynamics of comovement between
emerging market asset and currency returns series since 2000.
The main idea is to explore which events and / or factors
contributed to the increased comovement of returns.
For emerging market securities and currencies, there has been a
steady increase in comovement since 2000, characterized by several
events that drove return comovements higher.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Logarithmicplot of EME indexes
9
8
7
6
5
4
3
0
100
200
300
400
Nico Katzke
500
600
700
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Main Idea
The main idea is to isolate the bivariate return comovements,
aggregate the bivariate pairs of return comovement,
and then use a panel regression to assess which factors significantly
influence the comovements between the return series collectively.
This will also allow us to gain insight into which factors had been
contemporaneous to return comovements as a whole.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Main Idea
The main idea is to isolate the bivariate return comovements,
aggregate the bivariate pairs of return comovement,
and then use a panel regression to assess which factors significantly
influence the comovements between the return series collectively.
This will also allow us to gain insight into which factors had been
contemporaneous to return comovements as a whole.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Main Idea
The main idea is to isolate the bivariate return comovements,
aggregate the bivariate pairs of return comovement,
and then use a panel regression to assess which factors significantly
influence the comovements between the return series collectively.
This will also allow us to gain insight into which factors had been
contemporaneous to return comovements as a whole.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Overview
Plots
Main Idea
Main Idea
The main idea is to isolate the bivariate return comovements,
aggregate the bivariate pairs of return comovement,
and then use a panel regression to assess which factors significantly
influence the comovements between the return series collectively.
This will also allow us to gain insight into which factors had been
contemporaneous to return comovements as a whole.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
The ability to dynamically and jointly model the full multivariate density
dynamics of multiple returns series has very important implications for risk and
portfolio management.
In particular, the growing literature on MV volatility models allow modelers to
efficiently isolate the correlation components from the second order moments.
The most widely used methods of studying second order persistence: GARCH
models.
Generalizing the univariate GARCH processes to the multivariate framework has
proven to be challenging due to curse of dimensionality.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
The ability to dynamically and jointly model the full multivariate density
dynamics of multiple returns series has very important implications for risk and
portfolio management.
In particular, the growing literature on MV volatility models allow modelers to
efficiently isolate the correlation components from the second order moments.
The most widely used methods of studying second order persistence: GARCH
models.
Generalizing the univariate GARCH processes to the multivariate framework has
proven to be challenging due to curse of dimensionality.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
The ability to dynamically and jointly model the full multivariate density
dynamics of multiple returns series has very important implications for risk and
portfolio management.
In particular, the growing literature on MV volatility models allow modelers to
efficiently isolate the correlation components from the second order moments.
The most widely used methods of studying second order persistence: GARCH
models.
Generalizing the univariate GARCH processes to the multivariate framework has
proven to be challenging due to curse of dimensionality.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
The ability to dynamically and jointly model the full multivariate density
dynamics of multiple returns series has very important implications for risk and
portfolio management.
In particular, the growing literature on MV volatility models allow modelers to
efficiently isolate the correlation components from the second order moments.
The most widely used methods of studying second order persistence: GARCH
models.
Generalizing the univariate GARCH processes to the multivariate framework has
proven to be challenging due to curse of dimensionality.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
Generalization of univariate GARCH models to the multivariate
domain is a conceptually simple exercise:
Given the stochastic process, xt {t = 1, 2, ...T } of financial returns
with dimension N × 1 and mean vector µt , given the information set
It−1 :
xt |It−1 = µt + εt
(1)
where the residuals of the process are modelled as:
εt = Ht 1/2 zt ,
Nico Katzke
(2)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
Generalization of univariate GARCH models to the multivariate
domain is a conceptually simple exercise:
Given the stochastic process, xt {t = 1, 2, ...T } of financial returns
with dimension N × 1 and mean vector µt , given the information set
It−1 :
xt |It−1 = µt + εt
(1)
where the residuals of the process are modelled as:
εt = Ht 1/2 zt ,
Nico Katzke
(2)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
Generalization of univariate GARCH models to the multivariate
domain is a conceptually simple exercise:
Given the stochastic process, xt {t = 1, 2, ...T } of financial returns
with dimension N × 1 and mean vector µt , given the information set
It−1 :
xt |It−1 = µt + εt
(1)
where the residuals of the process are modelled as:
εt = Ht 1/2 zt ,
Nico Katzke
(2)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
1/2
Ht
is a N × N positive definite matrix such that Ht is the
conditional covariance matrix of xt .
zt is a N × 1 i.i.d. N(0,1) series.
Several techniques have been proposed that map the Ht matrix into
the multivariate plain:
VECH, BEKK, CCC-GARCH, DCC-GARCH, GOGARCH, etc.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
A large literature has developed that attempts to map Ht into the
multivariate space,
But MV Volatility models typically suffer from curse of high
dimensionality.
Particularly in this study, as I am looking at 21 series, it leads to a
variance-covariance matrix that becomes very large (21 × 21 matrix).
Studying correlation between these series, implies a total of 210 unique
bivariate combinations.
This requires a parsimonious and effective means of isolating the
conditional comovements.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
A large literature has developed that attempts to map Ht into the
multivariate space,
But MV Volatility models typically suffer from curse of high
dimensionality.
Particularly in this study, as I am looking at 21 series, it leads to a
variance-covariance matrix that becomes very large (21 × 21 matrix).
Studying correlation between these series, implies a total of 210 unique
bivariate combinations.
This requires a parsimonious and effective means of isolating the
conditional comovements.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
A large literature has developed that attempts to map Ht into the
multivariate space,
But MV Volatility models typically suffer from curse of high
dimensionality.
Particularly in this study, as I am looking at 21 series, it leads to a
variance-covariance matrix that becomes very large (21 × 21 matrix).
Studying correlation between these series, implies a total of 210 unique
bivariate combinations.
This requires a parsimonious and effective means of isolating the
conditional comovements.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
A large literature has developed that attempts to map Ht into the
multivariate space,
But MV Volatility models typically suffer from curse of high
dimensionality.
Particularly in this study, as I am looking at 21 series, it leads to a
variance-covariance matrix that becomes very large (21 × 21 matrix).
Studying correlation between these series, implies a total of 210 unique
bivariate combinations.
This requires a parsimonious and effective means of isolating the
conditional comovements.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
A large literature has developed that attempts to map Ht into the
multivariate space,
But MV Volatility models typically suffer from curse of high
dimensionality.
Particularly in this study, as I am looking at 21 series, it leads to a
variance-covariance matrix that becomes very large (21 × 21 matrix).
Studying correlation between these series, implies a total of 210 unique
bivariate combinations.
This requires a parsimonious and effective means of isolating the
conditional comovements.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Multivariate Volatility Modelling
For this reason, two methods will be used that provide convincing
and effective means of isolating conditional correlations from the Ht
matrix.
DCC-GARCH model
Generalized Orthogonal (GO)-GARCH model.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
DCC GARCH
Engle (2002) and Tse & Tsuy (2002) introduced a class of models that allow
the direct estimation of time-varying conditional correlation estimates.
The DCC model can be defined as:
Ht = Dt .Rt .Dt .
(3)
Equation 3 splits the varcovar matrix into identical diagonal matrices and an
estimate of the time-varying correlation. Estimating RT requires it to be
inverted at each estimated period, and thus a proxy equation is used (see Engle,
2002):
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
DCC equation:
0
Qij,t = Q̄ + a zt−1 zt−1
− Q̄ + b Qij,t−1 − Q̄
(4)
0
= (1 − a − b)Q̄ + azt−1 zt−1
+ b.Qij,t−1
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
DCC equation:
0
Qij,t = Q̄ + a zt−1 zt−1
− Q̄ + b Qij,t−1 − Q̄
(4)
0
= (1 − a − b)Q̄ + azt−1 zt−1
+ b.Qij,t−1
Note that equation 4 is similar in form to a GARCH(1,1) process,
with non-negative scalars a and b, and with:
Qij,t the unconditional (sample) variance estimate between series i
and j,
Q̄ the unconditional matrix of standardized residuals from each
univariate pair estimate.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
DCC equation:
0
− Q̄ + b Qij,t−1 − Q̄
Qij,t = Q̄ + a zt−1 zt−1
(4)
0
= (1 − a − b)Q̄ + azt−1 zt−1
+ b.Qij,t−1
We then use eq. 4 to estimate the
Rt = diag (Qt )−1/2 Qt .diag (Qt )−1/2 .
(5)
Which has bivariate elements:
Rt = ρij,t = √
Nico Katzke
qi,j,t
qii,t .qjj,t
(6)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
With the resulting DCC model formulated as:
εt ∼ N(0, Dt .Rt .Dt )
Dt2 ∼ Univariate GARCH(1,1) processes ∀ (i,j), i 6= j
zt = Dt−1 .εt
Qt = Q̄(1 − a − b) + a(zt0 zt ) + b(Qt−1 )
Rt = Diag (Qt−1 ).Qt .Diag (Qt −1 )
(7)
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
The time-varying conditional correlations are then estimated using the following
log-likelihood function,which can be convincingly and parsimoniously
decomposed into volatility and correlation components, with the latter then
estimated directly:
LL =
T
1 X
N log (2π) + 2 log |Dt | + log |Rt | + zt0 .Rt−1 .zt0
2 i=1
=
T
1 X
N log (2π) + 2 log |Dt | + ε0t .Dt−1 .Dt−1 .εt
2 i=1
−
T
1 X 0
z zt + log |Rt | + zt0 .Rt−1 zt0
2 i=1 t
= LLV (θ1 ) + LLR (θ1 , θ2 )
Nico Katzke
(8)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
The time-varying conditional correlations are then estimated using the following
log-likelihood function,which can be convincingly and parsimoniously
decomposed into volatility and correlation components, with the latter then
estimated directly:
LL =
T
1 X
N log (2π) + 2 log |Dt | + log |Rt | + zt0 .Rt−1 .zt0
2 i=1
=
T
1 X
N log (2π) + 2 log |Dt | + ε0t .Dt−1 .Dt−1 .εt
2 i=1
−
T
1 X 0
z zt + log |Rt | + zt0 .Rt−1 zt0
2 i=1 t
= LLV (θ1 ) + LLR (θ1 , θ2 )
Nico Katzke
(8)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
The time-varying conditional correlations are then estimated using the following
log-likelihood function,which can be convincingly and parsimoniously
decomposed into volatility and correlation components, with the latter then
estimated directly:
LL =
T
1 X
N log (2π) + 2 log |Dt | + log |Rt | + zt0 .Rt−1 .zt0
2 i=1
=
T
1 X
N log (2π) + 2 log |Dt | + ε0t .Dt−1 .Dt−1 .εt
2 i=1
−
T
1 X 0
z zt + log |Rt | + zt0 .Rt−1 zt0
2 i=1 t
= LLV (θ1 ) + LLR (θ1 , θ2 )
Nico Katzke
(8)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 1: DCC GARCH
The time-varying conditional correlations are then estimated using the following
log-likelihood function,which can be convincingly and parsimoniously
decomposed into volatility and correlation components, with the latter then
estimated directly:
LL =
T
1 X
N log (2π) + 2 log |Dt | + log |Rt | + zt0 .Rt−1 .zt0
2 i=1
=
T
1 X
N log (2π) + 2 log |Dt | + ε0t .Dt−1 .Dt−1 .εt
2 i=1
−
T
1 X 0
z zt + log |Rt | + zt0 .Rt−1 zt0
2 i=1 t
= LLV (θ1 ) + LLR (θ1 , θ2 )
Nico Katzke
(8)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 2: ADCC GARCH
The second model used to extract time-varying conditional correlation estimates
is the ADCC-GARCH model.
The specification generalizes the DCC model to control for leverage effects of
the standardized residuals: zt0− .
ADCC model:
εt ∼ N(0, Dt .Rt .Dt )
Dt2 ∼ Univariate GARCH(1,1) processes ∀ (i,j), i 6= j
zt = Dt−1 .εt
Qt = Q̄(1 − a − b − G ) + a(zt0 zt ) + b(Qt−1 ) + G 0 zt− zt0− G
Rt = Diag (Qt−1 ).Qt .Diag (Qt −1 )
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 2: ADCC GARCH
The second model used to extract time-varying conditional correlation estimates
is the ADCC-GARCH model.
The specification generalizes the DCC model to control for leverage effects of
the standardized residuals: zt0− .
ADCC model:
εt ∼ N(0, Dt .Rt .Dt )
Dt2 ∼ Univariate GARCH(1,1) processes ∀ (i,j), i 6= j
zt = Dt−1 .εt
Qt = Q̄(1 − a − b − G ) + a(zt0 zt ) + b(Qt−1 ) + G 0 zt− zt0− G
Rt = Diag (Qt−1 ).Qt .Diag (Qt −1 )
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 2: ADCC GARCH
The second model used to extract time-varying conditional correlation estimates
is the ADCC-GARCH model.
The specification generalizes the DCC model to control for leverage effects of
the standardized residuals: zt0− .
ADCC model:
εt ∼ N(0, Dt .Rt .Dt )
Dt2 ∼ Univariate GARCH(1,1) processes ∀ (i,j), i 6= j
zt = Dt−1 .εt
Qt = Q̄(1 − a − b − G ) + a(zt0 zt ) + b(Qt−1 ) + G 0 zt− zt0− G
Rt = Diag (Qt−1 ).Qt .Diag (Qt −1 )
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
Another different approach to estimating second order persistence models is
based on the assumption that returns are generated by a set of unobserved
orthogonal conditionally heteroskedastic factors (c.f. van der Weide (2002),
Boswijk & van der Weide (2006, 2011)).
These are measured by identifying independent and uncorrelated factors
that make up the var-covar matrix Ht .
The statistical transformations are done as follows:
rt = µt + εt
(10)
εt = A.ft
(11)
with A linking the unobserved uncorrelated components with the observed
residual process. A: constant and invertible ; ft : normalized, unit variance.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
Another different approach to estimating second order persistence models is
based on the assumption that returns are generated by a set of unobserved
orthogonal conditionally heteroskedastic factors (c.f. van der Weide (2002),
Boswijk & van der Weide (2006, 2011)).
These are measured by identifying independent and uncorrelated factors
that make up the var-covar matrix Ht .
The statistical transformations are done as follows:
rt = µt + εt
(10)
εt = A.ft
(11)
with A linking the unobserved uncorrelated components with the observed
residual process. A: constant and invertible ; ft : normalized, unit variance.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
Another different approach to estimating second order persistence models is
based on the assumption that returns are generated by a set of unobserved
orthogonal conditionally heteroskedastic factors (c.f. van der Weide (2002),
Boswijk & van der Weide (2006, 2011)).
These are measured by identifying independent and uncorrelated factors
that make up the var-covar matrix Ht .
The statistical transformations are done as follows:
rt = µt + εt
(10)
εt = A.ft
(11)
with A linking the unobserved uncorrelated components with the observed
residual process. A: constant and invertible ; ft : normalized, unit variance.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
Another different approach to estimating second order persistence models is
based on the assumption that returns are generated by a set of unobserved
orthogonal conditionally heteroskedastic factors (c.f. van der Weide (2002),
Boswijk & van der Weide (2006, 2011)).
These are measured by identifying independent and uncorrelated factors
that make up the var-covar matrix Ht .
The statistical transformations are done as follows:
rt = µt + εt
(10)
εt = A.ft
(11)
with A linking the unobserved uncorrelated components with the observed
residual process. A: constant and invertible ; ft : normalized, unit variance.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
Also: ft represents the unobserved independent factors assigned to each series
(factor weights), such that:
ft = H 1/2 .zt
(12)
with HT and zt as before and:
E [ft ] = 0;
E [ft ft0 ] = IN
E [εt ] = 0;
E [εt ε0t ] = AA0
(13)
So that the conditional covariance matrix is given by
Σt = AHt A0
Nico Katzke
(14)
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
What is happening is that we are using the residual series of a
simple mean return series to decompose the var-covar matrix into a
factor loading matrix, A, which is made up of:
a sample (unconditional) covariance estimate Σ1/2 ;
an orthogonal matrix, U, mapping the uncorrelated factors onto the covar
matrix: estimated using Independent Component Analysis (ICA).
Thus it assumes the variance process is driven by independent
orthogonal latent components.
The aim is then to model the independent factors as independent
univariate GARCH processes.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
What is happening is that we are using the residual series of a
simple mean return series to decompose the var-covar matrix into a
factor loading matrix, A, which is made up of:
a sample (unconditional) covariance estimate Σ1/2 ;
an orthogonal matrix, U, mapping the uncorrelated factors onto the covar
matrix: estimated using Independent Component Analysis (ICA).
Thus it assumes the variance process is driven by independent
orthogonal latent components.
The aim is then to model the independent factors as independent
univariate GARCH processes.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
What is happening is that we are using the residual series of a
simple mean return series to decompose the var-covar matrix into a
factor loading matrix, A, which is made up of:
a sample (unconditional) covariance estimate Σ1/2 ;
an orthogonal matrix, U, mapping the uncorrelated factors onto the covar
matrix: estimated using Independent Component Analysis (ICA).
Thus it assumes the variance process is driven by independent
orthogonal latent components.
The aim is then to model the independent factors as independent
univariate GARCH processes.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
What is happening is that we are using the residual series of a
simple mean return series to decompose the var-covar matrix into a
factor loading matrix, A, which is made up of:
a sample (unconditional) covariance estimate Σ1/2 ;
an orthogonal matrix, U, mapping the uncorrelated factors onto the covar
matrix: estimated using Independent Component Analysis (ICA).
Thus it assumes the variance process is driven by independent
orthogonal latent components.
The aim is then to model the independent factors as independent
univariate GARCH processes.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
What is happening is that we are using the residual series of a
simple mean return series to decompose the var-covar matrix into a
factor loading matrix, A, which is made up of:
a sample (unconditional) covariance estimate Σ1/2 ;
an orthogonal matrix, U, mapping the uncorrelated factors onto the covar
matrix: estimated using Independent Component Analysis (ICA).
Thus it assumes the variance process is driven by independent
orthogonal latent components.
The aim is then to model the independent factors as independent
univariate GARCH processes.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
An example of a Normally distributed GoGARCH(1,1) model is:
εt = A.ft = Σ1/2 .U
(15)
With each uncorrelated component driven by a GARCH(1,1)
process:
Ht = diag (h1,t , ..., hN,t ),
(16)
(with hi : conditional variances of the factors, ft ).
2
hi,t = γi + αi .fi,t−1
+ βi .hi,t−1 ,
∀i
(17)
The conditional covariances of εt are then driven by: Vt = ZHt Z
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
An example of a Normally distributed GoGARCH(1,1) model is:
εt = A.ft = Σ1/2 .U
(15)
With each uncorrelated component driven by a GARCH(1,1)
process:
Ht = diag (h1,t , ..., hN,t ),
(16)
(with hi : conditional variances of the factors, ft ).
2
hi,t = γi + αi .fi,t−1
+ βi .hi,t−1 ,
∀i
(17)
The conditional covariances of εt are then driven by: Vt = ZHt Z
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
An example of a Normally distributed GoGARCH(1,1) model is:
εt = A.ft = Σ1/2 .U
(15)
With each uncorrelated component driven by a GARCH(1,1)
process:
Ht = diag (h1,t , ..., hN,t ),
(16)
(with hi : conditional variances of the factors, ft ).
2
hi,t = γi + αi .fi,t−1
+ βi .hi,t−1 ,
∀i
(17)
The conditional covariances of εt are then driven by: Vt = ZHt Z
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The most widely used statistical technique for orthogonal transformation
(required here to estimate U): PCA.
For non-Gaussian data (which return series normally correspond to), we
can use Independent Component Analysis (ICA).
ICA separates a multivariate signal (x1 , ..., xN ) into maximally independent
(non-Gaussian) additive subcomponents,(s1 , ...sN ), so that: x = B.s
si are thus independent factors estimated using the FastICA technique
proposed by Hyvarinen and Oja (2000), which does not require
Gaussianity or distributional assumption of the series.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The most widely used statistical technique for orthogonal transformation
(required here to estimate U): PCA.
For non-Gaussian data (which return series normally correspond to), we
can use Independent Component Analysis (ICA).
ICA separates a multivariate signal (x1 , ..., xN ) into maximally independent
(non-Gaussian) additive subcomponents,(s1 , ...sN ), so that: x = B.s
si are thus independent factors estimated using the FastICA technique
proposed by Hyvarinen and Oja (2000), which does not require
Gaussianity or distributional assumption of the series.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The most widely used statistical technique for orthogonal transformation
(required here to estimate U): PCA.
For non-Gaussian data (which return series normally correspond to), we
can use Independent Component Analysis (ICA).
ICA separates a multivariate signal (x1 , ..., xN ) into maximally independent
(non-Gaussian) additive subcomponents,(s1 , ...sN ), so that: x = B.s
si are thus independent factors estimated using the FastICA technique
proposed by Hyvarinen and Oja (2000), which does not require
Gaussianity or distributional assumption of the series.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The two-step FastICA estimation procedure basically works as follows:
ˆ .εˆ , with
the standardized residual process is decomposed into: zt = Σ−1/2
t
ˆ
Σ−1/2
obtained from PCA type eigenvalue decomposition.
Step two uses the estimate of the independent factor components, ft , so
obtained to estimate (using the relatively strong assumption of independence of
the factors) the likelihood function of the GoGARCH model, where the
conditional log-likelihood is expressed as the sum of the individual conditional
marginal density log-likelihoods of the individual factor components in step 1.
see Hyvarinen and Oja (2002) for details.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The two-step FastICA estimation procedure basically works as follows:
ˆ .εˆ , with
the standardized residual process is decomposed into: zt = Σ−1/2
t
ˆ
Σ−1/2
obtained from PCA type eigenvalue decomposition.
Step two uses the estimate of the independent factor components, ft , so
obtained to estimate (using the relatively strong assumption of independence of
the factors) the likelihood function of the GoGARCH model, where the
conditional log-likelihood is expressed as the sum of the individual conditional
marginal density log-likelihoods of the individual factor components in step 1.
see Hyvarinen and Oja (2002) for details.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The two-step FastICA estimation procedure basically works as follows:
ˆ .εˆ , with
the standardized residual process is decomposed into: zt = Σ−1/2
t
ˆ
Σ−1/2
obtained from PCA type eigenvalue decomposition.
Step two uses the estimate of the independent factor components, ft , so
obtained to estimate (using the relatively strong assumption of independence of
the factors) the likelihood function of the GoGARCH model, where the
conditional log-likelihood is expressed as the sum of the individual conditional
marginal density log-likelihoods of the individual factor components in step 1.
see Hyvarinen and Oja (2002) for details.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The two-step FastICA estimation procedure basically works as follows:
ˆ .εˆ , with
the standardized residual process is decomposed into: zt = Σ−1/2
t
ˆ
Σ−1/2
obtained from PCA type eigenvalue decomposition.
Step two uses the estimate of the independent factor components, ft , so
obtained to estimate (using the relatively strong assumption of independence of
the factors) the likelihood function of the GoGARCH model, where the
conditional log-likelihood is expressed as the sum of the individual conditional
marginal density log-likelihoods of the individual factor components in step 1.
see Hyvarinen and Oja (2002) for details.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Model 3: GoGARCH model
The two-step FastICA estimation procedure basically works as follows:
ˆ .εˆ , with
the standardized residual process is decomposed into: zt = Σ−1/2
t
ˆ
Σ−1/2
obtained from PCA type eigenvalue decomposition.
Step two uses the estimate of the independent factor components, ft , so
obtained to estimate (using the relatively strong assumption of independence of
the factors) the likelihood function of the GoGARCH model, where the
conditional log-likelihood is expressed as the sum of the individual conditional
marginal density log-likelihoods of the individual factor components in step 1.
see Hyvarinen and Oja (2002) for details.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
The DCC model estimations allow for the direct modelling of the
conditional correlation.
Although efficient, this method has some drawbacks, as e.g. it assumes a
constant structure to the correlation dynamics.
The GoGARCH model uses a highly efficient and less parameter
intensive estimation technique to decompose the var-covar matrix
into orthogonal sources of volatility, which could then be calculated
using an additive log-likelihood approach because of the
independence of volatility factors.
Although computationally highly efficient, the assumption of linearly
indendent volatility factors is strong.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
The DCC model estimations allow for the direct modelling of the
conditional correlation.
Although efficient, this method has some drawbacks, as e.g. it assumes a
constant structure to the correlation dynamics.
The GoGARCH model uses a highly efficient and less parameter
intensive estimation technique to decompose the var-covar matrix
into orthogonal sources of volatility, which could then be calculated
using an additive log-likelihood approach because of the
independence of volatility factors.
Although computationally highly efficient, the assumption of linearly
indendent volatility factors is strong.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
The DCC model estimations allow for the direct modelling of the
conditional correlation.
Although efficient, this method has some drawbacks, as e.g. it assumes a
constant structure to the correlation dynamics.
The GoGARCH model uses a highly efficient and less parameter
intensive estimation technique to decompose the var-covar matrix
into orthogonal sources of volatility, which could then be calculated
using an additive log-likelihood approach because of the
independence of volatility factors.
Although computationally highly efficient, the assumption of linearly
indendent volatility factors is strong.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
The DCC model estimations allow for the direct modelling of the
conditional correlation.
Although efficient, this method has some drawbacks, as e.g. it assumes a
constant structure to the correlation dynamics.
The GoGARCH model uses a highly efficient and less parameter
intensive estimation technique to decompose the var-covar matrix
into orthogonal sources of volatility, which could then be calculated
using an additive log-likelihood approach because of the
independence of volatility factors.
Although computationally highly efficient, the assumption of linearly
indendent volatility factors is strong.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
As all the approaches have some benefits and drawbacks not discussed here in
detail, I will use all three the DCC, ADCC and GoGARCH (FastICA) models to
calculate the dynamic conditional moment estimates.
This should provide insight into which periods led to increased comovements
(and to what degree) of EME returns over the last decade.
These estimates will then be used in a fixed-effects panel regression to identify
the influence of common global factors on aggregate bivariate return
comovement between emerging market series.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
As all the approaches have some benefits and drawbacks not discussed here in
detail, I will use all three the DCC, ADCC and GoGARCH (FastICA) models to
calculate the dynamic conditional moment estimates.
This should provide insight into which periods led to increased comovements
(and to what degree) of EME returns over the last decade.
These estimates will then be used in a fixed-effects panel regression to identify
the influence of common global factors on aggregate bivariate return
comovement between emerging market series.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Approach
DCC
ADCC
GoGARCH
Which model should be preferred?
Main drawbacks of the models
As all the approaches have some benefits and drawbacks not discussed here in
detail, I will use all three the DCC, ADCC and GoGARCH (FastICA) models to
calculate the dynamic conditional moment estimates.
This should provide insight into which periods led to increased comovements
(and to what degree) of EME returns over the last decade.
These estimates will then be used in a fixed-effects panel regression to identify
the influence of common global factors on aggregate bivariate return
comovement between emerging market series.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
Data and Frequency
The data consists of the weekly aggregate equity market indexes
(TRI, and denominated in Dollars), of 21 EME markets as defined
by the MSCI EME index.
It also consists of the currencies of these countries relative to the
US Dollar.
The period is from 2000/01/21 to 2015/02/27
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
Statistics
Descriptive Statistics
Min
Max
Stdev
Skewness
Kurtosis
LB(1)-pval
LB(5)-pval
ARCH-LM(1)
Brazil
0.215
0.526
−33.056
25.617
5.255
−0.623
7.426
0.016
0.043
0.000
0.000
Chile
0.180
0.360
−34.607
19.134
3.356
−1.543
18.528
0.118
0.095
0.000
0.000
China
0.152
0.406
−22.110
17.937
4.231
−0.405
5.277
0.331
0.387
0.000
0.000
Colombia
0.316
0.368
−28.530
15.111
3.896
−0.895
8.703
0.160
0.000
0.054
0.000
Czech
Egypt
Greece
Mean
0.262
Median
0.417
−29.812
21.635
3.888
−0.717
9.652
0.360
0.024
0.000
JB p-value
0.000
0.285
0.457
−21.922
15.513
4.274
−0.554
6.016
0.031
0.043
0.000
0.000
−0.209
−0.008
−29.108
18.765
5.172
−0.656
5.947
0.806
0.114
0.000
0.000
Hungary
0.061
0.289
−43.448
22.731
5.174
−0.977
10.781
0.610
0.072
0.000
0.000
India
0.258
0.466
−21.879
18.366
4.010
−0.464
5.616
0.063
0.005
0.000
0.000
Indonesia
0.296
0.387
−26.842
21.542
4.909
−0.227
5.918
0.907
0.000
0.000
0.000
Korea
0.218
0.447
−27.901
28.635
4.741
−0.279
7.151
0.052
0.309
0.000
0.000
0.276
−12.513
Malaysia
0.240
0.283
7.300
Mexico
0.249
0.511
−30.677
22.572
4.087
−0.622
10.348
0.012
0.001
0.000
0.000
Peru
0.312
0.440
−29.362
22.054
14.370
3.980
2.698
−0.535
8.802
0.424
0.103
0.414
0.009
0.000
0.003
0.000
0.000
Philippines
0.152
0.328
−20.803
15.242
3.482
−0.311
5.834
0.466
0.108
0.006
0.000
Poland
0.129
0.355
−26.459
24.067
4.622
−0.525
6.682
0.901
0.431
0.000
0.000
Russia
0.283
0.485
−28.062
44.899
5.971
−0.044
9.033
0.977
0.147
0.000
0.000
South.Africa
0.239
0.531
−18.425
27.601
3.937
−0.121
7.723
0.022
0.020
0.000
0.000
Taiwan
0.094
0.361
−14.386
19.364
3.653
−0.145
5.400
0.597
0.213
0.049
0.000
Thailand
0.237
0.348
−29.026
17.264
4.214
−0.470
7.239
0.527
0.000
0.004
0.000
Turkey
0.197
0.573
−73.767
38.610
6.971
−1.253
20.532
0.159
0.290
0.000
0.000
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
Data
The returns show typical returns series behaviour:
excess kurtosis and skewness, as well as evidence of significant serial
autopersistence as well as conditional heteroskedasticity. This
motivates the use of the MV GARCH models employed to extract
the second order persistence series.
The data is also scaled by subtracting each series’ mean prior to
estimating the models.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
Data
The returns show typical returns series behaviour:
excess kurtosis and skewness, as well as evidence of significant serial
autopersistence as well as conditional heteroskedasticity. This
motivates the use of the MV GARCH models employed to extract
the second order persistence series.
The data is also scaled by subtracting each series’ mean prior to
estimating the models.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
Data
The returns show typical returns series behaviour:
excess kurtosis and skewness, as well as evidence of significant serial
autopersistence as well as conditional heteroskedasticity. This
motivates the use of the MV GARCH models employed to extract
the second order persistence series.
The data is also scaled by subtracting each series’ mean prior to
estimating the models.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
GoGARCH estimates: (Equities)
F_1
omega
F_2
F_3
F_4
F_5
F_6
F_7
F_8
F_9
F_10
0.07422551 0.007901069 0.02013517 0.05510071 8.672800e-04 0.09001604 0.02278301 0.02556973 0.03573081 0.003315177 0.0011
alpha1 0.11796657 0.054758822 0.05854870 0.10030617 2.578081e-09 0.07654145 0.08330919 0.08237253 0.03719492 0.058134152 0.0105
beta1
0.81151789 0.936294065 0.91978245 0.84566417 9.989999e-01 0.83264833 0.89327224 0.89545198 0.92673715 0.940865831 0.9873
omega
0.01935749 0.05709150 0.01980954 0.01706659 0.004233564 0.008182664 0.007875477 0.009033343 0.002555149 0.09481719
F_12
F_13
F_14
F_15
F_16
F_17
F_18
F_19
F_20
F_21
alpha1 0.04500304 0.04209236 0.05453154 0.08944808 0.056328861 0.069675464 0.049737695 0.029490802 0.039384955 0.19876847
beta1
0.93417703 0.90035262 0.92353795 0.89456896 0.939139202 0.924631787 0.939655777 0.960569894 0.959615035 0.71825986
=============================
GoGARCH Parameter estimates
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Statistics
GoGARCH estimates: (Currencies)
F_1
omega
F_2
F_3
F_4
F_5
F_6
F_7
F_8
F_9
F_10
F_1
0.01623448 0.03099957 0.0924535 0.008274239 0.03796785 0.04458345 0.003321745 0.02055873 0.01543423 0.01628214 0.0245642
alpha1 0.03782264 0.12455670 0.2255800 0.082767297 0.13514496 0.10511909 0.042638709 0.18679680 0.09627177 0.14218538 0.1857924
beta1
0.94464983 0.85017091 0.7032481 0.914802500 0.83175104 0.85499662 0.970799878 0.81220318 0.88943244 0.81054104 0.8132074
omega
0.0920156 0.1972719 0.03257469 0.003670243 0.04927513 0.1935921 0.009981032 0.05914329
F_12
F_13
F_14
F_15
F_16
F_17
F_18
F_19
alpha1 0.3549753 0.2147538 0.06641944 0.140942882 0.07413239 0.2891759 0.077231573 0.24591772
beta1
0.6027820 0.6041746 0.90242859 0.858057117 0.87921705 0.5129753 0.914310758 0.71207333
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Fitting Procedures
DCC Fitting:
Assume all the series follow AR(1)-GJR GARCH processes, which controls for
leverage in univariate GARCH specifications in the first step.
Use a DCC(1,1) order, assuming a MV Normal distribution (for simplicity, as
the Std-t adds a layer of parameter complexity which undermines accuracy for
large N).
GoGARCH Fitting:
Assume the factor series all follow AR(1) GARCH(1,1) processes, with factor
estimation carried out using the FastICA method used.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
DCC series:
Dynamic Conditional Correlation Aggregates (Equities): DCC:
0.45
0.40
DCC mean estimates
0.50
Mean DCC estimates across countries
●
●
●
●
●
●
●
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05/2006
GFC
BNP
Greece QE2
Taper
QE3
2000−01−21 2003−02−14 2006−03−10 2009−04−03 2012−04−27
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
DCC series:
Dynamic Conditional Correlation Aggregates (Equities): ADCC:
0.45
0.40
DCC mean estimates
0.50
Mean DCC estimates across countries
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05/2006
GFC
BNP
Greece QE2
Taper
QE3
2000−01−21 2003−02−14 2006−03−10 2009−04−03 2012−04−27
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
DCC series:
Dynamic Conditional Correlation Aggregates (Equities):
GoGARCH:
0.9
Mean DCC estimates across countries
●
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0.5
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0.3
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0.8
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BNP
Greece QE2
●●●
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2000−01−21 2003−02−14 2006−03−10 2009−04−03 2012−04−27
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
DCC series:
Dynamic Conditional Correlation Aggregates (Currencies): DCC:
0.30
0.25
DCC mean estimates
0.35
Mean DCC estimates across countries
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05/2006
GFC
BNP
Greece QE2
Taper
QE3
2000−01−21 2003−02−21 2006−03−24 2009−04−24 2012−05−25
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
DCC series:
Dynamic Conditional Correlation Aggregates (Currencies): ADCC:
0.30
0.25
DCC mean estimates
0.35
Mean DCC estimates across countries
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05/2006
GFC
BNP
Greece QE2
Taper
QE3
2000−01−21 2003−02−21 2006−03−24 2009−04−24 2012−05−25
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
DCC series:
Dynamic Conditional Correlation Aggregates (Currencies):
GoGARCH:
0.6
Mean DCC estimates across countries
●
0.5
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0.4
0.3
0.2
DCC mean estimates
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Taper
QE3
05/2006
BNP
Greece QE2
GFC
●
2000−01−21 2003−02−21 2006−03−24 2009−04−24 2012−05−25
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
VIX
Equity comovement with VIX index series:
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
VIX
Equity comovement with VIX index series: DCC:
Mean DCC estimates across countries
0.45
0.40
DCC mean estimates
0.50
80
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70
60
50
40
30
20
10
2000−01−21 2003−08−01 2007−02−09 2010−08−20 2014−02−28
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
VIX
Equity comovement with VIX index series: ADCC:
Mean DCC estimates across countries
0.50
0.45
0.40
DCC mean estimates
0.55
80
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50
40
30
20
10
2000−01−21 2003−08−01 2007−02−09 2010−08−20 2014−02−28
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
VIX
Equity comovement with VIX index series:
GoGARCH:
0.9
Mean DCC estimates across countries
80
●
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50
0.4
0.5
0.6
●
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DCC mean estimates
0.8
70
●
40
30
20
10
2000−01−21 2003−08−01 2007−02−09 2010−08−20 2014−02−28
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
GSCI index
Currency comovement with log(GSCI) series:
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
GSCI index
Currency comovement with log(GSCI) series: DCC:
0.30
0.25
DCC mean estimates
0.35
Mean DCC estimates across countries
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6.5
6.0
5.5
2000−01−21 2003−08−15 2007−03−09 2010−10−01 2014−04−25
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
GSCI index
Currency comovement with log(GSCI) series: ADCC:
0.30
0.25
DCC mean estimates
0.35
Mean DCC estimates across countries
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6.5
6.0
5.5
2000−01−21 2003−08−15 2007−03−09 2010−10−01 2014−04−25
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
GSCI index
Currency comovement with log(GSCI) series:
GoGARCH:
0.6
Mean DCC estimates across countries
●
6.5
0.5
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0.3
0.4
●
6.0
5.5
0.2
DCC mean estimates
●
2000−01−21 2003−08−15 2007−03−09 2010−10−01 2014−04−25
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Variables used
After fitting the three different models (which all adhere to their constraints and
all converged), the next step is to create a Panel data set.
Included in the Panel set are the following variables:
QE1, QE2, QE3: all indicator variables identifying periods of US
quantitative easing measures.
GFC: Global Financial Crisis period (Lehman : 31/12/2009).
AQE1, AQE2, AQE3: IVs corresponding to the two month period after
each round of QE - so as to measure the unwinding effect of QE policies.
VIX30, which corresponds to periods where VIX is above 30, indicating
periods of high uncertainty in global markets, as proxied for by the CBOE
VIX series.
GSCI: the global commodity price index, used as a proxy for global price
pressures.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Variables used
After fitting the three different models (which all adhere to their constraints and
all converged), the next step is to create a Panel data set.
Included in the Panel set are the following variables:
QE1, QE2, QE3: all indicator variables identifying periods of US
quantitative easing measures.
GFC: Global Financial Crisis period (Lehman : 31/12/2009).
AQE1, AQE2, AQE3: IVs corresponding to the two month period after
each round of QE - so as to measure the unwinding effect of QE policies.
VIX30, which corresponds to periods where VIX is above 30, indicating
periods of high uncertainty in global markets, as proxied for by the CBOE
VIX series.
GSCI: the global commodity price index, used as a proxy for global price
pressures.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Variables used
After fitting the three different models (which all adhere to their constraints and
all converged), the next step is to create a Panel data set.
Included in the Panel set are the following variables:
QE1, QE2, QE3: all indicator variables identifying periods of US
quantitative easing measures.
GFC: Global Financial Crisis period (Lehman : 31/12/2009).
AQE1, AQE2, AQE3: IVs corresponding to the two month period after
each round of QE - so as to measure the unwinding effect of QE policies.
VIX30, which corresponds to periods where VIX is above 30, indicating
periods of high uncertainty in global markets, as proxied for by the CBOE
VIX series.
GSCI: the global commodity price index, used as a proxy for global price
pressures.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Panel
Fixed effect Panel approach used, as the means between the country estimates
differ significantly: Equities (GoGARCH):
0.7
Heterogeineity across DCC estimates
●
●
●
●
0.6
●
●
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0.5
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dcc1
dcc12 dcc142 dcc167 dcc19 dcc21 dcc41 dcc62 dcc83
Nico Katzke
Date
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Panel
Fixed effect Panel approach used, as the means between the country estimates
differ significantly: Currencies (GoGARCH):
Heterogeineity across DCC estimates
0.8
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dcc1 dcc116 dcc136 dcc156
Nico Katzke
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dcc2 dcc36 dcc53 dcc7 dcc86
Date
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Panel: Equities
Dependent variable:
Aggregate Dynamic Conditional Comovement Estimates
(DCC)
(ADCC)
(GoGARCH)
(DCC)
(ADCC)
(GoGARCH)
0.038∗∗∗
0.036∗∗∗
0.060∗∗∗
0.042∗∗∗
0.041∗∗∗
0.071∗∗∗
(0.0003)
(0.0003)
(0.001)
(0.0003)
(0.0003)
(0.001)
qe2
−0.009∗∗∗
−0.013∗∗∗
−0.029∗∗∗
(0.0004)
(0.0004)
(0.001)
qe3
−0.029∗∗∗
−0.026∗∗∗
−0.033∗∗∗
(0.0003)
(0.0003)
(0.001)
0.011∗∗∗
0.017∗∗∗
0.048∗∗∗
(0.0005)
(0.001)
(0.001)
−0.009∗∗∗
−0.005∗∗∗
0.015∗∗∗
gfc
aqe2
aqe3
0.049∗∗∗
(0.0005)
(0.001)
(0.001)
0.024∗∗∗
0.040∗∗∗
0.010∗∗∗
(0.0003)
(0.0003)
(0.001)
(0.0003)
(0.0003)
(0.001)
lgsci
0.040∗∗∗
0.034∗∗∗
0.092∗∗∗
0.033∗∗∗
0.027∗∗∗
0.078∗∗∗
(0.0002)
(0.0002)
(0.0005)
(0.0002)
(0.0002)
(0.0004)
165,690
Observations
0.027∗∗∗
0.009∗∗∗
vix30
165,690
165,690
165,690
165,690
165,690
R2
0.351
0.294
0.270
0.315
0.270
Adjusted R2
0.350
0.294
0.269
0.315
0.270
0.266
17,864.670∗∗∗
13,794.590∗∗∗
12,220.070∗∗∗
15,236.990∗∗∗
12,264.970∗∗∗
12,031.160∗∗∗
F Statistic (df = 5; 165475)
Note:
Nico Katzke
0.267
p<0.1;
p<0.05; Returns
p<0.01
Exploring EME
Asset
Conditional Comovement
∗
∗∗
∗∗∗
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Fitting Procedures
Graphs
Variables Used
Regression Outputs
Panel: Currencies
Dependent variable:
Aggregate Dynamic Conditional Comovement Estimates
(DCC)
(ADCC)
(GoGARCH)
(DCC)
(ADCC)
(GoGARCH)
0.025∗∗∗
0.022∗∗∗
−0.001
0.026∗∗∗
0.023∗∗∗
0.004∗∗∗
(0.0003)
(0.0003)
(0.001)
(0.0003)
(0.0003)
(0.001)
qe2
0.014∗∗∗
0.014∗∗∗
−0.012∗∗∗
(0.0005)
(0.0005)
(0.001)
qe3
−0.008∗∗∗
−0.012∗∗∗
−0.023∗∗∗
(0.0004)
(0.0004)
(0.001)
0.025∗∗∗
0.024∗∗∗
0.012∗∗∗
(0.001)
(0.001)
(0.001)
−0.005∗∗∗
−0.011∗∗∗
0.074∗∗∗
gfc
aqe2
aqe3
−0.005∗∗∗
(0.001)
(0.001)
(0.001)
0.009∗∗∗
−0.001
0.005∗∗∗
(0.0003)
(0.0003)
(0.001)
(0.0003)
(0.0003)
(0.001)
lgsci
0.042∗∗∗
0.045∗∗∗
0.059∗∗∗
0.040∗∗∗
0.043∗∗∗
0.052∗∗∗
(0.0002)
(0.0002)
(0.001)
(0.0002)
(0.0002)
(0.0005)
136,287
Observations
0.007∗∗∗
0.007∗∗∗
vix30
136,287
136,287
136,287
136,287
136,287
R2
0.251
0.290
0.089
0.256
0.291
Adjusted R2
0.251
0.289
0.089
0.256
0.291
0.103
9,143.967∗∗∗
11,098.710∗∗∗
2,668.757∗∗∗
9,363.376∗∗∗
11,167.790∗∗∗
3,124.307∗∗∗
F Statistic (df = 5; 136111)
Note:
Nico Katzke
0.103
p<0.1; Asset
p<0.05;
p<0.01
Exploring EME
Returns Conditional Comovement
∗
∗∗
∗∗∗
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Models
In conclusion, we see the following:
The dynamics of the GoGARCH model are significantly more responsive
to new information.
This follows from the comparatively lower persistence parameters in
the univariate GARCH estimates.
In contrast, the aggregate joint correlation dynamics of the DCC model
has a = 0.009 and b = 0.95 (a = 0.006, b = 0.932 and g = 0.012).
This implies that the DCC model reacts slower to new information.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Models
In conclusion, we see the following:
The dynamics of the GoGARCH model are significantly more responsive
to new information.
This follows from the comparatively lower persistence parameters in
the univariate GARCH estimates.
In contrast, the aggregate joint correlation dynamics of the DCC model
has a = 0.009 and b = 0.95 (a = 0.006, b = 0.932 and g = 0.012).
This implies that the DCC model reacts slower to new information.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
The aggregate bivariate return comovement of equities and currencies are
roughly 40% and 30%, respectively.
Currency returns (relative to the Dollar) are also less likely to spike
significantly compared to equity returns.
Significant spikes in equity comovement following: Greek bailout in 2010;
Bernanke’s Taper talk in 2013 ; following the unwinding of QE3
GoGARCH picks up sustained higher comovement following QE2’s
unwinding, with a spike in comovement of currencies again following
unwinding of QE3.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
The GFC saw a significant rise in equity comovement (equities: between
4-7% rise).
In contrast, the GFC had a comparatively moderate effect on currency
comovement (currencies: between 1 - 2%, insignificant for GoGARCH
estimates).
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
QE2 produced relatively little change in comovements, with it being
negative for equities and slightly positive for currencies (between 1% and
-1% for DCC and GoGarch estimates).
During QE3, equity and currency comovements again experienced a
relative dampening of comovements (roughly 3% for equities and 1-2%for
currencies).
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
The two months following QE2 saw a modest rise in comovements of
both eq’s and curr’s of roughly 2-4% for eq’s and 2% for currencies.
The two month period following QE3 also saw a modest downward
adjustment for eq’s and curr’s (DCC) and upward adjustment using the
GoGARCH estimates.
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
Periods of large equity market uncertainty saw equity comovements rise
significantly (1%, 2.7% and 4.9% for the DCC, ADCC & GoGARCH
respectively)
Periods of large equity market uncertainty saw no great influence on
currency comovement (0.1%, 0.7% and -0.5% for the DCC, ADCC &
GoGARCH respectively)
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Conclusion: Panel Findings
From the panel regressions, we note the following:
Commodity price movements saw equity comovements rise significantly
(4%, 3% and 9% price elasticities for the DCC, ADCC & GoGARCH
respectively)
Commodity price movements saw currency comovements rise
significantly(4%, 4.5% and 6% for the DCC, ADCC & GoGARCH
respectively)
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
BONUS: BRICS equity return comovements
Equity comovement: BRICS returns
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
BONUS: BRICS equity return comovements
Equity comovement: BRICS returns DCC:
0.7
Mean DCC estimates across BRICS
0.6
0.5
0.4
DCC mean estimates
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2000−01−21 2003−02−14 2006−03−10 2009−04−03 2012−04−27
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
BONUS: BRICS equity return comovements
Equity comovement: BRICS returns ADCC:
0.7
Mean DCC estimates across BRICS
0.6
0.5
DCC mean estimates
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2000−01−21 2003−02−14 2006−03−10 2009−04−03 2012−04−27
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
BONUS: BRICS equity return comovements
Equity comovement: BRICS returns
GoGARCH:
Mean DCC estimates across BRICS
0.6
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0.4
0.3
0.2
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2000−01−21 2003−02−14 2006−03−10 2009−04−03 2012−04−27
Date
Nico Katzke
Exploring EME Asset Returns Conditional Comovement
Introduction
Methodological Discussion
Data
Results
Conclusion
Bonus!
Comments?
Nico Katzke
Exploring EME Asset Returns Conditional Comovement