1. No category

FONDATION POUR LES ETUDES ET RECHERCHES SUR LE DEVELOPPEMENT INTERNATIONAL
Measuring macroeconomic volatility
Applications to export revenue data, 1970-2005
by
Joël Cariolle
Policy brief no. 47
March 2012
The FERDI is a Public Interest Foundation.
In cooperation with the Fonddri it implements the Initiative for Development and Global Governance
(IDGM).
In cooperation with the Iddri and the Cerdi it implements the IDGM+ project “Laboratoire d’excellence.”
1
Measuring volatility: applications to export revenue data, 1970-2005.
By Joël Cariolle
Joël Cariolle is a research assistant at the FERDI. Contact: [email protected]
The literature on macroeconomic volatility covers an extremely wide field, reflected in the
very broad spectrum of indicators used to grasp this phenomenon. The choice of indicator is
generally little discussed, on the grounds that the different methods give rise to volatility
scores that are strongly correlated. However, while these indicators do seem to converge when
used to measure the average magnitude of volatility, they diverge significantly when one
studies its asymmetry (predominance of positive or negative shocks) or the occurrence of
extreme deviations.
The volatility of an economic variable refers to the notion of disequilibrium, measured by the
deviation between the values taken by this variable and a reference value or a trend. The first
stage is therefore to identify and isolate the trend or permanent component of the change in an
economic variable. Traditionally, volatility indicators measure the mean deviation range of
the variable relative to the reference value, generally on the basis of standard deviation. But
such an approach masks other important dimensions of volatility, such as the asymmetry of
the deviations (predominance of positive or negative shocks) and the occurrence of extreme
deviations. Economic agents may behave or react quite differently depending on whether the
volatility is dominated by positive or negative shocks, but also on whether the shocks are
frequent and weak or infrequent and strong. We illustrate our analysis based on the annual
changes in the export revenues of 134 developed and developing countries over the period
1970-2005 from the World Development Indicators.
Calculation of trend components or reference values
The first stage is to identify the trend component of an economic variable in order to measure
the deviations between the values taken by that variable and that trend or reference. Since this
first stage may influence the volatility indicators, we put forward here several methods for
calculating the reference. The first two methods are based on a parametric approach in which
the trend, which takes a mixed (deterministic and random) form, is estimated econometrically:
yt = α + βt + δyt −1 + ε t
2
The trend or reference value is then yˆ t = α + βˆt + δˆy t −1 and the deviation is εˆt = yt − yˆ t . The
first alternative is to estimate the trend over the whole period (the so-called “global” trend);
the second is to estimate the trend on a rolling basis for each year based on the data for each
year and that of the twelve previous years (the “rolling” trend).
The other two methods of trend computation are based on the Hodrick-Prescott filter. The HP
trend is derived from the algorithm:
−
∗
and the deviation is
=
−
+λ
∆
∗
The two alternatives are obtained by selecting a smoothing parameter (λ) of 6.5 or 100,
generating respectively a fluctuating or a stable trend. The four reference values and the
deviations they generate are illustrated in Figure 1 below, for the case of Argentina.
Figure 1. Reference values applied to the case of Argentina
Filter method
0
0
2,000e+10
2,000e+10
4,000e+10
4,000e+10
Parametric method
1970
1980
1990
2000
1970
1980
Year
Exports (USD, 2000)
Rolling mixed trend
1990
2000
Year
Global mixed trend
Exports (USD, 2000)
Filtered exports (λ=100)
Filtered exports (λ=6.5)
3
0
-20
-40
as % of trend
20
40
60
Deviations compared (as % of trend)
1970
1980
1990
2000
Year
Rolling mixed trend
Global mixed trend
HP filter (6.5)
HP filter (100)
Magnitude of volatility
The most commonly used method is to compute the standard deviation (StdDev) of the
variable around its reference value. Here we normalize the deviations by the reference value
so as to make them comparable between countries. The formula is the following:
1  yt − reft
StdDev = 100 ×
∑
T t  reft



2
with T=[1982;2004-05]
where ref t is one of the four reference values previously presented ( yˆ t over the whole
period, or rolling, or HPt of HP filter 6.5 or HP filter 100). Table 1 shows that the indicators
of magnitude derived from the different reference values are very strongly correlated.
Table 1. Correlations among volatility magnitude indicators
(1)
Global mixed trend
(2)
Rolling mixed trend
(3)
HP 6.5
(4)
HP 100
Volatilities calculated over period 1982-2004/05
(1)
1.00
(2)
0.92*
1.00
(3)
0.96*
0.95*
1.00
(4)
0.87*
0.80*
0.87*
1.00
* Significant at 5%. Sample = 134 countries.
4
Asymmetry of volatility
Indicators of magnitude do not make it possible to identify a possible asymmetry of shocks.
The coefficient of asymmetry (CA), or dissymmetry, identifies the profile of the volatility by
revealing whether it is dominated by negative or positive shocks. This coefficient is calculated
as follows:
CA = 100 ×
1  yt − ref t
∑
T t  ref t
 1  y − ref
t

 t
T ∑
ref
t
 t 






3
2




3/ 2
with T = 1,..., t
A symmetrical distribution of deviations gives a coefficient equal to zero, while a distribution
dominated by positive (negative) deviations gives a positive (negative) CA. The greater the
positive or negative shocks, the higher the CA. Erreur ! Source du renvoi introuvable. 2
shows that the correlations among the CA derived from the different reference values are
weak, suggesting that the choice of reference values is primordial when one is interested in
the asymmetry of shocks.
Table 2. Correlations among coefficients of asymmetry (CA) calculated over the period 1982-2005.
(1)
CA (Global mixed trend)
(2)
CA (Rolling mixed trend)
(3)
CA (HP(6.5))
(4)
CA (HP(100))
CA calculated over the period 1982-2005
(1)
1
(2)
0.23*
1
(3)
0.08*
0.14*
1
(4)
0.29*
0.02
0.65*
1
* Significant at 10%. Sample = 134 countries.
Figure 2 in the appendix shows a positive but weak correlation between measures of
magnitude and measures of asymmetry: two countries may have a similar magnitude of
volatility but exhibit a radically different asymmetry. The asymmetry of the deviations from
the reference value is thus a distinct dimension of volatility, which cannot be grasped by
magnitude indicators alone.
5
Frequency of extreme deviations
A final dimension of the volatility of a macroeconomic variable concerns the occurrence of
extreme deviations. This dimension is measured by the fourth aspect of the distribution of
observations around their reference value, kurtosis (or coefficient of peakedness). The
kurtosis of normalized deviations is calculated by means of the following formula:
Kurtosis = 100 ×
1
T
 y − ref
∑t  t ref t
t




1

T

 y − ref
∑t  t ref t
t




4
2




2
with T = 1,..., t
Kurtosis indicates the extent to which observations close to the mean are numerous relative to
observations distant from it. In the case of a normal distribution kurtosis is equal to 3 (or
300% when expressed as a percentage of the trend). A higher kurtosis value represents a
staggered distribution with thick distribution tails, whereas a lower value represents a
distribution concentrated around its mean with thin distribution tails. Combined with the
coefficient of asymmetry, the kurtosis can provide information on a country’s propensity to
undergo extreme negative or positive shocks.
Table 3 sets out the correlations among the kurtoses derived from four trends or reference
values. These correlations are stronger than those of the asymmetries but weaker than those of
the volatility magnitude indicators, showing that the choice of reference values influences the
diagnosis on the occurrence of extreme shocks.
Table 3. Correlations among kurtoses calculated over the period 1982-2004/05.
(1)
Kurt. (Global mixed trend)
(2)
Kurt. (Rolling mixed trend)
(3)
Kurt. (HP(6.5))
(1)
1
(2)
0.39*
1
(3)
0.38*
0.28*
1
(4)
0.49*
0.22*
0.62*
(4)
Kurt. (HP(100))
1
* Significant at 5%. Sample = 134 countries.
Figure 3 in the appendix shows that the correlation between the measures of magnitude and
the measures of kurtosis is relatively weak, indicating that the two dimensions are relatively
independent. Figure 4 shows the correlation between the asymmetry scores and the kurtosis
scores. A U-shaped relationship can be observed between these two measures: at negative and
6
weakly positive levels of asymmetry, the two dimensions are relatively independent, whereas
high kurtosis is associated with strong positive asymmetry, for the export data used here.
Overall, the three measures of magnitude, asymmetry and kurtosis appear relatively
independent, at least for the data used here, which leads us to consider that these three
dimensions generate different information on volatility. It is therefore important to use several
types of indicators in relation to the subject studied, or if one wants to establish a complete
diagnosis on volatility.
The method is set out in detail in:
Cariolle J. (2012), Mesurer l’instabilité macroéconomique: applications aux données de
recettes d’exportation, 1970-2005, FERDI Working Paper No.I.14.
If you use these data, please cite this reference, adding: “Data available at:
http://www.ferdi.fr/en/Innovative-indicators.html”.
7
ANNEXE :
Figure 2. Correlation between measures of magnitude and of asymmetry of
volatility, by reference value.
Rolling mixed trend
Global mixed trend
Correlation = 36%
80
60
Correlation = 23%
KIR
TCD
Magnitude
40
60
40
SLE
100
Asymmetry
200
0
-200
300
-100
0
100
200
DOM
300
Asymmetry
HP filter 6.5
HP filter 100
Correlation = 18%
Correlation = 38%
LAO
50
0
50
-100
UGA
KWT
SLE ALB
IRN
SOM
GHA
GNBNGATCD
RWA
HTI
ARG
COM SUR
SAUAGO
SLB
ZAR
TON
GAB
STP
TGO
DZA
BDI
LSO
NIC
BFA
PER
COG
NER
PRY
PNG
GUY
ZMB
OMN
BGD
SLV
BGR
ARE
SWZ
VEN
ETH
SEN
CMR
BEN
MWI
DMA
BOL
VCT
TTO
SYR
TUR
ATGLAO
MDG
BWA
BHR
NAM
ECU
EGY
GMB
MOZ
IDN
NPL
CIV
CAF
MRT
MLT
MLI
BLZ
PRT
CRI
DEU
HUN
URY
BTN
AUT
CHE
COL LKA
HND
CHL
MEX
ZWE
GRC
ISL
BRB
LCA
CYP
GTM
BEL
MUS
PAN
KNA
FJI
SWE
MAR
BRA
PAK
AUS
KOR
KEN
MYS
ZAF
ITA
DNK
PHL
SYC
TUN
FIN
THA
VUT
FRA
JAM
ESP
HKG
IRL
IND LUX
JOR
MAC
NZL
NLD
JPN
NOR
CHN
CAN PRI
ISR USA
GBR
20
IRN
KWT
ALB
GNB
UGA
HTI BDI
SOM
NGA
DOM
GHA
COM
SURRWA
ZAR
TON
STP
SAU
SLB
DZABFA
MDG
ARG
GAB
COG
PRY
PNG
NIC
AGO
BGD
BGR
LAO
LSO
VEN
OMN
TGO
SLV ZMB
SWZ
NER
PER
VUT BTN
CMR DMA
ARE BEN
GUY
ATG
MWI
GMB
SYR
BWA
TTO
ETH
NPL
BOL
CAF
ZWE
CIV
BLZ
SEN
LCA
URY
KNA
VCT
MOZ
MUS
BHR
MRT
CRI
ECU IDN
CHL
MLT
HUN
MLI
TUR
FJI
PAN
NAM
COL
PRT
PHL
HND
ZAF
EGY
THA
DEU
CYP
AUT
GRC
ISL
GTM
KEN
BRA
PAK
BRB
KOR
HKG
MEX
MYS
LKA
LUX
FIN
SWE
MAR
BEL
ITAIRL CHE
SYC
TUN
IND
DNK
JPN
PRI
AUS
JOR
FRA
CHN
ESP
NZLCAN
JAM
NOR
NLD
MAC
ISR
GBR
USA
0
20
Magnitude
KIR
KIR
Magnitude
20
30
40
Magnitude
20
30
40
KIR
TCD
HTI
GNB SLE
IRN
SOM NGA
UGA
GHABDI RWA SUR ZAR
COM
SLB
GAB
BFA
COG
STP
AGO
DZA
SAU
PNG
TON
LAO
ARG
LSO
NIC
OMN
NER
BGR
MWIPERVUT
BEN
MDG
TGO
VEN
SLV
SWZ
GUY
ZMB
PRY
BGD
BTN
SYR
CAF
DMA
ATG
CIV
GMB
ETH
ECU
BOL
ARE
MOZ
TTO
KNA
BWA
BHR
CRI
CMR
COL
BLZ
URY
NPL
PAN
ZAF
SEN
MLI
ZWE
EGY
MUS MLT
NAM
FJI
HND
LCA
BRA
VCT
GTM
TUR
GRC
HUN
CHL
ISL
FIN
SYC
MEX
MRT
KOR
CHE
AUT
DEU
KENISR
SWE
PRT
LUX
IDN
LKA
PHL
JOR
BRB
MYS
IND
BEL
PRI
ITA
PAK
CHN
NZL
ESP
FRA
MAR
DNK
AUS
JPN
NOR
CYP
TUN
THA
NLD
IRL
MAC
JAM
HKG
GBR
CAN
USA
-200
ALB
-100
0
Asymmetry
100
10
DOM
DOM
0
0
10
KWT
TCD
SLE HTI
SOM
UGA
ALB
IRN
NGA
GNB GHA
SUR
KWT
RWA
COM
BGR
SAU
SLB
GABPRYBDI
BFAZAR VUT
PNG
TGO
LSO
COG
STP
NIC
DZA
TON
BTN
MOZ
AGO
PER
SLV
ATG
GUY
SWZ
NER
ETH
OMN
ZMB
MWI
SYR
BWA
ARG
DMA
GMB
BEN
KNA
ARE
MDG
NPL
CIV
VEN
MLT
CAF
CMR
EGY
SEN
PRT
ZWE
ECU
ZAF
MUS
LCA
NAM
HND
THA
AUT
URY
VCT
SYC
BGD
HUN
MLI
IDN
DEU
ISL
TTO
CHE
MEX
CRI
LUX
BLZ
BOL
BEL
PAN
COL
SWE
PHL
HKG
CHL
MRT
BHR
DNK
CHN
FIN
GRC
KOR
ITA
MYS
MAR
BRB
FRA
BRA
CYP
GTM
FJI
TUR
IND
LKA
PRI
KEN
PAK
NLD
MAC
TUN
ESP
JPN
NOR
ISR
JOR
AUS
GBR
JAM IRL
CANNZL
USA
200
-200
-100
0
100
Asymmetry
200
300
Figure 3. Correlation between measures of magnitude and of peakedness of
volatility, by reference value.
Rolling mixed trend
Global mixed trend
Correlation = 20%
KIR
80
60
Correlation = 29%
TCD
60
40
UGA
KWTIRN
SLE
ALB
TCD
NGA
SOM
GHA RWA
GNB
HTI
ARG
COM
AGO
SAU
SUR
SLB
ZAR
TON
STP
GAB
TGO
DZA
BDI
LSO
NIC
BFA
PER
NER
COG
PNG
PRY
GUY
ZMB
OMN
BGD
SLV
BGR
ARE
SWZ
VEN
ETH
SEN
BEN
MWI
CMR
DMA
BOL
VCT
TTO
SYR
TUR
BWA
MDG
BHR
ATG
NAM HUN
EGY
ECU
MOZ
GMB
NPL
IDN
CIV
MRT
CAF
LAO
MLT
LKA
MLI
CRI
BLZ
PRT
DEU
BTN
URY
AUT
COL
CHE
HND
CHL
LUX
ISL
GRC
ZWE
MEX
CYP
LCA
GTM
BRB
BEL
KNA
MAR
BRA
PAK
MUS
SWE
PAN
FJI
AUS
KOR
KEN
MYS
ZAF
ITA
DNK
SYC
TUN
THA
FIN
PHL
VUT
JAM
FRA
HKG
PRI
IND
ESP
IRL
MAC
NZL
NLD
JOR
JPN
NOR
CHN
CAN
ISR
GBR
USA
20
UGA
DOM
Magnitude
40
SLE
DMA
LAO
0
IRN
ALB
KWT
GNB
HTI
NGA
SOMBDI
GHA
RWA
COM
SUR
ZAR
TON
STP
SAU
SLB
BFA
DZA
ARG
MDG
GAB
COG
PRY
PNG
NIC
AGO
BGD
BGR
LSO
OMN
VEN
TGO
SLV
NER
SWZ
VUT
PERBTN
CMR
ZMB
ARE
GUY
MWI
BEN
ATG
GMB
SYR
BWA
TTO
ETH
NPL
BOL
CAF
ZWE
CIV
BLZ
KNA
SEN
LCAHUN
URY
VCT
MOZ
MUS
BHR
MRT
CRI
ECU
MLT
CHL
MLI
TUR
COL
PAN
FJI
NAM
PRT
PHL
HND
ZAF
IDN
EGY
CHE
THA
AUT
DEU
GRC
CYP
ISL
KEN
HKG
BRA
PAK
KOR
BRB
LUX
FIN
MYS
LKA
MEX GTM
BEL
SWE
MAR
ITA
IND
SYC
TUN
DNK
AUS
PRI
JPN
FRA
JOR
CHN
ESP
NZL
JAM
NLD
MAC
NOR
ISR
IRL
GBR
U
SA
CAN
0
20
Magnitude
KIR
200
400
600
800
1000
0
500
HP filter 100
Correlation = 41%
LAO
50
50
HP filter 6.5
Correlation = 37%
KIR
200
400
600
Peakedness
800
20 30
Magnitude
BGD
10
DOM
TCD
HTI
SLE
SOM
UGA ALB
IRN
GHA
NGA
GNB
SUR
KWT
BGR
COM RWA
SAU
SLB
ZAR
GAB
BDI
BFA
PRY
VUT
PNG
TGO
LSO
COG
STP
DZA
NIC
BTN
TON
MOZ
AGO
PER SWZ
SLV
ATG
NER
GUY
ETH
OMN
ZMB
MWI
SYR
BWA
GMB
DMA
ARG
BEN
NPL
CIV
KNA
MDGBGD
CAF
CMR
ARE
VEN
MLT
SEN
EGY
ZWE
PRT
ZAF
ECU
NAM
HND
LCA
VCT
URY
AUT
THA
TTO
MLI
HUN
SYC
ISL
DEU
IDN
MEX
CHE
CRI
BOL
BLZ
LUX
PAN
BEL
COL
PHL
SWE
CHL
MRT
HKG
BHRMUS
FIN
DNK
CHN
GRC
KOR
MYS
ITA
MAR
BRB
BRA
TUR
FRA
FJI
GTM
CYP
IND
LKA
PRI
PAK
KEN
NLD
IRL
ESP
MAC
TUN
NZL
JPN
NOR
ISR JOR
AUS
GBR
CAN
JAM
USA
DOM
0
TCD
HTI
GNB SLE
IRN ALB
KWT
SOM
NGA UGA
RWA
COM
SUR
BDI GHA
SLBZAR
GAB
BFA
STP
COG
AGO
DZA
VUT
PNG
SAU
TON
LAO
ARG
NER
LSO
OMN
NIC SLV
MWI
BGR
BEN
MDG
TGO
VEN
SWZ
ZMB
GUY
PRY
SYR
BTN
CAF
DMA
CIV
ATG PER
GMB
ETH
ECU
ARE
BOL
MOZ
TTO
KNA
B
WA
CRI
BHR
CMR
COL
PAN
SEN
URY
BLZ
NPL
ZAF
ZWE
MLI
EGY
NAM
HND
FJI
VCT
MUS
BRA
LCA
TUR
CHL
GRCGTM
FIN
MLT
ISL
HUN
KOR
MEX
SYC
AUT
MRT
DEU
C
HE
KEN
PRT
LUX
SWE
IDN
PHL
LKA
JOR
BRB
MYS
PAK
ITA
CHN
IND
NZL
ESP
PRI
BEL
MAR
AUS
FRA
JPN
DNK
ISR
NOR
TUN
CYP
NLD
THA
IRL
MAC
GBR
JAM
HKG
CAN
USA
40
KIR
40
30
Magnitude
20
10
1500
Peakedness
Peakedness
0
1000
DOM
1000
0
500
1000
1500
Peakedness
8
Figure 4. Correlation between measures of asymmetry and of kurtosis, by
reference value.
Rolling mixed trend
1500
UGA
DOM
LAO
DMA
TCD
-100
0
100
200
1000
GHA
BGD
MDG HUN CMR
LUX
CHE
LCA
GTM
SLE
MEX
BTN
HTI
COL
MUS
IRL
PER
BWA
VEN
CRI
VUT
ISLTUR
DEU
KWT ARG
IDNTTO
IRN
DNK
RWA
MRT
KOR
SEN
DZA
ITA
EGY
CAF
ARE
ATG
ALB
LKA
ZAR
ECU OMN
GUY
NAM
BOL
BEL
AUT
JPN
ZAF
PRY
KNA
MAR
ISR
SWE
SYC
NICBGR
JOR
COM
BFA
IND
NPL
PAK
SWZ
SLV
JAM
BRB
CAN
KIR
ZWE
ZMB
CYP
VCT
BEN
MOZ
TON
COG
HND
NER
PRT
FRA
THA
BDI
SLB
KEN
GAB
MYS
NOR
PHL
MLI
AGO
ETH
BLZ
TGO
PRI
BHR
USA
PNG
GRC
SYR
CIV
NZL
SUR
BRA
MWI
CHL
ESP
STP
AUS
URY
GMB
LSO
CHN
NLD
HKG
TUN
FIN
MLT
GNB
MAC
FJI
SOM
SAU
GBR
PAN
NGA
500
Peakedness
DOM
HUN
NAM
RWA
LKA
UGA
CHE
TUR
COL
GHA
ATG
BHR
BEL
ARG
MEX
DZA
BRB
LUX
IRN KIR
ZAR
ZMB
SEN
FRA
DNK
DEU
ZWE
MDG
AUT
PER
PHL
JOR
GMB
IRL
CAF
ITA
AUS BOL
JAM
SWZ
CHL
ZAFESP
ZAF
CMR
OMN
KWT
ESP
FJI
GRC
COG
KEN
ISLIND
ISL
SYR
IND
SLV
NLD
MRT
VEN
GUY
PRT
MLT
ARE
PRI
ECU
BFA
SLE
BWA
PAN
SLB
SUR
TCD
ALB
GAB
LSO
SWE
NER
SAU
MUS
BDI
TTO
NGA
FIN
URY
HKG
ETH
PAK
BGD
CHN
MLI
MWI
EGY
PRY
JPN
BRA
THA
CRI
NOR
CAN
MOZ
LAOBLZ
HND
HTI
AGOBGR
KOR
TGO
USA
GNB
NIC
DMA
STP
SOM
CIV
VCTISR
TUN
GBR
BEN
MAR
GTM
KNA
B
BTN
TN
COM
MYS
NZL
PNG
SYC
MAC
TON
IDN
NPL
LCA
VUT
CYP
0
800 1000
600
200
400
Peakedness
Global mixed trend
300
-200
-100
0
Asymmetry
0
Asymmetry
100
KIR
1500
LAO
1000
Peakedness
MDG
COL
ECU
MUS
JOR
COM
GHA
SLV PERVUT
SYC
ISR
KEN
LKA
BDI
ZAR
NIC RWA
ALBMEX
ATG
SLE
BHR
NZL
ARG
HND
IDN
SLB
VEN
HUN
GUY
KOR
GTM
EGY
MYS TUR
IND
MOZ
MLI
BWA
BFA
OMN
CYP
BLZ
TCD
BEN
MAR
CRI
BRB
SUR
ZMB
IRN
BGR
AGO
TON
BTN
HKG
CHE
LAO
MAC
UGAARE
UGA
LSO
BOL
MWI
ARE
GBR
GRC
JAM
CHL
ISL
CIV
URY
DNK
PRY
ETH
GNB
PHL
KNA
NAM
MRT
COG
USA
SYR
MLT
TGO
DMA
BEL
PRI
ZWE
THA
SWE
CAN
STP
PNG
GAB
NER
SOM
SEN
VCT
CAF
AUT
LUX
LCA
CMR
CHN
FIN
ZAF
DZA
FRA
JPN
DEU
ITA
PAK
BRA
PAN
TTO
PRT
NPL
AUS
GMB
TUN
FJI
ESP
NOR
SAU
IRL
NGA
NLD
500
HTI
-100
300
DOM
KWT
HTI
MUS
SWZ BGD
JOR VUT
MDG
GHA
RWA
BHR
IRN
CRI
SYC
MLT
PER
TCD
ECU
ISR
COL
BRB
LUXKNA
TON
HUN
VEN
MAC
GBR
ALB
IND
SLV
EGY
PRI
BDI
GRC
NIC
ARG
COM
THA
CHE
ZAR
BGR
ARE
SLE
TUN
BEL
FRA
ATG
CYP
JAM
LKA
LCA
GUY
IDN
HND
SUR
CMR
LSO
MAR
OMN
NZL
AUT
ITA
BWA
BTN
HKG
URY
STP
MRT
BLZ
DEU
AGO
SLB
PHL
CHN
NLD
DNK
ISL
CIV
MWI
ZMB
MOZ
KOR
NPL
BEN
PAN
ETH
PNG
ZAF
AUS
GTM
NOR
KEN
PRT
JPN
KIR
DMA
ESP
GNB
NAM
NGA
MLI
SYR
TUR
CAN
VCT
BFA
GAB
SAU
BOL
MEX
PRY
COG
CHL
USA
PAK
TGO
SEN
MYS
FJI
NER
SWE
ZWE
DZA
UGA
GMB
BRA
TTO
CAF
FIN
IRL
SOM
0
Peakedness
200 400 600 800 1000
DOM
BGD
-200
200
HP filter 100
HP filter 6.5
KWT
SWZ
100
Asymmetry
200
-200
-100
0
100
200
300
Asymmetry
9