Exchange Rate and Oil Prices

7/29/2019 Exchange Rate and Oil Prices

1/37Electronic copy available at: http://ssrn.com/abstract=1746318

Exchange Rates and Oil Prices: A Multivariate Stochastic

Volatility Analysis

Minh Vo

Metropolitan State University

1501 Hennepin Ave. M2220

Minneapolis, MN 55403, U.S.A.

([email protected])

Liang Ding

Macalester College

1600 Grand Avenue

St. Paul, MN 55105, U.S.A.

([email protected])

Abstract

In contrast with the large literature that studies the interactions between the oil and the foreign

exchange (FX) markets at the return level, this paper examines their relationship at the risk level. We

employ the multivariate stochastic volatility (MSV) and the multivariate conditional correlation GARCH

(CC-MGARCH) framework to investigate the volatility interactions between the two in an attempt to

extract information intertwined in both markets for risk prediction. We oer three major ndings. First,

the volatility in each market is very persistent. It varies over time in a predictable manner, conditioned

on the past information. Second, the volatility in the oil market Granger-causes the volatility in theFX markets but not the other way around. Thus, including the oil market into the information set will

improve the FX volatility forecast. Finally, the MSV models outperform the CC-MGARCH counterparts

in forecasting FX volatility.

Keywords: Oil price risk; Exchange rate risk; Multivariate stochastic volatility; Multivariate GARCH;

Volatility forecast

Corresponding author, phone: 612-659-7305

1



1 Introduction

It is well-known that oil prices and the U.S. dollar exchange rates are highly correlated. Given the fact that

oil is quoted in U.S. dollars, it is natural to hypothesize that exchange rates drive oil prices. More specically,

other things equal, when the U.S. dollar depreciates, oil-exporting countries would raise oil prices in order

to stabilize the purchasing power of their (U.S. dollar) export revenues in terms of their (predominately)

euro-denominated imports. This is equivalent to a reduction in supply or a leftward shift in the supply curve.

On the demand side, the U.S. dollar depreciation makes oil less expensive for consumers in other countries

(in local currency), thereby increasing their crude oil demand. Both eects, the reduction in supply and

the increase in demand, cause an increase in oil prices denominated in U.S. dollars. The exchange-rate-to-

oil-price causality relationship is supported by the empirical evidence found in Zhang, Fan, Tsai, and Wei

(2008), Krichene (2005) and Youse and Wirjanto (2004).

From the other perspective, exchange rates are believed to be determined by expected future fundamental

conditions, among which oil is surely an important factor. Increasing oil prices lead to stronger economies

for oil-exporters and higher production costs for oil-importers, hence it would cause the appreciation of oil-

exporter currencies relative to those of oil-importers. So, it is likely that the causality runs from oil prices to

the exchange rate. Benassy-Querea, Mignonb, and Penot (2007), Coudert, Mignon, and Penot (2007), Chen

and Chen (2007), Ayadi (2005), Chaudhuri and Daniel (1998) and Krugman (1984) all provide evidence

supporting this view.

These studies, despite their mixed implications, tend to suggest that oil prices and exchange rates prob-

ably both contain information that can aect each other. Accordingly, Chen, Rogo, and Rossi (2008) and

Groen and Pesenti (2010) use exchange rates to obtain a better forecast of oil (and other commodities) prices,

while Amano and Norden (1998) improve the exchange rate forecast by including oil price in the model.

The current literature that examines the relationship between oil price and exchange rate, as cited above,

mainly focuses on their returns. As noted by Clark (1973), Tauchen and Pitts (1983), and Ross (1989), the

volatility of an asset is also related to the rate of information ow across interacted markets. So the link

between the oil and the FX markets should appear not only in return but also in volatility. Examining the

volatility interaction between exchange rates and oil prices can shed light on the direction of the causality

relationship from a new perspective. Furthermore, if a signicant connection does exist, extracting and using

the information intertwined in both markets would improve prediction of exchange rate and oil risks, which

are critical in many areas of modern nance.Instead of focusing on the relationship between exchange rate and oil returns, which many papers cited

above have investigated, this paper rst examines how the oil and the FX markets interact on the risk level.

Second, the paper attempts to extract information intertwined in the two markets, if detected, for a better

forecast of the exchange rate and oil volatility.

Based on the preliminary analysis of the data, we posit a bivariate model of vector of autoregression

VAR(5) with stochastic volatility for the joint processes governing the returns of various exchange rates and

2



the oil prices. We model the stochastic volatility using both the multivariate stochastic volatility (MSV)

and the conditional correlation multivariate GARCH (CC-MGARCH) models. We t two variants of the

models: the constant conditional correlation and the dynamic conditional correlation to identify the better

one for the data. For comprehensive discussion of the MSV and CC-MGARCH, the reader is referred to

Asai, McAleer, and Yu (2006) and Bauwens, Laurent, and Rombouts (2006). To estimate the MSV models,we use the Bayesian Markov chain Monte Carlo (MCMC) method by Jacquier, Polson, and Rossi (1994) and

Kim, Shephard, and Chib (1998). For the CC-MGARCH models, we use the maximum likelihood methods

proposed by Bollerslev (1990) and Engle (2002).

On the return level, our empirical results show that the increase in oil prices Granger-causes the oil

exporting (importing) currencies to appreciate (depreciate), which is an intuitive result. On the contrary, we

did not nd consistently robust and signicant evidence showing that exchange rates Granger-cause oil prices

to change. With regard to volatility, our study oers three major ndings. First, the daily volatility in each

market is very persistent. It varies over time in a predictable manner, conditioned on the past information.

Second, the volatility in the oil market Granger-causes the volatility in FX markets but not the other way

around. In other words, innovations that hit the oil market also have some impact on the volatility of FX

market. Thus, including the oil market into the information set will improve the FX volatility forecast.

Third, the MSV models outperform the MGARCH counterparts in tting the data and forecasting exchange

rate volatility.

Overall, these results suggest that the causality relationship is more likely to run from oil markets to

FX markets. The possible mechanisms that exchange rates aect oil prices, such as the purchasing power

channel and the local price channel noted above, are based on supply and demand in the oil market, while the

mechanism of the opposite direction, such as the currency market expectation channel, is through markettrading behavior based on expectations of market participants. Oil prices and exchange rates, although

considered by many to be fundamental macro variables, are both asset prices that are determined mainly

by speculation-initiated transactions in the nancial markets. So the mechanisms based on the nancial

markets information expectation channel rather than the goods markets demand and supply framework is

more likely to dominate.

The remainder of the paper is organized as follows. Section 2 describes the data set and conducts a

preliminary analysis of the data. Section 3 discusses the models. Section 4 explains estimation methodology.

Section 5 presents estimation results. Section 6 checks the models in terms of goodness-of-t and evaluates

their forecast power, and Section 7 concludes the paper.

2 Data and Preliminary Analysis

The data set used in this study consists of a daily oil spot price time series and ve daily time series of

exchange rates against the U.S. dollar including the Canadian dollar (CAD), the Norwegian krone (NOK),

3


4/37

the Euro (EUR), the Indian rupee (INR), and the U.S. dollar trade weighted index. The Canadian dollar

and Norwegian krone are chosen to represent the exchange rates of oil exporting countries. The Euro and

the Indian rupee are to represent developed and developing oil consumers. The dollar index provides more

general sense to the results. Other major oil exporters (such as the Middle East countries) and importers

(such as China) are not included because their exchange rates are either pegged to the U.S. dollar or strictlymanaged. All series span from July 28, 2005 to July 28, 2009 for a total of 1; 000 observations. The daily

oil spot price time series is based on the West Texas Intermediate (WTI) crude oil. It is obtained from the

historical database of the U.S. Department of Energy. The daily exchange rate data are extracted from the

Federal Reserve Bank of St. Louis website. Despite their dierent quoting habits, all the exchange rates are

converted to foreign currency per dollar. The daily return rt, in percentage, for each series pt is approximated

by rt = 100[ln(pt) ln (pt1)].

Table 1 presents a wide range of descriptive statistics for all time series. All series have small mean and

standard deviations that are much greater than the mean in absolute value, indicating that the mean is

not signicantly dierent from zero. This is consistent with common knowledge that nancial time series

at this frequency usually follow a random walk. Except USD/INR, other exchange rate series have negative

skewness. The excess kurtosis for each is signicantly positive, indicating that they have heavy tails relative to

the normal distribution, which is also typical in these nancial data. Both Kolmogorov-Smirnov and Jarque-

Bera tests reject the null hypothesis that the return distributions are normal at 5% level of signicance.

Ljung-Box portmanteau tests on return and squared return series up to 6 and 12 lags indicate a high serial

correlation in the rst and second moments. The high autocorrelation in the second moment may be due

to changing conditional volatility over time. The ARCH tests at 6 and 12 lags reject the null hypothesis of

homoscedasticity in the data at 5% signicance level. Thus, the GARCH and SV framework is appropriateto model the volatility of these time series.

[Insert Table 1 here]

Figures 1 and 2 graph the return time series and their distributions. We observe that for all series, the

return displays volatility clustering, another typical feature for high frequency nancial data. That is to say,

large changes tend to follow large changes, and small changes tend to follow small changes. However, the sign

of the change from one period to the next is unpredictable. The QQ-plots against the normal distribution

show that the distribution has heavier tail than normal.

[Insert Figure 1 here]


In short, the preliminary analysis shows that the data exhibit heavy tails, autocorrelation and het-

eroscedasticity. This suggests the importance of using the stochastic volatility framework to model condi-

tional volatility of return in all series.

4


5/37

3 The Model

Based on the preliminary analysis in the previous section and using the optimal lag-length algorithm with

the Akaike information criterion (AIC), we posit the bivariate V AR (5) with stochastic volatility models

for the joint processes governing the exchange rates and the oil returns. For comparison, we use both the

bivariate SV and the bivariate GARCH(1; 1) to model the joint volatility process. Two variants of the

multivariate volatility models, the constant conditional correlation and the dynamic conditional correlation,

are used to t the data. This section discusses the model and the estimation methodology.

Let rt =

ret rot

0

be the vector of returns of exchange rate and oil at time t (rate of change in

log-prices between time t1 and time t). rt is modeled as a vector process consisting of a deterministic part

mt and a stochastic part et:

rt = mt+et: (1)

The deterministic part mt is specied as a vector autoregressive process of order ve V AR(5):

mt = C +5X

k=1

Bkrtk;

where C =h

ce co

i0

and Bk is a (2 2) matrix with fBkgij = bijk for i; j = e; o. The subscripts e and

o stand for exchange rate and oil, respectively. The stochastic part et =h

eet eot

i0

involves the bivariate

stochastic volatility element of the model and depends on the model being used.

3.1 The Multivariate Stochastic Volatility Model (MSV)

The MSV model can be specied as follows:

et = tt; (2)

where, t, given t, is bivariate and normally distributed with mean E(ztjt) = 021 and variance

var (tjt) = Zt =

24 1 t

t 1

35 :

The correlation coecient between eet and eot , t, can be either constant or time-varying, depending on the

model. When t is a constant, we have the constant conditional correlation MSV (CCC-MSV) model. When

it is time-varying, we have the dynamic conditional correlation (DCC-MSV) model. t is a (2 2) diagonal

matrix of standard deviation with the following form:

t =

24 exp

het

2

0

0 exphot

2

35 ;

where het ; hot are conditional log-variances at time t of r

et , r

ot , respectively.

5


6/37

3.1.1 The Constant Conditional Correlation MSV Model

The V AR (5) model with constant conditional correlation multivariate stochastic volatility (CCC-MSV) can

be specied as follows:

rt = C +5X

k=1

Bkrtk + tt; (3)

tjt N

0@021;

24 1

1

351A (4)

ht+1 = + (ht ) + t; (5)

where ht =h

het hot

i0

is the vector of log-variances of ret and rot , =

he o

i0

is the unconditional

mean vector of ht. =

ij

; for i; j = e; o, represents the persistence and interaction between markets.

The error term t =h

et ot

i0

in the volatility equation is a bivariate normal random variable, t

N

021;diag

2e; 2o

:

According to (3)(5) , conditioned on the conditional mean, C+5P

k=1

Bkrtk, the return series of exchange

rate and oil are jointly normally distributed with variance-covariance matrix tZt0

t: The correlation between

the two series are assumed to be a constant . Equation (5) models the time-varying cross-dependent

volatilities of the two series. In this equation, the diagonal parameters of the matrix (ee and oo) capture

the persistence of the volatility in each market while the o-diagonal parameters, eo and oe, measure the

dependence of the conditional volatility of the FX market on the oil market and vice versa. If eo (oe) is

dierent from zero, oil (FX) volatility may Granger-cause FX (oil) volatility.

3.1.2 The Dynamic Conditional Correlation MSV

When the correlation between the two returns is allowed to vary over time, we get the dynamic conditional

correlation MSV model (DCC-MSV). The DCC-MSV model with V AR (5) in the mean has the following

form:

rt = C +5X

k=1

Bkrtk + tt; (6)

ht+1 = + (ht ) + t;

tjt N

0@021;

24 1 t

t 1

351A

t =exp(qt) 1

exp(qt) + 1

qt = ! + (qt1 !) + qzt; ztiid N(0; 1) :

6


7/37

This model captures the dynamic correlation between the two markets. To constrain t to the interval

[1; 1], we use the Fisher transformation as suggested by Christodoulakis and Satchell (2002), in which t

is a function of qt which follows an AR (1) stochastic process.

3.2 The Multivariate GARCH Model with Conditional Correlations

In addition to MSV, we also use the MGARCH model to t our data. The bivariate GARCH(1; 1) model

of exchange rate and oil returns has the following form:

rt = mt + et;

et = H1=2t t;

where H1=2t is a 2 2 positive denite matrix and t is a 2 1 random vector with the following rst and

second moments:

E(t) = 021;

V ar (t) = I2;

where I2 is the identity matrix of order 2.

Thus, given the information at time t 1, the conditional variance-covariance matrix of rt is:

V art1 (rt) = V ar (

et) =

H1=2

t V art1 (t)H1=2

t0

=H

t:

The specications of Ht depend on the specic MGARCH-type model. We examine the conditional

correlation multivariate GARCH models in this paper.

3.2.1 The Constant Conditional Correlation Multivariate GARCH (CCC-MGARCH)

The constant conditional correlation multivariate GARCH(1; 1) model of Bollerslev (1990) and Jeantheau

(1998) has the following form:

Ht

= DtRD

t; (7)

Dt = diag

h1=2e;t ; h

1=2o;t

;

where he;t and ho;t can be considered as any univariate GARCH model of the two variables. R is their

constant correlation matrix which is a symmetric positive denite matrix with 1s on the diagonal.

7


8/37

3.2.2 The Dynamic Conditional Correlation Multivariate GARCH (DCC-MGARCH)

The DCC-MGARCH model of Engle (2002) is similar to the CCC-MGARCH model but it allows the cor-

relation matrix R in (7) to vary over time. Specically, Rt can be specied as follows for the bivariate

case:

Rt = (Qt I2)1=2

Qt (Qt I2)1=2

where is the Hadamard product of two identically sized matrices, computed by element-by-element mul-

tiplication, I2 is the identity matrix of order 2, Qt is a 2 2 symmetric positive denite matrix, given

by

Qt = (1 ) Q + et1e0

t1 + Qt1;

where Q is the unconditional variance-covariance matrix ofet, and and are non-negative scalar parameters

satisfying the stationary condition: + < 1:

4 Estimation Methodology

4.1 MSV Models

4.1.1 The Algorithm

Estimating SV-type models is a challenge since they do not have closed-form likelihood functions due to

the latent structure of the variance. Several estimation methods have been proposed in literature, such

as, the quasi maximum likelihood (QML) of Harvey, Ruiz, and Shephard (1994), the generalized method

of moments (GMM) by Andersen and Sorensen (1996), Melino and Turnbull (1990), Sorensen (2000), the

ecient method of moments by Gallant, Hsieh, and Tauchen (1997), the simulated maximum likelihood by

Danielsson (1994), Durbin and Koopman (1997), and Sandmann and Koopman (1998), and the Bayesian

MCMC methods by Jacquier, Polson, and Rossi (1994), and Kim, Shephard, and Chib (1998). However,

Jacquier, Polson, and Rossi (1994) nd that the MCMC method is superior to both the QML and the GMM.

Furthermore, while most classical methods rely on asymptotic arguments to make inference, MCMC uses

exact posterior distributions of the parameters. This will yield more accurate results. In this paper, we use

the Bayesian MCMC for model estimation. For a comprehensive discussion of Bayesian inference and the

MCMC method, the reader is referred to Geweke (2005), Gammerman (1997), and Johannes and Polson

(2006).

The basic idea of Bayesian estimation lies on the Bayes theorem, which states that the posterior joint

distribution function of the parameters is proportional to the product of their prior distribution function and

the likelihood function of the data. In particular, let be the vector of parameters to be estimated, Ht be

the vector of latent log volatility, and rt be the vector of observed data. Bayesian inference is then based on

8


9/37

the joint posterior distribution of unobservables

Ht

given the data rt. Let f(:) be the probability

density function. Using the Bayes theorem, we get:

f(; Htjrt) _ f(rtj; Ht) f(Htj) f() :

In a sense, the posterior distribution function is a balance between the prior belief, f(Htj) f(), and the

likelihood of the data, L (; Htjrt) f(rtj; Ht). Inference is then conducted by evaluating its moments.

For simple and low-dimensional problems, the posterior distribution function may have tractable forms and

so evaluating its moments is a simple task. However, in complex and higher-dimensional problems, such

as the MSV model in this paper, the posterior distribution functions often do not have familiar functional

forms and we have to rely on simulation to make inferences.

The Markov chain Monte Carlo (MCMC) is a computational method to generate random samples from

a given distribution. It was rst introduced by Metropolis et al. (1953) and subsequently generalized by

Hastings (1970). It is based on the construction of a Markov chain in the parameter space. Under some mild

regularity conditions (see Tierney 1994) the chain asymptotically converges to the joint posterior distribution.

Thus, the realized value of the chain can be used to make inferences about the joint posterior distribution.

An MCMC algorithm called Gibbs sampler, introduced by Geman and Geman (1984), is based on the

Cliord-Hammersley theorem which states that a joint distribution can be characterized by its complete

conditional distributions. It is the natural choice in MCMC sampling when the conditionals from which

samples are drawn can be specied. This paper uses Gibbs sampler to generate Markov chains.

4.1.2 Estimation

The CCC-MSV model in (3) (5) can be rewritten elementwise as follows:

ret = ce +5X

i=1

beei reti +

5Xi=1

beoi rot1 + e

et ; (8)

rot = co +5X

i=1

boei reti +

5Xi=1

booi roti + e

ot ; (9)

eet = exp

het2

et ; (10)

eot = exphot

2

ot ; (11)

= cov (et ; ot ) ; (12)

het+1 = e + ee (het e) + eo (h

ot o) +

et ;

etiid N

0; 2e

; (13)

hot+1 = o + oe (het e) + oo (h

ot o) +

ot ;

otiid N

0; 2o

; (14)

To estimate this system, we rst use the maximum likelihood method to estimate the parameters C and

B in the mean equations (8)(9), then extract the residuals et. In the second step, we employ the Bayesian

9


10/37

MCMC method with Gibbs sampling algorithm to estimate parameters in (10) (14) : To ensure that ht is

stationary, we constrain the persistent coecients ee and oo to the interval (1; 1) by setting ii = 2

ii1

for i = e; o, where ii has beta prior.

In the same manner, the DCC-MSV model (equation 6) can be written elementwise as follows:

ret = ce +5X

i=1

beei reti +

5Xi=1

beoi rot1 + e

et ; (15)

rot = co +5X

i=1

boei reti +

5Xi=1

booi roti + e

ot ;

eet = exp

het2

et

eot = exp

hot2

ot

t = cov (e

t ;

o

t ) =

exp(qt) 1

exp(qt) + 1 ;

qt = ! + (qt1 !) + qzt; ztiid N(0; 1) ;


ot o) +

et ;

etiid N

0; 2e

;

hot+1 = o + oe (het s) + oo (h

ot o) +

ot ;

otiid N

0; 2o

:

The estimation strategy used in the constant correlation MSV model is also applied to this model.

4.2 CC-MGARCH Models

We use maximum likelihood to estimate the CC-MGARCH models. Like the MSV models, we rst estimateV AR (5) models for the mean and extract the residuals et for volatility estimation. Let Ft1 be the eld

generated by all the available information up to time t 1, then:

etjFt1 N(0; Ht) :

4.2.1 CCC-MGARCH Model

Given the CCC-MGARCH model:

etjFt1 N(0; Ht)

Ht = DtRDt;

10


11/37

let be the vector of all parameters in the model, the log likelihood function can be written as

L () = 1

2

TXt=1

N ln(2) + ln jHtj + e

0

tH1t et

= 1

2

T

Xt=1

N ln(2) + ln jDtRDtj + e0t (DtRDt)1 et=

1

2

TXt=1

N ln(2) + ln jRj + 2ln jDtj + z

0

tR1zt

where N is the number of time series, T is the sample size and zt = D1t et is the standardized residual.

4.2.2 DCC-MGARCH Model

Given the DCC-MGARCH model:

etjzt1 N(0; Ht) ;

Ht = DtRDt:

Let and be the vectors of parameters in Dt and Rt, respectively. The log likelihood for this estimator

can be written as:

L (;) = 1

2

TXt=1

N ln(2) + ln jHtj + e

0

tH1t et

(16)

= 1

2

TXt=1

N ln(2) + ln jDtRtDtj + e

0

tD1t R

1t D

1t et

= 1

2

TXt=1

N ln(2) + 2ln jDtj + ln jRtj + z

0

tR1t zt

= 1

2

TXt=1

N ln(2) + 2ln jDtj + e

0

tD1t D

1t et z

0

tzt + ln jRtj + z0

tR1t zt

;

where N is the number of time series, T is the sample size and zt = D1t et is the standardized residual.

L (;) can be rewritten as a sum of a volatility component Lv () and a correlation component Lc (;):

L (;) = Lv () + Lc (; )

where

Lv () = 1

2

TXt=1

N ln(2) + 2ln jDtj + e

0

tD2t et

is the sum of individual GARCH likelihoods, and

Lc (;) = 1

2

TXt=1

ln jRtj + z

0

tR1t zt z

0

tzt

is the likelihood for correlations.

11


12/37

We use two-step estimation methodology proposed by Engle (2002). In the rst step, we estimate

= arg max [Lv ()]

and then we take as given in the second step to estimate :

= arg maxh

Lc

;

i

5 Empirical Results

5.1 Mean Estimates

Tables 2 and 3 report the results of estimating the V AR for the mean. We use the optimal lag length of

5 as determined by the AIC. For the case of the USD/CAD (Table 2) the coecients of lags 1 and 3 of oil

returns are small but negative at 5% level of signicance in the FX equation, indicating that oil prices have

some positive but small impact on the CAD.1 This could be due to the fact that Canada is one of the major

oil exporting countries. Other things equal, an increase in oil prices can be considered as a positive shock

to the Canadian economic fundamentals, which would therefore cause the Canadian dollar to appreciate.

This is also the case for Norway, another major oil exporting country, albeit at dierent lags. In a similar

argument, the increase in oil prices would raise production costs for oil importers. This is certainly a negative

fundamental shock for the biggest oil consumers in the world the U.S., which causes the USD to depreciate.

This is reected in the case of the USD index in the rst and second lags of oil returns and the rst lag for

the USD/EUR.



The impact, however, is insignicant for the USD/INR. Although the Indian rupee is market determined,

the Reserve Bank of India (the central bank of India) trades actively in the USD/INR currency market to

impact the eective exchange rates. Such managed oat rate might reect the policy makers goals more

than the markets interpretation of the fundamental news such as oil price shocks.

In the other direction, we see that the coecient on the third lag of USD/CAD in the oil equation is

signicant, as is the case for the USD index and USD/INR. The coecients for the USD/NOK and the

USD/EUR however are insignicant. Overall, the causality relationship from exchange rate to oil price is

not as signicant and robust as the relationship in the opposite direction.

The ARCH tests of Engle (1982) on residuals at 1, 6; and 12 lags reject the null hypothesis of homoscedas-

ticity for all cases. Thus, the MSV and MGARCH are appropriate for modeling volatility.

1 A decrease in the USD/CAD exchange rate implies the CAD appreciates relative to the USD.

12


13/37

5.2 Volatility Estimates

5.2.1 CCC-MSV Model

Table 4 reports the estimates of the following CCC-MSV model:

eet = exp

het2

et ;

eot = exp

hot2

ot ;

= cov (et ; ot )


ot o) +

et ;

etiid N

0; 2e

;

hot+1 = o + oe (het s) + oo (h

ot o) +

ot ;

otiid N

0; 2o

:


We observe that both exchange rate and oil returns are very persistent. The persistent coecient for

exchange rates ee ranges from :8439 for USD/INR to :9728 for USD/CAD. For oil, oo varies from :9005

to :9855. These results are consistent with the fact that exchange rate and oil price volatilities are often

clustered.

A majority of the transmission coecients (eo and oe) are signicant but small (the 95% condence

interval does not contain 0.) The volatility transmission coecient from the oil markets to the FX markets

eo is positive and signicant in all cases, suggesting that shocks to volatility of oil markets cause the volatility

in the FX market to increase at a later date. eo is the largest for the USD/EUR and the USD/INR. Otherthings equal, a shock that increases oil price volatility by 1% will increase the volatilities of USD/EUR

and USD/INR by approximately :1% and :14%, respectively. Intuitively, oil shocks increase uncertainty of

economic fundamentals which causes exchange rates to be more volatile.

For the transmission coecient from FX markets to oil markets, the result is mixed. oe is not signicantly

dierent from zero for the USD index, the USD/INR and the USD/EUR at 5% signicance level. Thus, it

is unclear whether shocks to volatility of FX market cause volatility in oil markets to rise.

Except for USD/INR, the contemporaneous correlation between oil and exchange rates is negative and

quite large in absolute value. This result is consistent with empirical ndings in other studies that dollar

value and oil price are overall inversely correlated. Figures 3 and 4 show the posterior densities of parameters

estimated in the model for the cases of the USD/CAD and the USD index.



Figures 5 and 6 show the volatility estimates of exchange rates and oil. To the naked eye it seems that

the estimates reect the variations of the residuals.

13


14/37



5.2.2 DCC-MSV Model

Table 5 reports the estimates of the DCC-MSV model:

eet = exp

het2

et ;

eot = exp

hot2

ot ;

t = cov (et ;

ot ) =

exp(qt) 1

exp(qt) + 1;

qt = ! + (qt1 !) + qzt; ztiid N(0; 1) ;


ot o) +

et ;

etiid N

0; 2e

;

hot+1 = o + oe (het e) + oo (h

ot o) +

ot ;

otiid N

0; 2o

:


Like the estimates of the CCC-MSV model, the persistent coecients (ee and oo) are quite close to

one, except the case of USD/NOK where ee drops from :9139 in the CCC-MSV to :669 in the DCC-MSV

model. The transmission coecient eo are all found to be signicantly dierent from zero. Except for the

USD index, this coecient signicantly increases compared to CCC-MSV model. Like the CCC-MSV case,

the transmission coecient from FX markets to oil market, oe; is signicant in most cases except for the

USD/INR and the USD/CAD, suggesting exchange rate volatility also contains information that can aect

oil market volatility in later dates.

We also observe that in all cases, the DIC (deviance information criterion) is smaller in the DCC-MSV

than the CCC-MSV, suggesting that the former ts the data better. Considering that regime switch and

structural breaks are often identied in time series of exchange rate and oil price, their relationship is very

likely time-varying so that DCC model can capture such a feature better. Nevertheless, which model is more

appropriate depends on its forecasting power. We will assess the forecasting performance of each model

later in the paper. Figures 7 and 8 show the posterior densities of parameters estimated for the cases of

USD/CAD and the USD index.



Figures 9 and 10 graph the estimated volatilities of all exchange rates and oil and their correlation

coecients for DCC-MSV model. As in the CCC-MSV model, we see that the estimated volatilities reect

14


15/37

quite well the variation of the residuals. Except for USD/INR, the correlation coecients are negative and

quite volatile, varying from around :1 to around :5. For USD/INR, it ranges from :2 to :4.



5.2.3 CCC-MGARCH Model

Table 6 reports the parameter estimates for the following CCC-MGARCH(1,1) model, written in elementwise

form:

ee;t =p

he;te;t;

eo;t =p

ho;to;t;

= cov (e;t

; o;t

)24 he;t

ho;t

35 =

24 c1

c2

35+

24 a11 a12

a21 a22

3524 e2e;t1

e2o;t1

35+

24 b11 b12

b21 b22

3524 he;t1

ho;t1

35 :


Parameters aii, bii, i = 1; 2 represent the persistence of the volatility, while aij , bij, i; j = 1; 2 and i 6= j;

are transmission coecients, representing the impact of volatility in one market on the other. We observe

that as in the MSV models, volatilities are very persistent (the sum aii + bii is close to unity), once again

conrming the clustered volatilities in these nancial time series.

Unlike the MSV models, the transmission coecients a12 and b12, from the oil market to the FX market,

are not signicantly dierent from zero for all cases, suggesting that volatility in the oil market does not have

signicant impacts on the FX market. However, the coecients a21 and b21, from the FX to the oil market

are signicant in most cases. a21 is signicant for CAN/USD, USD/EUR and USD/INR; b21 is signicant

for all but USD/INR. It seems that the MGARCH and MSV are quite inconsistent in terms of the direction

of the volatility causality. A further evaluation of the model selection later would help us to judge which

one is more reliable.

The estimated correlations between exchange rates and oil prices are comparable those in the CCC-MSV.

The pattern that rising oil price is usually associated with depreciation of the dollar seems to be robust toboth MSV and MGARCH frameworks.

5.2.4 DCC-MGARCH Model

Table 7 reports the estimates of the DCC-MGARCH(1,1) model. This model is similar to the CCC-

MGARCH(1,1), except that the coecient between et and ot is not a constant but time-varying. The

result is similar to that in the CCC-MGARCH model.

15


16/37


Figures 11 and 12 graph the dynamic correlations.



6 Comparing Models

6.1 Model Checking

In this section, we check the goodness-of-t of each model and compare them. To check the goodness-of-t,

we test whether the volatility in each market indicated by each model is sucient to explain the stylized facts,

such as heavy tail, volatility clustering, etc. In particular, we test if the residuals in the mean equations,

having been standardized by the corresponding volatility in the variance equations, are standard normal.Tables 8 and 9 present the test results.

Table 8 reports various statistics of the standardized residual for CCC-MSV and DCC-MSV models.

We observe that for all cases, the mean in each market is close to zero while the standard deviation is

close to one. Furthermore, the kurtosis for both markets in both models are close to 3, indicating that the

thick tail has been removed. We use both the Jarque-Bera and the Kolmogorov-Smirnov methods to test

for normality. In all cases, the Kolmogorov-Smirnov test cannot reject the null hypothesis of normality at

5% level of signicance. The results for the Jarque-Bera tests are mixed, however. For CCC-MSV, the test

rejects the null at 5% level of signicance for exchange rate in the cases of the USD index and the USD/EUR.

For DCC-MSV, it rejects the null for exchange rate in the USD index case. Despite that, in a majority of

cases, it does not reject the null hypothesis of normality. Thus, both CCC-MSV and DCC-MSV models do

quite well in modelling heteroscedasticity in the data.


To compare CCC-MSV and DCC-MSV, in terms of goodness-of-t, we use the deviance information

criterion (DIC) proposed by Spiegelhalter, Best, Carlin, and der Linde (2002) which is a Bayesian version

of the Akaike Information Criterion (AIC) (Akaike 1973) and closely related to the Bayesian (or Schwarz)

Information Criterion (BIC) (Schwarz 1978). Like the AIC and the BIC, it trades o the model adequacy,measured by the log-likelihood, against the model complexity, measured by the number of free parameters.

The smaller the DIC, the better the model. For a discussion of the use of the DIC to compare SV models,

the reader is referred to Berg, Myer, and Yu (2004) . We see that in all cases, the two models have similar

DICs, although the DCC-MSV model has slightly lower DIC than the CCC-MSV model; thus, it is hard

to tell which model is better for the data. Later in the paper, we will revisit the issue by comparing their

forecasting performance.

16


17/37

Table 9 reports similar statistics for CCC-MGARCH and DCC-MGARCH models. We observe that the

tail thickness has been reduced (kurtosis is close to 3); however, it is still thicker than in the cases of MSV

models. Jarque-Bera tests reject the null hypothesis of normality at 5% level of signicance in most cases.

Thus, it seems that MSV models outperform MGARCH counterparts in terms of goodness-of-t. This in

turn implies that the volatility causality detected by MSV should be more reliable than MGARCH.


Comparing DCC-MGARCH with CCC-MGARCH, in all cases, the value of log likelihood is much higher

in DCC-MGARCH than in CCC-MGARCH, suggesting that the DCC-MGARCH model better t the data

than the CCC-MGARCH.

6.2 Forecast Performance

To evaluate the forecasting power of a volatility model, we rst need realized volatility. There are a numberof ways in literature to obtain realized volatility (see, for example Merton 1980; Perry 1982; Akgiray 1989;

Ding, Granger, and Engle 1993.) In this paper, we use the approach of Merton (1980) and Perry (1982) by

simply using the square of daily return as a proxy of realized daily return.

To evaluate the forecast performance, we use two popular metrics: the root mean square error (RMSE)

and the mean absolute error (MAE). They are given by:

RMSE =

vuut

1

N

N

Xi=1

2i

2i 2

;

M AE =1

N

NXi=1

2i 2i ;

where 2i is the forecast volatility of date i indicated by the model, 2i is the realized volatility at date i.

N is the number of observations in the sample. The lower the metrics, the better is the model in terms of

forecast performance.

To conduct the forecast experiment, we use the estimates for each model in the previous section to

forecast volatilities for the next two weeks and calculate the two metrics. To see how multivariate models

perform compared to the univariate counterparts, we also include GARCH(1,1) and the univariate stochastic

volatility model in the experiment. Table 10 reports the results.


For exchange rates, we observe that both univariate and multivariate SV models signicantly outperform

the GARCH counterparts in all cases. Among them, the CCC-MSV is ranked number one in three cases,

USD/CAD, USD/NOK and USD index. DCC-MSV is ranked number one in the other two cases. However,

17


18/37

both RMSE and MAE metrics indicate that there is no signicant dierence between the two models. The

univariate SV is ranked number 3 in all cases. We also see that in most cases, multivariate GARCH models

outperform the univariate GARCH in forecasting FX volatility. For oil, the result is completely dierent,

and the univariate GARCH outperforms all others. Thus, oil volatility helps predict exchange rate volatility

but not the other way around. This result strongly suggests that their causality relationship runs from oilmarket to the FX market, not the opposite. This is consistent with the empirical result of the MSV models.

Recall potential mechanisms connecting exchange rate and oil price mentioned in the literature: From

exchange rate to oil price, purchasing power channel argues that the depreciation of the USD reduces

purchasing power of oil exporters so that they want to raise price for compensation. The local price channel

suggests that the U.S. dollar depreciation makes oil less expensive for consumers in non-U.S. dollar regions

(in local currency), thereby increasing their crude oil demand, which eventually causes adjustments in the

oil price denominated in U.S. dollars. From oil price to exchange rate, a possible mechanism is through the

currency market channel. The exchange rate is determined by expected future fundamental conditions of two

countries. Increasing oil prices lead to stronger economies of oil exporters, hence causing the appreciation

of their currencies. On the other hand, increasing oil price implies higher production costs for oil importers

and hence should cause the depreciation of their currencies.

Apparently, the mechanisms from exchange rates to oil prices mentioned above are based on supply

and demand in the oil market, while the mechanism of the opposite direction is through market trading

behavior based on expectations of market participants. Oil prices and exchange rates, though considered

by many to be fundamental macroeconomic variables, are both asset prices that are determined mainly by

speculation-initiated transactions in nancial markets. So the mechanisms based on supply and demand

in goods markets are probably not as strong as the mechanisms based on nancial markets informationexpectation channel. The empirical results found in this paper tends to imply this intuition.

7 Conclusion

This paper studies the possible connection between the oil market and the FX market. Instead of analyzing

the relationship of their returns which has been done extensively in the literature, we focus on the volatility

association of both markets in an attempt to extract information intertwined in the two for better risk

predictions. We model the volatility interactions with the multivariate stochastic volatility as well as the

multivariate GARCH framework, allowing the volatility in each market to Granger-cause that in the other.

We oer three major ndings. First, conditioned on the past information, the daily volatility in each market

is very persistent. Second, the volatility in the oil market Granger-causes the volatility in the FX market

but not the other way around. In other words, innovations that hit the oil market also have some impact on

the volatility of FX market and thus using such a dependence signicantly enhances the forecasting power

of the models. Third, the MSV models do a better job than the MGARCH counterparts in tting the data

18


19/37

and forecasting exchange rate volatility.

References

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N.

Petrov and F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory,

Budapest, pp. 267281. Akademiai Kiado.

Akgiray, V. (1989). Conditional heteroscedasticity in time series of stock returns: Evidence and forecast.

Journal of Business 62, 5580.

Amano, R. A. and S. Norden (1998). Oil prices and the rise and fall of the US real exchange rate. Journal

of International Money and Finance 17, 299316.

Andersen, T. and B. Sorensen (1996). GMM estimation of a stochastic volatility model: A Monte Carlo

study. Journal of Business and Economic Statistics 14, 329352.

Asai, M., M. McAleer, and J. Yu (2006). Multivariate stochastic volatility: A review. Econometric Re-

view 25, 145175.

Ayadi, F. O. (2005). Oil price uctuations and the Nigerian economy. OPEC Review 29, 199217.

Bauwens, L., S. Laurent, and J. V. K. Rombouts (2006). Multivariate GARCH models: A survey. Journal

of Applied Econometrics 21, 79109.

Benassy-Querea, A., V. Mignonb, and A. Penot (2007). China and the relationship between the oil price

and the dollar. Energy Policy 35, 57955805.

Berg, A., R. Myer, and J. Yu (2004). Deviance information criterion for comparing stochastic volatility

models. Journal of Business and Economic Statistics 22, 107120.

Bollerslev, T. (1990). Modeling the coherence in short-run nominal exchange rates: A multivariate gener-

alized ARCH model. Review of Economics and Statistics 72, 498505.

Chaudhuri, K. and B. C. Daniel (1998). Long-run equilibrium real exchange rates and oil prices. Economics

Letters 58, 231238.

Chen, S. S. and H. C. Chen (2007). Oil prices and real exchange rates. Energy Economics 29, 390404.

Chen, Y. C., K. Rogo, and B. Rossi (2008). Can exchange rates forecast commodity prices? NBER

Working Paper No. 13901 .

Christodoulakis, G. A. and S. E. Satchell (2002). Correlated ARCH (CorrARCH): Modelling the time-

varying conditional correlation between nancial asset returns. European Journal of Operational Re-

search 139, 351370.

19


20/37

Clark, P. (1973). A subordinate stochastic process model with nite variance for speculative prices. Econo-

metrica 41, 135155.

Coudert, V., V. Mignon, and A. Penot (2007). Oil price and the dollar. Energy Studies Review 15, 4865.

Danielsson, J. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood.

Journal of Econometrics 64, 375400.

Ding, Z., C. W. J. Granger, and R. F. Engle (1993). A long memory of stock returns and a new model.

Journal of Empirical Finance 1, 83106.

Durbin, J. and S. Koopman (1997). Monte Carlo maximum likelihood estimation for non-Gaussian state

space models. Biometrika 84, 669684.

Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autore-

gressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20(3),

339350.

Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K.

ination. Econometrica 50, 9871007.

Gallant, A. R., D. Hsieh, and G. Tauchen (1997). Estimation of stochastic volatility models with diagnos-

tics. Journal of Econometrics 81, 159192.

Gammerman, D. (1997). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chap-

man & Hall.

Geman, S. and D. Geman (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration

images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721741.

Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. Wiley & Sons.

Groen, J. J. J. and P. A. Pesenti (2010). Commodity prices, commodity currencies and global economic

developments. NBER Working Paper 15743.

Harvey, A. C., E. Ruiz, and N. Shephard (1994). Multivariate stochastic variance models. Review of

Economic Studies 61, 247264.

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications.

Biometrika 57(1), 97109.

Jacquier, E., N. G. Polson, and P. E. Rossi (1994). Bayesian analysis of stochastic volatility models.

Journal of Business and Economic Statistics 12, 371389.

Jeantheau, T. (1998). Strong consistency of estimators for multivariate ARCH models. Econometric The-

ory 14, 7086.

Johannes, M. and N. Polson (2006). MCMC methods for continuous-time nancial econometrics. In Y. At-

Sahalia and L. Hansen (Eds.), Handbook of Financial Econometrics. Elsevier.

20


21/37

Kim, S., N. Shephard, and S. Chib (1998). Stochastic volatility: Likelihood inference and comparison with

ARCH models. Review of Economic Studies 65, 363393.

Krichene, N. (2005). A simultaneous equations model for world crude oil and natural gas markets. IMF

Working Paper.

Krugman, P. R. (1984). Oil shocks and exchange rate dynamics. Frankel, J. A. (ed.). Exchange Rates and

International Macroeconomics. University of Chicago Press.

Melino, A. and S. M. Turnbull (1990). Pricing foreign currency options with with stochastic volatility.

Journal of Econometrics 45, 239265.

Merton, R. (1980). On estimating the expected return on the market: An explanatory investigation.

Journal of Financial Economics 8, 323361.

Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller (1953). Equations of

state calculations by fast computing machines. Journal of Chemical Physics 21 (6), 10871092.

Perry, P. (1982). The time-variance relationship of security returns: Implications for the return-generating

stochastic process. Journal of Finance 37, 857870.

Ross, S. (1989). Information and volatility: The no-arbitrage martingale approach to timing and resolution

irrelevancy. Journal of Finance 44, 117.

Sandmann, G. and S. J. Koopman (1998). Estimation of stochastic volatility models via Monte Carlo

maximum likelihood. Journal of Econometrics 87, 271301.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6, 461464.

Sorensen, M. (2000). Prediction-based estimating functions. Econometrics Journal 3, 123147.

Spiegelhalter, D. J., N. G. Best, B. P. Carlin, and A. V. der Linde (2002). Bayesian measures of model

complexity and t. Journal of the Royal Statistical Society 64, 583639.

Tauchen, G. and M. Pitts (1983). The price variability-volume relationship on speculative markets. Econo-

metrica 51, 485505.

Tierney, L. (1994). Markov chains for exploring posterior distributions. Annals of Statistics 22(4), 1701

1762.

Youse, A. and T. S. Wirjanto (2004). The empirical role of the exchange rate on the crude-oil price

formation. Energy Economics 26, 783799.

Zhang, Y. J., Y. Fan, H. T. Tsai, and Y. M. Wei (2008). Spillover eect of US dollar exchange rate on oil

prices. Journal of Policy Modeling 30, 97391.

21


22/37

-4

-2

0

2

4

Time

CAD/USD

2 00 6 2 00 7 2 00 8 2 00 9

-3 -2 -1 0 1 2 3

-4

-2

0

2

4

Theoretical Quantiles

SampleQuantiles

-4 - 2 0 2 4

0.0

0.2

0.4

0.6

0.8

Density

C A D / U S D

Nor mal

-6

-2

0

2

4

Time

NOK/USD

2 00 6 2 00 7 2 00 8 2 00 9

-3 -2 -1 0 1 2 3

-6

-2

0

2

4


SampleQuantiles

-6 - 4 - 2 0 2 4

0.0

0.2

0.4

0.6

Density

N O K / U S D

Nor mal

-4

-2

0

2

Time

EUR/USD

2 00 6 2 00 7 2 00 8 2 00 9

-3 -2 -1 0 1 2 3

-4

-2

0

2


SampleQuantiles

-4 -2 0 2

0.0

0.4

0.8

Density

E U R / U S D

Nor mal

Figure 1: Exchange rate returns and their distributions for CAD, NOK and EUR

-4

-2

0

2

4

Time

INR/USD

2 00 6 2 00 7 2 00 8 2 00 9

-3 -2 -1 0 1 2 3

-4

-2

0

2

4


SampleQuantiles

-4 - 2 0 2 4

0.0

0.4

0.8

1.2

Density INR/USDNor mal

-4

-2

0

1

2

Time

USD

Inde

x

2 00 6 2 00 7 2 00 8 2 00 9

-3 -2 -1 0 1 2 3

-4

-2

0

1

2


SampleQuantiles

-4 -3 -2 -1 0 1 2

0.0

0.4

0.8

Density

USD inde x

Nor mal

-10

0

5

15

Time

Oil

2 00 6 2 00 7 2 00 8 2 00 9

-3 -2 -1 0 1 2 3

-10

0

5

15


SampleQuantiles

-15 -5 0 5 10 15

0.0

0

0.0

5

0.1

0

0.1

5

Density Oil

Nor mal

Figure 2: Exchange rate returns and their distributions for INR, USD index and oil

22


23/37

-2.5 -2.0 -1.5 -1.0 -0.5

0.0

0.5

1.0

1.5

Density of e

e

Density

0. 0 0 .5 1. 0 1. 5 2. 0 2 .5

0.0

0.5

1.0

1.5

Density of o

o

Density

0.90 0.92 0.94 0.96 0.98 1.00

0

5

10

15

20

25

Density of ee

ee

Density

0 .8 5 0 .9 0 0 .9 5 1 .0 0

0

5

10

15

20

Density of oo

oo

Density

-0.02 0.00 0.02 0.04 0.06 0.08

0

5

10

15

20

25

30

35

Density of eo

eo

Density

0 .0 0 0 .0 5 0 .1 0 0 .1 5

0

5

10

15

20

Density of oe

oe

Density

-0. 40 -0 .3 0

0

2

4

6

8

10

12

14

Density of

Density

0 .0 5 0. 10 0. 15 0. 20

0

5

10

15

Density of e

e

Density

0 .1 0 0. 15 0. 20 0. 25

0

2

4

6

8

10

12

14

Density of o

o

Density

Figure 3: Posterior densities of parameters estimated for CCC-MSV model for USD/CAD

-2. 5 -2 .0 - 1. 5 -1. 0

0.0

0.5

1.0

1.5

Density of e

e

Density

1.0 1.5 2.0

0.0

0.5

1.0

1.5

2.0

Density of o

o

Density

0.6 0.7 0.8 0.9 1. 0

0

5

10

15

Density of ee

ee

Density

0.90 0.94 0.98

0

5

10

15

20

25

30

Density of oo

oo

Density

0.0 0.1 0.2 0.3

0

5

10

15

20

Density of eo

eo

Density

-0. 02 0 .0 2 0. 06 0. 10

0

5

10

15

20

25

Density of oe

oe

Density

-0 .4 5 - 0. 35 -0. 25

0

2

4

6

8

10

Density of

Density

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5

0

2

4

6

8

Density of e

e

Density

0.08 0.10 0.12 0.14 0.16

0

5

10

15

20

25

30

Density of o

o

Density

Figure 4: Posterior densities of parameters estimated for CCC-MSV for USD index

23


24/37

0

1

2

3

4

5

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

CAD/USD

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Time

V

olatility

2 00 6 2 00 7 2 00 8 2 00 9

0

1

2

3

4

5

6

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

NOK/USD

0.5

1.0

1.5

2.0

Time

V

olatility

2 00 6 2 00 7 2 00 8 2 00 9

0

2

4

6

8

10

12

14

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

USD/EUR

2

3

4

5

6

Time

V

olatility

2 00 6 2 00 7 2 00 8 2 00 9

Figure 5: Estimated volatilities of USD/CAD, USD/NOK and USD/EUR for CCC-MSV model

0

1

2

3

4

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

U SD Inde x

0.4

0.6

0.8

1.0

Time

V

olatility

2 00 6 2 00 7 2 00 8 2 00 9

0

1

2

3

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

INR/USD

0.5

1.0

1.5

Time

V

olatility

2 00 6 2 00 7 2 00 8 2 00 9

0

5

10

15

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

Oil

2

3

4

5

6

Time

V

olatility

2 00 6 2 00 7 2 00 8 2 00 9

Figure 6: Estimated volatilities of the USD index, USD/INR and oil for CCC-MSV model

24


25/37

- 2. 0 - 1. 5 - 1. 0 - 0. 5

0.0

0.5

1.0

1.5

Density of e

e

Density

0.5 1.0 1.5 2.0

0.0

0.5

1.0

1.5

Density of o

o

Density

0.90 0.95 1. 00

0

5

10

20

Density of ee

ee

Density

0 .8 5 0 .9 0 0 .9 5 1 .0 0

0

5

10

20

Density of oo

oo

Density

0 .0 0 0. 04 0. 08 0. 12

0

5

10

20

Density of eo

eo

Density

0 .0 0 0 .0 5 0 .1 0 0 .1 5

0

5

10

20

Density of oe

oe

Density

0.10 0.15 0.20 0.25 0.30

0

5

10

15

20

25

Density of e

e

Density

0. 08 0 .1 2 0 .1 6 0 .2 0

0

5

10

15

Density of o

o

Density

- 0. 8 - 0. 6 - 0. 4 - 0. 2

0

1

2

3

4

Density of

Density

0 .0 8 0. 12 0 .1 6 0. 20

0

5

10

15

Density of

De

nsity

0.1 0.2 0.3 0.4

0

2

4

6

8

10

Density of q

q

De

nsity

Figure 7: Posterior densities of parameters estimated for DCC-MSV for USD/CAD

-2.5 -2. 0 -1.5 -1.0

0.0

0.5

1.0

1.5

Density of e

e

Density

1.0 1.5 2.0

0.0

0.5

1.0

1.5

Density of o

o

Density

0.70 0.80 0.90 1.00

0

5

10

15

Density of ee

ee

Density

0.90 0.95 1.00

0

5

10

20

Density of oo

oo

Density

0.00 0.10 0.20

0

5

10

15

Density of eo

eo

Density

0. 00 0. 05 0. 10

0

5

10

20

Density of oe

oe

Density

0.05 0.15 0.25

0

2

4

6

8

12

Density of e

e

Density

0. 10 0. 15 0. 20

0

5

10

20

Density of o

o

Density

-0 .8 -0. 6 - 0. 4 - 0. 2

0

1

2

3

4

Density of

Density

0 .1 0 0. 15 0. 20

0

5

10

20

Density of

Density

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0

1

2

3

4

5

Density of q

q

Density

Figure 8: Posterior densities of parameters estimated for DCC-MSV for USD index

25


26/37

0

1

2

3

4

5

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

CAD/USD

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Time

Volatility

2 00 6 2 00 7 2 00 8 2 00 9

-0.4

-0.3

-0.2

-0.1

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

0

1

2

3

4

5

6

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

NOK/USD

0.5

1.0

1.5

2.0

Time

Volatility

2 00 6 2 00 7 2 00 8 2 00 9

-0.5

-0.4

-0.3

-0.2

-0.1

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

0

1

2

3

4

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

USD/EUR

0.4

0.6

0.8

1.0

1.2

1.4

Time

Volatility

2 00 6 2 00 7 2 00 8 2 00 9

-0.4

0

-0.3

0

-0.2

0

-0.1

0

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

Figure 9: Estimated volatilities of CAD/USD, NOK/USD and USD/EUR for DCC-MSV model

0

1

2

3

4

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

U SD Inde x

0.4

0.6

0.8

1.0

Time

Volatility

2 00 6 2 00 7 2 00 8 2 00 9

-0.4

-0.3

-0.2

-0.1

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

0

1

2

3

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

INR/USD

0.5

1.0

1.5

Time

Volatility

2 00 6 2 00 7 2 00 8 2 00 9

-0.3

-0.2

-0.1

0.0

0.1

0.2

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

0

5

10

15

Time

Abs

.Res

.

2 00 6 2 00 7 2 00 8 2 00 9

Oil

2

3

4

5

6

Time

Volatility

2 00 6 2 00 7 2 00 8 2 00 9

Figure 10: Estimated volatilities of the USD index, INR/USD and oil for DCC-MSV model

26


27/37

-4

-2

0

2

4

Time

CAD/USD

2 00 6 2 00 7 2 00 8 2 00 9

CAD/USD

-10

-5

0

5

10

15

Time

Oil

2 00 6 2 00 7 2 00 8 2 00 9

-0.45

-0.3

5

-0.2

5

-0.1

5

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

-6

-4

-2

0

2

4

Time

NOK/USD

2 00 6 2 00 7 2 00 8 2 00 9

NOK/USD

-10

-5

0

5

10

15

Time

Oil

2 00 6 2 00 7 2 00 8 2 00 9

-0

.5

-0.4

-0.3

-0.2

-0.1

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

-4

-2

0

2

Time

USD/EUR

2 00 6 2 00 7 2 00 8 2 00 9

USD/EUR

-10

-5

0

5

10

15

Time

Oil

2 00 6 2 00 7 2 00 8 2 00 9

-0.4

-0.3

-0.2

-0.1

0.0

Time

Correlation

2 00 6 2 00 7 2 00 8 2 00 9

Figure 11: Estimated time-varying correlations between oil and CAD/USD, NOK/USD, USD/EUR in the

DCC-MGARCH(1,1) model

-4

-3

-2

-1

0

1

Time

Inde

x

2006 2007 2008 2009

U SD Inde x

-10

-5

0

5

10

15

Time

Oil

2006 2007 2008 2009

-0.4

-0.3

-0

.2

-0.1

0.0

Time

Correlation

2006 2007 2008 2009

-4

-2

0

2

4

Time

INR/USD

2006 2007 2008 2009

INR/USD

-10

-5

0

5

10

15

Time

Oil

2006 2007 2008 2009

-0.2

5

-0.1

5

-0.0

5

Time

Correlation

2006 2007 2008 2009

Figure 12: Estimated time-varying correlations between oil and USD index, INR/USD in the DCC-

MGARCH(1,1) model

27


28/37

Table1:Descriptivestatisticsforexchangeratereturn

timeseries

Statistics

Oil

USD/CAD

USD/NOK

US

D/EUR

USD/INR

USDIn

dex

Mean(%)

:0128

:0

133

:0

065

:0

166

:0106

:

0134

Std.Dev.(%

)

2:9

064

:7547

:9569

:6783

:5385

:

5324

Skewness

:0748

:2

758

:1

681

:4

119

:1698

:

7419

ExcessKurtosis

4:3

522

6:3

511

4:9

596

4:9

780

9:4

428

6:

1535

Kolmogorov-

Smirnov

:1946

:1393

:0876

:1499

:2097

:1933

Jarque-Bera

794:7

2

1701:6

6

1035:1

8

1066:4

6

3736:0

1

1677:5

0

ARCH(6)

443:4

8

192:5

0

105:8

6

148:3

6

69:7

8

77:5

5

ARCH(12)

705:7

6

453:3

2

280:5

0

289:9

6

83:6

7

165:6

4

Ljung-Box(6)

75:2

9

21:7

3

19:3

0

22:4

2

14:8

3

18:5

8

Ljung-Box(12)

103:2

7

71:0

7

75:9

1

53:9

3

32:7

6

53:0

9

Ljung-Box(6)onsquaredreturns

360:5

8

232:0

8

135:5

7

207:9

6

44:8

6

83:9

1

Ljung-Box(12)onsquaredreturns

758:7

5

441:8

6

310:5

5

344:8

1

136:2

8

191:6

6

Note:*indicatessignicanceatthe5%

level.

28


29/37

Table2:Estimatesfro

m

VARmodelsforexchangeratea

ndoilreturns

USD/CAD

USD/NOK

USDIn

dex

Parameters

Lag

FX

Oil

FX

Oil

FX

Oil

Coef.

p-value

Coef.

p-value

Coef.

p-value

Coe

f.

p-value

Coef.

p-value

Coef.

p-value

Exchangerate

1

:0031

(:9

287)

:0638

(:6264)

:1

325

(:0

001)

:087

9

(:4

055)

:0

428

(:2

014)

:3340

(:0

662)

2

:0

047

(:8

919)

:0

533

(:6841)

:0

566

(:1

038)

:1

15

1

(:2

786)

:0

488

(:1

450)

:0

518

(:7

752)

3

:0072

(:8

330)

:2942

(:0244)

:0

198

(:5

706)

:165

0

(:1

211)

:0124

(:7

117)

:3613

(:0

467)

4

:0136

(:6

910)

:0

396

(:7623)

:0

307

(:3

773)

:093

7

(:3

782)

:0189

(:5

724)

:0758

(:6

758)

5

:0

349

(:3

076)

:1483

(:2559)

:0

643

(:0

602)

:0

14

8

(:8

873)

:0

055

(:8

680)

:0478

(:7

910)

Oil

1

:0

198

(:0

272)

:0

108

(:7509)

:0

595

(:0

000)

:0

04

8

(:8

896)

:0

203

(:0

010)

:0002

(:9

946)

2

:0

095

(:2

883)

:0

121

(:7247)

:0

138

(:2

290)

:0

14

8

(:6

732)

:0

145

(:0

189)

:0

049

(:8

839)

3

:0

217

(:0

148)

:1570

(:0000)

:0

270

(:0

183)

:142

8

(:0

000)

:0

116

(:0

583)

:1507

(:0

000)

4

:0

116

(:1

992)

:0

229

(:5051)

:0

251

(:0

292)

:0

05

0

(:8

863)

:0

108

(:0

803)

:0

133

(:6

924)

5

:0

044

(:6

283)

:0

987

(:0041)

:0

114

(:3

217)

:1

11

6

(:0

015)

:0

024

(:6

989)

:1

033

(:0

021)

Constant

:0

112

(:6

389)

:0150

(:8695)

:0

031

(:9

182)

:011

1

(:9

032)

:0

117

(:4

845)

:0195

(:8

306)

Ftestsoflags

1:8

76

(:0

448)

3:9

3

(:0000)

4:8

29

(:0

000)

3:81

(:0

000)

2:6

14

(:0

039)

3:9

99

(:0

000)

ARCHtests

ARCH(1)

18:5

498

(:0

000)

58:1

985

(:0000)

5:9

254

(:0

149)

56:1

61

4

(:0

000)

3:6

309

(:0

567)

53:6

61

(:0

000)

ARCH(6)

87:2

031

(:0

000)

164:3

826

(:0000)

54:8

088

(:0

000)

164:6

61

9

(:0

000)

44:1

72

(:0

000)

1

54:9

898

(:0

000)

ARCH(12)

1

67:4

066

(:0

000)

181:5

921

(:0000)

106:9

276

(:0

000)

183:7

70

1

(:0

000)

79:5

204

(:0

000)

1

74:9

295

(:0

000)

29


30/37

Table3:EstimatesfromV

ARmodelsforexchangeratesand

oilreturns(cont.)

U

SD/EUR

USD/INR

Parameters

Lag

FX

Oil

F

X

Oil

Coef.

p-va

lue

Coef.

p-value

Coef.

p-value

Coef.

p-value

Exchangerate

1

:0

095

(:7

7

49)

:1838

(:1

922)

:1

048

(:0

013)

:1

230

(:4

770)

2

:0

583

(:0

7

87)

:0

600

(:6

701)

:0

005

(:9

890)

:3065

(:0

781)

3

:0287

(:3

8

62)

:2153

(:1

266)

:0289

(:3

761)

:3576

(:0

400)

4

:0227

(:4

9

28)

:0

186

(:8

949)

:0208

(:5

256)

:0857

(:6

234)

5

:0

150

(:6

4

94)

:0

469

(:7

383)

:0187

(:5

654)

:0480

(:7

822)

Oil

1

:0

154

(:0

4

79)

:0

049

(:8

824)

:0015

(:8

058)

:0

256

(:4

270)

2

:0

136

(:0

7

99)

:0

063

(:8

498)

:0

036

(:5

558)

:0070

(:8

269)

3

:0

094

(:2

2

55)

:1430

(:0

000)

:0

082

(:1

725)

:1382

(:0

000)

4

:0

105

(:1

7

85)

:0

224

(:4

999)

:0

043

(:4

770)

:0

221

(:4

918)

5

:0008

(:9

1

66)

:1

149

(:0

005)

:0

014

(:8

175)

:1

132

(:0

004)

Con

stant

:0

143

(:5

0

64)

:0111

(:5

154)

:0032

(:9

722)

Fte

stsoflags

1:5

7

(:1

1

03)

3:6

64

(:0

000)

1:5

53

(:1

157)

4:0

19

(:0

000)

ARCHtests

ARCH(1)

2:8

647

(:0

9

05)

56:9

85

(:0

000)

18:4

211

(:0

000)

58:4

709

(:0

000)

ARCH(6)

83:8

639

(:0

0

00)

162:7

133

(:0

000)

61:1

246

(:0

000)

162:9

035

(:0

000)

ARCH(12)

132:9

413

(:0

0

00)

180:2

011

(:0

000)

64:4

418

(:0

000)

181:7

463

(:0

000)

30


31/37

Table 4: Posterior estimates of CCC-MSV models for exchange rates and oil returns

Para. Stat. USD/CAD USD/NOK USD Index USD/EUR USD/INR

e Mean 1:2697 :5860 1:7533 1:3465 2:537

95%CI (1:83;:09) (1:07;:21) (2:22;1:23) (1:86;:85) (3:24;1:91)

ee M ean :9728 :9139 :9211 :8853 :8439

95%CI (:93; :99) (:80; :98) (:72; :98) (:52; :98) (:75; :91)

eo M ean :0219 :0757 :0681 :1026 :1393

95%CI (:00; :05) (:02; :18) (:05; :22) (:01; :45) (:07; :22)

e M ean :1107 :1369 :1264 :1277 :6255

95%CI (:03; :17) (:10; :20) (:06; :33) (:08; :24) (:07; :77)

M ean :3355 :3470 :2955 :2680 :0938

95%CI (:39;:28) (:41;:29) (:38;:22) (:32;:21) (:16;:02)

o

Mean1

:3987 1

:6157 1

:4548 1

:4556 1

:2702

95%CI (:26; 1:84) (1:10; 2:00) (1:05; 1:89) (:94; 1:32) (:69; 1:91)

oo M ean :9524 :9005 :9713 :9272 :9855

95%CI (:02; :98) (:78; :97) (:94; :99) (:81; :99) (:97; :99)

oe M ean :0392 :0953 :0240 :0698 :0071

95%CI (:01; :1) (:02; :22) (:00; :07) (:00; :19) (:00; :02)

o M ean :1573 :1333 :1088 :1298 :1167

95%CI (:03; :22) (:09; :20) (:02; :14) (:08; :20) (:08; :15)

DI C 6192 6683 5622 6075 5228

31


32/37

Table 5: Posterior estimates of DCC-MSV model for exchange rates and oil returns

Para. Stat. USD/CAD USD/NOK USD Index USD/EUR USD/INR

e Mean 1:2314 :6848 1:8780 1:2757 2:3684

95%CI (1:77;:78) (1:13;:2) (2:28;1:41) (1:75;:74) (3:14;1:77)

ee M ean :9658 :6690 :9386 :8733 :8434

95%CI (:91; :99) (:32; :85) (:8; :98) (:62; :99) (:76; :91)

eo M ean :0283 :3222 :0545 :1138 :1413

95%CI (:00; :07) (:14; :70) (:01; :17) (:01; :35) (:06; :24)

e M ean :1441 :2739 :1314 :1475 :6227

95%CI (:1; :25) (:15; :43) (:08; :25) (:07; :26) (:49; :78)

o Mean 1:5033 1:5584 1:4955 1:6152 1:4524

95%CI (1:01; 1:91) (1:13; 2:04) (1:11; 1:94) (:23; 2:05) (:81; 1:99)

oo M ean :9641 :9205 :9576 :909 :9887

95%CI (:89; :99) (:8; :98) (:91; :98) (:67; :98) (:97; :99)

oe M ean :0283 :0735 :0349 :0912 :0042

95%CI (:00; :11) (:01; :20) (:01; :08) (:01; :37) (:00; :02)

o M ean :1289 :0911 :1209 :1085 :1022

95%CI (:09; :18) (:04; :13) (:08; :18) (:07; :16) (:07; :14)

! M ean :5857 :5521 :4801 :5454 :1243

95%CI (:77;:32) (:89;:20) (:67;:27) (:69;:3) (:36; :18)

M ean :8672 :9065 :8412 :8855 :9246

95%CI (:67; :97) (:78; :99) (:53; :96) (:66; :97) (:76; :98)

q M ean :1219 :1710 :1834 :12 :1607

95%CI (:06; :26) (:07; :32) (:06; :43) (:03; :21) (:09; :28)

DI C 6173 6636 5567 6057 5191

32


33/37

Table6:EstimatesofCCC-MGARCH(1,1

)mo

del

Para.

USD/CAD

USD/N

OK

USDIndex

USD/EUR

USD/INR

Mean

p-value

Mean

p-value

Mean

p-value

Mean

p-value

Mean

p-value

a10

:0005

(:4

297)

:0206

(:3

893)

:0000

(:4

998)

:000

0

(:5

000)

:0009

(:3

073)

a20

:1562

(:0

000)

:0610

(:0

798)

:0491

(:0

246)

:119

7

(:0

000)

:0671

(:0

004)

a11

:0609

(:0

000)

:0000

(:0

139)

:0000

(:4

949)

:031

9

(:0

000)

:1174

(:0

000)

a12

:0000

(:5

000)

:0024

(:4

962)

:0000

(:5

000)

:000

0

(:5

000)

:0000

(:5

000)

a21

:1781

(:0

000)

:2127

(:1

653)

:6276

(:2

700)

:151

1

(:0

000)

:1237

(:0

000)

a22

:0944

(:0

878)

:0400

(:4

208)

:0359

(:2

508)

:091

9

(:1

071)

:0617

(:0

478)

b11

:9230

(:0

000)

:0016

(:0

137)

:0107

(:4

911)

:941

0

(:0

005)

:8645

(:0

000)

b12

:0012

(:4

986)

:1041

(:4

944)

:0345

(:4

993)

:001

5

(:4

991)

:0011

(:4

985)

b21

:0974

(:0

000)

:0739

(:0

000)

:7458

(:0

000)

:679

5

(:0

000)

:0000

(:4

999)

b22

:8619

(:0

000)

:9182

(:2

437)

:9084

(:1

112)

:842

0

(:0

000)

:9232

(:0

000)

:3

218

(:0

000)

:3

433

(:0

000)

:2

858

(:0

000)

:2

70

6

(:0

000)

:1

002

(:0

000)

logl

ik

30870

112168

209681

74462

28693

33


34/37

Table7:EstimatesofDCC-MGARCH(1,1

)mo

del

Para.

USD/CAD

USD/NOK

USDIndex

USD

/EUR

USD/INR

Mean

p-value

Mean

p-value

Mean

p-value

Mean

p-value

Mean

p-value

a10

:0000

(:4

999)

:0287

(:3

168)

:0004

(:4

795)

:0031

(:4

534)

:0004

(:4

409)

a20

:0862

(:0

000)

:0041

(:4

328)

:0417

(:0

211)

:0222

(:1

445)

:0604

(:0

282)

a11

:0622

(:0

000)

:0013

(:3

794)

:0005

(:2

870)

:0000

(:4

918)

:1174

(:0

000)

a12

:0000

(:5

000)

:0029

(:4

882)

:0000

(:5

000)

:0000

(:4

998)

:0000

(:5

000)

a21

:1487

(:0

000)

:2675

(:3

882)

:6884

(:0

325)

:4012

(:3

878)

:0129

(:3

808)

a22

:0773

(:0

746)

:0472

(:4

351)

:0490

(:2

164)

:0383

(:2

640)

:0626

(:0

544)

b11

:9225

(:0

000)

:4349

(:0

727)

:6549

(:1

367)

:1531

(:3

875)

:8657

(:0

000)

b12

:0012

(:4

984)

:0543

(:4

965)

:0120

(:4

994)

:0469

(:4

990)

:0011

(:4

986)

b21

:0345

(:1

070)

:5955

(:0

000)

1:4

001

(:0

000)

:8919

(:0

000)

:1335

(:0

000)

b22

:8974

(:0

000)

:8590

(:1

056)

:8719

(:0

065)

:8863

(:2

040)

:9223

(:0

000)

:0078

(:0

591)

:0239

(:0

411)

:0317

(:0

668)

:0239

(:0

670)

:0065

(:0

985)

:9886

(:0

000)

:9346

(:0

000)

:8672

(:0

000)

:9287

(:0

000)

:9907

(:0

000)

loglik

3558:8

63

4059:2

72

2946:3

86

34

15:7

39

2969:2

22

34


35/37

Table8:MSVmodelchecking

Para.

USD/CAD

U

SD/NOK

USDIndex

USD/EUR

USD/INR

Ex.rate

Oil

Ex.rate

Oil

Ex.rate

Oil

Ex.rate

Oil

Ex.rate

Oil

CCC-MSV

Mean

:0

111

:0238

:0137

:0232

:0

075

:0251

:0

117

:0271

:0

104

:0275

Std

:9576

:9737

:9871

:9827

:9338

:9897

:9778

:9994

:9988

:9789

Skewness

:0

816

:0034

:0450

:0089

:1

663

:0351

:1

037

:0286

:1054

:0071

Kurtosis

3:0

87

2:6

539

3:2321

2:7

766

3:4

476

2:7

850

3:3

485

2:7

577

3:2

393

2:7

779

Kolmogorov-S

mirnov

:0286

:0197

:0233

:0214

:0383

:0227

:0301

:0214

:0254

:0199

(p

value)

(:3

891)

(:8

348)

(:6561)

(:7

515)

(:1

092)

(:6

86)

(:3

3)

(:7

52)

(:5

457)

(

:8273)

Jarque-Bera

1:4

702

4:8

130

2:6918

1:9

761

13:1

420

2:0

187

7:0

04

2:4

541

4:3

447

1:9

471

(p

value)

(:4

794)

(:0

901)

(:2603)

(:3

723)

(:0

014)

(:3

645)

(:0

301)

(:2

932)

(:1

139)

(

:3777)

DIC

6275

6754

5696

6146

5439

DCC-MSV

Mean

:0

126

:0238

:0165

:0236

:0

099

:0249

:0

130

:0258

:0

104

:0264

Std

:9786

:9833

1:0014

:9981

1:0

004

:9900

:9817

:9791

:9982

:9761

Skewness

:1

013

:0165

:0265

:0311

:1

499

:0406

:0

872

:0346

:1209

:0186

Kurtosis

2:9

192

2:7

331

3:2480

2:8

915

3:2

566

2:7

938

3:2

300

2:8

145

3:2

751

2:8

002

Kolmogorov-S

mirnov

:0224

:0217

:0195

:0196

:0224

:024

:0305

:0186

:027

:0174

(p

value)

(:6

998)

(:7

364)

(:8458)

(:8

385)

(:7

036)

(:6

145)

(:3

153)

(:8

808)

(:4

639)

(

:9245)

Jarque-Bera

1:9

372

2:8

722

2:7984

:5966

6:5

935

1:9

389

3:5

778

1:5

366

5:7

088

1:6

171

(p

value)

(:3

796)

(:2

379)

(:2468)

(:7

421)

(:0

370)

(:3

793)

(:1

671)

(:4

638)

(:0

576)

(

:4455)

DIC

6275

6749

5664

6142

5417

35


36/37

Table9:MGARCHmodelchecking

Para.

USD/CAD

USD/NOK

USDIndex

USD/EUR

USD/INR

Ex.rate

Oil

Ex.rate

Oil

Ex.rate

Oil

Ex.rate

Oil

Ex.rate

Oil

CCC-MGAR

CH

Mean

:0

110

:0193

:0

101

:0193

:0

129

:0197

:0

125

:0199

:0

105

:0175

Std

:9966

:9982

:9989

:9989

:9999

:9962

:9981

:9989

:9959

:9964

Skewness

:1

408

:0478

:0329

:0662

:2

506

:1023

:1

475

:0624

:2

554

:0479

Kurtosis

3:6

386

3:1

881

3:7

099

3:2

015

4:0

631

3:4

589

3:8

32

3:2

007

8:0

562

3:3

527

Kolmogorov-Smirnov

:0302

:0202

:0271

:0193

:0371

:0214

:0341

:0193

:0768

:0246

(p

value)

(:3

261)

(:8

123)

(:45

78)

(:8

536)

(:1

295)

(:7

536)

(:1

989)

(:8

548)

(:0

000)

(:5

825)

Jarque-Bera

20:5

719

1:9

466

21:4

951

2:5

185

57:9

732

10:7

259

32:8

353

2:4

232

107:6

472

5:7

341

(p

value)

(:0

000)

(:3

778)

(:00

00)

(:2

839)

(:0

000)

(:0

047)

(:0

000)

(:2

977)

(:0

000)

(:0

569)

Loglik

30;8

70

704;4

02

209;6

81

74;4

62

28;6

9

Documents

Exchange Rate and Oil Prices