Identifying the dynamic connectedness between propane and oil prices: Evidence from wavelet analysis
International Journal of Energy Economics and
Policy
ISSN: 2146-4553
International Journal of Energy Economics and Policy, 2020, 10(5), 315-326.
Identifying the Dynamic Connectedness between Propane and Oil
Prices: Evidence from Wavelet Analysis
Ngo Thai Hung*
University of Finance-Marketing, Ho Chi Minh City, Vietnam. *Email: hung.nt@ufm.edu.vn
Received: 23 March 2020
Accepted: 20 June 2020
ABSTRACT
This paper takes into account the LPG markets and aims to examine the short run and long run dependencies between crude oil and propane prices
during the period 2006-2018. Our empirical study is based on the wavelet transform approach, which allows us to evaluate the co-movement in both
time-frequency spaces. The techniques employed on the dataset includes maximal overlap discrete wavelet transform, wavelet covariance, wavelet
correlation, continuous wavelet power spectrum, wavelet coherence and wavelet-based Granger causality tests to measure the intercorrelation between
crude oil and propane markets. The findings suggest that the existence of strong interconnectedness between crude oil and propane series in the short
and medium run. However, there is a unidirectional impact of propane returns on crude oil markets in the very long term. Furthermore, we construct
the wavelet-based Granger causality test at different time scales to provide additional support to our nexus results. Our results provide significant
implications for policymakers, portfolio managers, and practitioners who are invited to consider the dynamics of return and volatility spillovers between
crude oil and propane markets to create sound policy based on a clear comprehension of the transmission between these markets.
Keywords: Crude Oil, Liquefied Petroleum Gas, Co-movement, Wavelet analysis, Propane
JEL classifications: G13, C22, F30.
A vast literature on energy markets has been directed towards
the nexus between oil and natural gas markets. However, less
1. INTRODUCTION
attention has been paid to other crucial petroleum products
and their relations with oil markets. PLG, such as propane, is
connected with crude oil prices both on the demand side and
supply side. High liquids prices owing to high oil prices, would
rise propane production and hence depress propane prices. This
implies that the intercorrelation between crude oil and propane
prices do not only depend on direct inter-fuel substitution or
gas-to-gas prices competition but also the state of the liquid
markets (Oglend et al., 2015).
Propane is by-products of crude oil refining and natural gas
processing, which is a part of liquefied petroleum gases (PLG).
Nowadays, PLG plays a prominent role in the global energy
market and would be used for divergent purposes, such as heating,
cooking, and serving as an underlying petrochemical feedstock.
As per Oglend et al. (2015), PLG, together with other natural gas
liquids, has a significant role in the current US shale gas boom.
Changes in gas prices in recent years have made pure natural gas
operations less profitable. The connectedness between propane,
crude oil, and natural gas supply is dictated by chemistry and
technology, and so has been somewhat significant over time.
One vital part of the dialogue with regard to the short-run
correlation between crude oil prices and PLG prices is the speed
and magnitude of product prices response to changes in the oil
market (Ederington et al., 2019).
Two main hypotheses in connection with the causal relationship
between crude oil prices and PLG have been represented in the
literature. The first asserts that the primary association from oil
prices to product prices (Asche et al., 2003; Shi et al., 2013),
while rests on the hypothesis that the marginal price of a barrel of
This Journal is licensed under a Creative Commons Attribution 4.0 International License
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
a petroleum product may be determined by the highest marginal
and of the links between oil and the PLG market. We find that
the unidirectional running from three propane returns to crude oil
prices in the long-run and very long-run. In contrast, the strong
bidirectional causal connectedness between both variables in the
short and medium-run is found.
cost of oil used. Furthermore, causality runs in the opposite
direction (Oglend et al., 2013; Bai and Lam, 2019). The direction
of causality has significant implications for the policymakers,
regulation, and organization of these markets and the facilitation of
trade (Acikalin et al. 2018;Al-Sharkas, 2004; Ditimi and Sunday,
2018; Lee and Brahmasrene, 2018).
The remainder of the paper is structured as follows. Section 2
reviews the relevant literature. Section 3 represents the methodology
and data. Section 4 discusses the empirical results. Lastly, a
conclusion is made in Section 5.
Recently, the vast majority of papers examining the interrelatedness
between oil price changes and PLG price changes have taken the
direction of causation and said that the dominant channel is from
oil prices to product prices (Bai and Lam, 2019). On the other
hand, some evidence indicates that causality would run from
PLG prices to oil prices (Caporin et al., 2019). Specifically, there
is very limited research determining that causal interaction runs
from product prices to oil prices as well as the data behavior is
measured at a quarterly or more extended frequency (Ederington
et al., 2019).
2. LITERATURE REVIEW
Prior empirical studies in the interdependence between crude
oil and liquefied petroleum gas (PLG) prices produced mixed
results with many suggesting the causality differs from location
to location and also varies over time. Asche et al. (2003) examine
the causal relationship between crude oil and refined prices by
employing a multivariate framework. They conclude that the
crude price is weakly exogenous and that the spread is constant
in the relationship, but the linkages between crude oil prices and
some refined product prices imply market integration. Oglend
et al. (2015) publish an empirical study on the connectedness
between LPG (propane and butane) oil and natural gas prices in
the US. Based on cointegration tests, the findings reveal that the
PLG-oil relationship is significantly weak in recent years with a
move towards cheaper liquids relative to oil, which is in line with
developments in the gas sector with increased liquids production.
The US natural gas operations are thus unable to rely on high
liquids prices to make economic gains automatically. Shi et al.
(2013) study the relationship between fluctuations in oil prices and
the freight market using a structural vector autoregressive model,
provide evidence that crude oil supply innovations have dramatic
impacts on the contemporaneous tanker market. Additionally,
the paper also interprets that there is a positive relationship
between the accumulated responses of the tanker market to crude
oil non-supply shocks and crude oil supply shocks. Sun et al.
(2014) carry out empirical research on the multiscale correlation
between freight rates and oil prices using intrinsic mode function
extraction, multiscale component construction and multiscale
relevance examined. The paper highlights that tanker freight rates
and oil prices show various multiscale properties in terms of the
long-run trend, medium-run pattern in low frequency, and short-
run fluctuation in high frequency. Specifically, the correlation
between the two variables is somewhat high and positive in low
frequencies, which suggests that it is crucial and rationale to take
into account the dynamic connectedness in multi-scales under
the relevant structure. In a same vein, Dahl and Oglend (2016)
focus on the changes in the stability of energy prices and provide
evidence that in the current regime, oil and natural gas in Europe
and the US have become unstable.
Therefore, the question is whether PLG prices respond more
strongly and rapidly to crude oil increases than to oil prices
decreases. This study primarily concentrates on the dependence
of crude oil markets and propane prices in different locations. It
would be beneficial for individual consumers, industrial producers,
and consumers, as well as public policymakers and academics,
to resort to the frequency domain in order to provide a better
understanding of crude oil-PLG co-movement behavior at the
frequency level. This study seeks to fill this gap.
Furthermore, crude oil-PLG co-movement has been intensively
studied utilizing different empirical methods, but less attention
has been paid to the link analysis in the frequency domain.
As a consequence, linear and other traditional models are not
appropriate for modeling crude oil and PLG price distributions
(Bai and Lam, 2019). This paper employs the wavelet approach
to analyze the frequency components of the crude oil and propane
time series without losing the time information. More precisely,
the wavelet transform frameworks allow us to detect oil-propane
interactions, which hard to test out using other modern economic
time-series models.
To our knowledge and based on a detailed literature review of
the most popular academic journal databases, this paper differs
in several ways: First, the interaction between the oil price and
propane prices in different locations is estimated by using the
newly developed technique named Wavelet. In this study, we use
maximal overlap discrete wavelet transform, wavelet covariance,
wavelet correlation, continuous wavelet power spectrum, wavelet
coherence and wavelet-based Granger causality tests to capture the
time-frequency co-movements between crude oil and three propane
series which adequately obstacles most of the methodological
issues that present literature suffers from. Secondly, we investigate
the nexus between crude oil prices and propane markets by using
the weekly data to analyze instead of using the monthly or annual
observation, which is mostly employed in the previous literature.
Finally, our findings provide individual consumers, industrial
producers, and consumers, as well as public policymakers and
academics, with further insights into the international portfolio
More recently, Bai and Lam (2019) investigate both the constant
and time-varying conditional dependence dynamics among LPF
freight rates, crude oil price, and propane location arbitrage by
a conditional copula-GARCH model. The results report that the
Baltic PLG freight rate and the arbitrage between propane Far
East and the Middle East prices have a significant conditional
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
time-varying correlation. Furthermore, the paper shows that
oil prices with economic activity in the US. The interdependency
between the daily returns of major stock markets and foreign
exchange rates has also been extensively studied using the wavelet
transform framework (Yang et al., 2016; Polanco-Martínez et al.
2018; Aloui and Hkiri, 2014; Dahir et al., 2018). Mishra et al.
(2019) also adopt the multiple wavelet analysis to highlight the
dynamic linkages between tourism, transportation, growth, and
carbon emission in the USA. Tiwari et al. (2018) explore the time-
frequency co-movement of and lead-lag connectedness between
oil prices and 21 agricultural commodities. Results from wavelet
coherency, phase-difference, multiple correlation, and multiple
cross-correlations show a high degree of co-movement at a long-
run horizon during the research period.
Middle East propane prices strongly influence crude oil prices in
comparison with the Far East and US propane prices. Caporin et
al. (2019) analyze returns and volatility spillovers between the
S&P 500 index and crude oil, natural gas, ethanol. The paper
documents that the connectedness varies according to the trading
range among these variables.
With regard to the linkages between freights and commodity
prices, Yu et al. (2007) explore the spatial price relatedness in the
US and transportation markets using cointegration analysis. The
paper provides strong interaction between grain and freight rates
in the long run. Similarly, Kavussanos et al. (2014) concentrate on
return and volatility spillover effects between various ocean freight
and future commodity markets. The main results confirm that the
economic nexus tested empirically linkages the derivative price of
the commodities transport with the derivative on the freight rate
of the vessel transporting it.
Among all the references mentioned herein, very limited research
has been implemented on the propane-oil relationship. Moreover,
the most popular often used techniques for interdependence
analysis in energy product literature are cointegration tests
and ARDL, which do not imply the fundamental time-varying
correlation between crude oil and propane series in different
locations for different investment horizons. In this paper, we
employ the wavelet transform approach providing regions that
capture the direction and degree of dependency of the oil and
propane returns and expose associations between cause and effect
over time and frequency.
With reference to the dependency between crude oil and natural
gas prices, Ramberg and Parsons (2012) explore the apparent
contradiction of the nexus between crude oil and natural gas
prices. They find evidence supporting that natural gas-crude oil
relationship is cointegrated and changes over time.Arfaoui (2018)
investigates the relationship between spot and futures prices of
crude and refined petroleum using the ARDL frameworks. The
author points out that the short and long-run elasticities exist
between spot and futures prices and between crude and refined
oil prices except for gasoline. Lovcha and Perez-Laborda (2020)
examine the dynamic volatility relationship between oil, and
natural gas using decomposes connectedness measures. Their
results show that interaction is typically generated at low-
frequencies with volatility innovations across markets having long-
lasting influence and provide evidence that the natural gas market
was a net transmitter during the research period. la Torre-Torres
et al. (2020) shed light on the practical use of Markov-switching
models for trading in energy commodity markets, either oil and
or natural gas futures. Their findings reveal that with time-fixed
variance, the use of the MS Gaussian model results in the best
performance in the oil market. However, the authors find no benefit
of using trading rule against a buy and hold strategy in the US
Treasury bill in the case of natural gas.
3. METHODOLOGY
The wavelet model is a robust estimator that applies signal
processing, providing a single chance to investigate co-movements
between crude oil prices and propane product prices in the time-
frequency dimension. In this paper, we employ wavelet approach
in terms of continuous wavelets and cross-wavelet transforms to
explore how the local variance and covariance of two-time series
make progress, and wavelet coherence and phase analysis to
estimate the co-movement correlation between two variables in
the time-frequency domain (Reboredo et al., 2017). In addition,
discrete wavelets can be used to measure the connectedness
between crude oil prices and propane product prices. In this
section, we briefly note on wavelet approach.
3.1. Discrete Wavelet Transform
A series y(t) can be decomposed into various time scales as:
When it turns to the wavelet transform frameworks for time-
frequency co-movements modeling, Dahir et al. (2018) suggest
that the wavelet model is a very powerful estimator that employs
signal processing, providing a single opportunity to investigate the
co-movements between economic time series in time-frequency
dimension. The wavelet approach gives more straightforward
insights into potential intercorrelations at various scales along
periods. Further, it outperforms the standard OLS regression,
ARDL, ECM or VAR, cointegration that are currently the most
popular methodologies for examining interdependencies between
time series (Hung, 2019). Recently, Raza et al. (2019) study
the time-frequency relationship between energy consumption,
economic growth, and environmental degradation in the US
utilizing the wavelet transform approach. Raza et al. (2018) based
on similar approaches to investigate the empirical association of
y(t) =
++
sJ ,k
J ,k (t) +
dJ ,k
J ,k (t) +
dJ −1,kJ −1,k (t)
∑
∑
∑
k
k
k
d1,k1,k (t)
(1)
∑
k
Where
and
are the father wavelet and mother wavelet
functions, denoting the smooth (low frequency) parts of a signal
and the detail (high frequency) components. The functions sJ(t)
and dJ(t) are the smooth signals and the detail signals, respectively.
Therefore, the time series y(t) can be rewritten as:
y(t) = S j (t) + Dj (t) + DJ −1(t) ++ D (t)
(2)
1
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
where the highest-level approximation Sj(t) is the smooth signal,
wavelet is squared. Therefore, we use the phase difference tool to
examine the dependency and causality interconnections between
time series. The phase difference between x(t) and y(t) is defined
as follows: (Reboredo et al., 2017).
and D1(t),D2(t),…, Dj(t) are associated with oscillations of lengths
2-4, 4-8,…, 2j+2j+1, respectively. In our empirical study, we employ
monthly data and establish J = 8 for multi-resolution level J
because past studies have proved that a moderate filter is suitable
for financial data (Reboredo et al., 2017).
−1
ℑ{S(s WXY (u,s)}
XY = tan−1
ℜ{S(s−1W (u,s)}
(6)
XY
3.2. The Continuous Wavelet Transform
The continuous wavelet transform Wx(s) allow us to investigate
the joint behavior of time series for both frequency and time. The
wavelet us defined as:
Where
and
are the imaginary and real parts of the smooth
power spectrum, respectively. Phase interrelatedness between two
variables are shown in the coherence phase by means of arrows:
(1) the correlation is positive (negative) when the arrows point to
the right (left); and the second (first) variable leads the first
(second) variable by 90° when the arrows point to down (up).
∞
1
t
Wx (s) = x(t)
*
(3)
∫
s
s
−∞
where * denotes the complex conjugate and where the scale
parameter s identifies whether the wavelet can detect higher
or lower components of the series x(t), possible when the
admissibility condition yields.
3.5. Data
We implemented our empirical analysis of intercorrelation and
causality between crude oil prices and propane product prices at
different time scales using weekly average prices of Brent Crude
(OIL), and three propane prices, including PropaneArgus Far East
Index (PAFEI), Propane CPswap (PCPS) and Propane Mt Belvieu
prices (PMB). Our data, spanning the period January 2006-March
2018, were sourced from Baltic Exchange and Datastream. The
original data are transformed into the first difference of the natural
logarithm ratio by taking the logarithm difference of the two
successive weekly prices to compute prices index returns.
3.3. Wavelet Coherence
To specify the joint behavior of both time and frequency between two
time series variables, we employ three specific techniques of wavelet
including the wavelet power spectrum, cross-wavelet power and
cross-wavelet transform. While the wavelet power spectrum explore
contribution to the variance of the series at each time scale, cross-
wavelet power measures covariance contribution in the time-frequency
space. The cross-wavelet of two series x(t) and y(t) can be defined as:
Table 1 represents the descriptive statistics of the returns of OIL,
PMB, PAFEI, and PCPS indices during the sample period 2006-
2018. It is worth noting that the average weekly return series are
negative except OIL. Similarly, all four series display negative
skewness, while its kurtosis coefficients are positive. Therefore,
four concerned variables are far from normally distributed, which
means that these indices are fatter tailed. These findings are
formally affirmed by the Jarque-Bera test statistics. Additionally,
Augmented Dickey-Fuller test rejects the null hypothesis of unit
root test for all the return series at the 5% significance level.
Finally, statistics from ARCH test for heteroskedasticity reveal
that all return series present ARCH effects. These results are thus
suitable for further statistical analysis. The graphs in Figure 1
exhibit the price developments of Brent Crude, and three selected
propane prices in the whole sample period. It describes a similar
fluctuation for the four variables under investigation.
WnXY (u,s) = WnX (u,s)WnY*(u,s)
(4)
where u denotes the position, s is the scale, and * denotes the
complex conjugate.
Torrence and Webster (1999) develops the wavelet coherence
which can measure the co-movement between two selected time
series. The squared wavelet coefficient is defined as:
| S s−1W XY (u,s)) |2
(
)
n
Rn2 (u,s) =
(5)
S s−1 |W (u,s) |2 S s−1 |WY (u,s) |2
(
X
where S is a smoothing parameter for both time and frequency.
R2(u,s) is in the range 0≤R2(u,s)≤1, which is similar to correlation
coefficient. If its value is close to zero, evidence of weak
interdependence will be determined and vice versa.
4. EMPIRICAL RESULTS AND DISCUSSION
3.4. Phase Difference
We cannot shed light on the dichotomy between positive or negative
dependency using the wavelet coherence since the coherence
We use the wavelet transform approach to evaluate the dynamic
connectedness between crude oil prices (OIL) and propane prices
(PAFEI), (PCPS), (PMB) in different locations.
Table 1: Statistical properties of daily returns over the in-sample period
Variables
OIL
PMB
PAFEI
PCPS
Mean
Std.dev.
4.185372
4.860190
4.162931
4.083194
Skewness
−0.101646
−0.896543
−0.483477
−0.525440
Kurtosis
4.791726
6.717160
6.168709
6.906483
JB
ADF
ARCH
0.023048
−0.087830
−0.0˗44090
−0.035252
81.96769*
429.3593*
276.6795*
412.5334*
−20.34999*
−10.62148*
−18.22874*
−8.140399*
31.34196*
41.63234*
26.55984*
17.58269*
JB and ADF refer to the empirical statistics of the Jarque-Bera test for normality, the augmented Dickey-Fuller unit root tests with an intercept. The ARCH test is used to test the presence
of ARCH effect in the datasets. *indicates the null hypothesis rejected at the 1% level
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
wavelet transform (MODWT) based on the least asymmetric
4.1. The Discrete Wavelet Transform (DWT)
wavelet filter. The orthogonal component graphs (D1, D2,…, D6)
are plotted to demonstrate the divergent frequency elements of
the original series in detail and a smoothed component (S6).
From Figure 2, we can see that high frequency is found in the
short period of the variables under investigation. We further
divide these levels into four holding periods, namely, short-run
In this subsection, we document the results of the DWT of the
returns on the variables under examination. In order to assess the
degree of energy integration, we use the time-frequency-based
wavelet framework to study the various time horizon in the time
series. Figure 2 shows the multi-resolution analysis of order j = 6
for the selected variables by applying maximal overlap discrete
Figure 1: Time-series of the selected indices
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
Figure 2: MODWT decomposition of the selected indices on J = 6 wavelet level
(D1+D2), medium-run (D3+D4), long-run (D5+D6), and very
4.2. Continuous Wavelet Transform (CWT)
long-run (S6).
Figure 3 reports the raw data variations based on the CWT. The
yellow region at the bottom (top) of the continuous power spectra
depicts substantial variation at low (high) frequencies while
the yellow region on the left-hand side (right-hand) side shows
significant variation at the beginning (end) of the sample period,
Variations in the selected variables often occur in the short run. We can
observethatthesefourindexesillustratethehighestvariation, atdifferent
timescales, around 2009, when the global financial crisis completed.
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
Figure 3: Continuous wavelet power spectra of OIL, PAFEI, PCPS and PMB. The thick black contour displays the 5% significance level against
the yellow noise. The color code for power ranges from blue (low power) to yellow (high power). The vertical axis displays the frequency element,
while horizontal axis displays the time element
and areas in blue illustrate weak variation or low intensity between
the time series. Put differently, Figure 3 indicates that crude oil
prices and propane prices exhibit significant volatility at the 5%
significance level. Oil prices show an evolution of variances,
revealing high variation at scale (64-128 weeks) around 2010.
With regard to the propane indexes (PAFEI, PCPS, PMB), we
note high variation and structural changes over the short (2-16
weeks), medium (16-32 weeks), and long term (64-128 weeks)
during the period 2007-2010 and 2016-2017. All these outcomes
demonstrate that the global financial crisis had a significant effect
on crude oil and propane prices.
the right-hand side. Put another way, strong covariance is shown in
64-128-week scales around 2007-2010 and 2016-2017. Therefore,
the findings show that the volatility of these indices witnessed
underlying changes over the period shown, which means that the
energy markets are exposed to long-term volatility. In addition,
phase differences suggest that interconnectedness between OIL
and the three propane indices is not homogeneous throughout the
time and scales, as indicated by arrows that point up, down, right,
and left at various times and frequencies.
4.3. Wavelet Coherence
In the section, we examine the co-movements and causal
association between OILand the selected propane returns (PAFEI,
PCPS, PMB) using the pairwise plots of wavelet coherence.
Figure 5 represents the wavelet coherence power spectrum between
these variables. In a similar way to Figure 4, the yellow region
at the bottom (top) of the wavelet coherence illustrates strong
relationship at low (high) frequencies, while the yellow region
on the left-hand (right-hand) side signifies significant relationship
at the beginning (end) of the sample period. More precisely, the
horizontal axis shows the time component, while the vertical axis
shows the frequency components, and color code measures the
degree of correlation between pairs of indices. The yellow areas
represent that the two series are highly dependent, while blue color
areas represent that the two series are less dependent.Additionally,
the wavelet coherence effectively performs zones in different time
Cross-wavelet transform (XWT) for the pairs are summarized in
Figure 4. XWT is analogous to the CWT plots in Figure 3, the
black contour shows 5% significance level. The thin black curved
line shows the region affected by edge effects. The XWT reflects
the local covariance between OILand the selected propane returns
(PAFEI, PCPS, PMB) at different scales and periods. The XWT
reports that the interrelatedness between OIL and propane returns
is statistically significant at medium and high frequencies (high
scales) using phase arrow, which shows the cause-effect nexus
between the selected markets. Arrows pointing right highlight in-
phase pairs, such as OIL and PAFEI returns. Arrows pointing left
highlight anti-phase pairs such as OILand PCPS indexes.An arrow
pointing straight down means that the right side leads the left side.
By contrast, if an arrow points straight up, the left-hand side leads
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
Figure 4: Cross-wavelet transforms for OIL, PAFEI, PCPS and PMB. The thick black contour displays the 5% significance level against the yellow
noise. The color code for power ranges from blue (low power) to yellow (high power). The vertical axis displays the frequency element, while
horizontal axis displays the time element. Right up and down presents in-phase, while left up and down presents out-phase
Figure 5: Wavelet coherence of OIL, PAFEI, PCPS and PMB. The thick black contour displays the 5% significance level against the yellow noise.
The color code for power ranges from blue (low power) to yellow (high power). The vertical axis displays the frequency element, while horizontal
axis displays the time element. Right up and down presents in-phase, while left up and down presents out-phase
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
and scales where each pair of series is significantly dependent
or otherwise, corresponding to the local correlation coefficients
spanning from 0 to 1.
difference shows that the pairs of these returns move in opposite
directions (negative correlation) over a specific time and frequency
bands. The right-up and left-down arrows suggest that OILreturns,
as the dependent variables, are leading, and the right-down and
left-up arrows show that the PAFEI, PCPS, PMB returns, as an
independent variable, are leading.
Therefore, wavelet coherence indicates the correlation of index
pairs, while the wavelet phase difference finds out the dynamic
relationships of variables by observing lead-lag interaction
through various investment horizons. Arrows pointing phase
differences suggest the intercorrelation direction and cause-effect
connectedness. Furthermore, arrows representing the right and
left reveal that the paired indexes are in-phase and out-phase,
respectively. The in-phase difference indicates that OIL and the
propane series PAFEI, PCPS, PMB move jointly in the same
direction (positive correlation), while the out-phase wavelet phase
We report the results of the wavelet coherence on the bases of four
major periods such as short-run (D1+D2), medium-run (D3+D4),
long-run (D5+D6) and very long-run (S6). The findings of the
wavelet coherence are summarized in Table 2.
Overall, the wavelet coherence approach result highlights that
in the short and medium-run, we have an out-phase situation in
Figure 6: Wavelet covariance and correlation between OIL and propane series. The upper and lower bound are denoted with “U” and “L”
respectively at 95% confidence interval. The black dotted line presents the covariance and correlation among the selected series
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Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
which OIL is leading (OIL has a causal influence on the propane
Figure 6 reports the interconnectedness between OIL and PAFEI,
PCPS, PMB using MODWT-based wavelet covariance, and
correlation analysis, which reveal the interdependence between
two variables at different time scales. It is clear from the graph
that the positive covariance exists between OIL and three propane
series in the short and medium run, whereas negative covariance
is found between these pairs in the long and very long term.
These findings affirm that OIL positively hit the propane prices
in the short and medium run. Similarly, the results of the wavelet
correlation between variables are also reported in Figure 6.
Overall, the positive and strong correlation between OIL and
PAFEI, PCPS, PMB is found in the four periods (short, medium,
long, and very term). Hence, we can conclude that the increase in
crude oil prices upsurges the propane prices and vice versa. Also,
OILfluctuation is a crucial fundamental element that dramatically
raises the propane returns.
markets). By contrast, in the long and very long-run, we see an
in-phase situation, propane returns are leading (PMB, PCPS,
PAFEI have a positive effect on OIL), and an anti-phase situation,
OIL are leading (OIL have a causal impact on the propane series).
In other words, crude oil prices significantly impact the propane
prices, whereas, in the long and very long-run, the propane returns
have a positive influence on crude oil prices. Moreover, in the
short and medium run, there is a unidirectional influence from
OIL to PAFEI, PCPS, and PMB, while in the long and very long
run, strong unidirectional causality of the propane prices on the
OIL returns is found.
Table 2: Wavelet coherence findings summary
Frequencies
Cross-wavelet coherence
OIL - PAFEI
Very high frequency
High frequency
↑PAFEI →↑ OIL
↑OIL →↑PAFEI
↑PAFEI →↑OIL
↑PAFEI →↑OIL
↑OIL →↑PAFEI
↑OIL →↑PAFEI
↑PAFEI →↑OIL
In the final step of the analysis, we follow the research of Raza
et al. (2018) to implement the Granger causality tests on the
wavelet-decomposed data. The results demonstrate that there
is a bidirectional causal relationship between OIL and propane
returns in the short and medium terms, as indicated in Table 3.
In contrast, PAFEI, PCPS, PMB returns have a unidirectional
influence on OIL in the long and very long run. In light of this
evidence, we can confirm that the co-movements among the model
parameters explored through the wavelet coherence framework are
subsequently validated by the findings of causality analysis. Hence,
we can conclude that there exists a dynamic relationship among
variables, and significant causal interaction among variables can
be found over the four periods shown.
Medium frequency
Low frequency
OIL - PCPS
Very high frequency
High frequency
↑PCPS →↑ OIL
↑ OIL →↑PCPS
↑PCPS→↑OIL
↑OIL → PCPS
↑OIL →↑PCPS
Medium frequency
Low frequency
OIL - PMB
Very high frequency
High frequency
↑ PMP→↑OIL
↑ PMP→↑OIL
↑OIL→↑PMP
↑PMP →↑OIL
↑OIL →↑PMP
Medium frequency
Low frequency
Our findings, in line with previous papers on dynamic linkages,
highlights the existence of liquefied petroleum gas, crude oil,
and propane prices. For example, Bai and Lam (2019) document
↑ denotes an increase in, ↓denotes a decrease in, →denotes the variable on the left side
of arrow leads the variable on the right side of the arrow
Table 3: Results of wavelet-based granger causality test at different time scales
Time domain
Result
Null hypothesis
Oil does not cause propane prices
Propane prices do not cause oil
F-test
P-value
F-test
p-value
OIL - PAFEI
D1 (2-4 W)
D2 (4-8W)
D3 (8-16W)
D4 (16-32W)
D5 (32-64W)
D6 (64-128W)
OIL - PMB
D1 (2-4 W)
OIL→PAFEI
OIL→PAFEI
OIL↔PAFEI
OIL↔PAFEI
PAFEI → OIL
PAFEI → OIL
6.83929
6.46189
4.49754
2.62115
1.32326
0.09455
0.0012
0.0017
0.0115
0.0736
0.2670
0.9098
0.71696
0.34280
2.44660
0.71872
3.32701
1.10065
0.4887
0.7099
0.0875
0.4878
0.0366
0.0989
No causality
OIL↔PMP
PMP → OIL
PMP → OIL
OIL↔PMP
PMP → OIL
2.37370
2.26813
1.86626
1.31783
13.6992
0.69233
0.0940
0.1000
0.1556
0.2685
0.000
0.09261
2.61959
3.16679
3.84780
13.6992
2.0652
0.9116
0.0737
0.0428
0.0219
0.000
D2 (4-8W)
D3 (8-16W)
D4 (16-32W)
D5 (32-64W)
D6 (64-128W)
OIL - PCPS
D1 (2-4 W)
0.5008
0.0341
PCPS→OIL
OIL→ PCPS
OIL↔ PCPS
OIL→ PCPS
PCPS→OIL
PCPS→OIL
1.40331
6.91737
3.35778
2.59780
2.19078
0.27452
0.2466
0.0011
0.0355
0.0753
0.1127
0.7600
2.69674
2.10841
6.02137
1.53575
4.15943
2.1185
0.0682
0.1223
0.0026
0.2161
0.0161
0.0784
D2 (4-8W)
D3 (8-16W)
D4 (16-32W)
D5 (32-64W)
D6 (64-128W)
324
International Journal of Energy Economics and Policy | Vol 10 • Issue 5 • 2020
Hung: Identifying the Dynamic Connectedness between Propane and Oil Prices: Evidence from Wavelet Analysis
that crude oil and propane markets have conditional time-varying
dependence, and propane markets are found to have a strong
correlation with crude oil prices. Dahl and Oglend (2016) provide
evidence that the associations of oil and natural gas prices have
become unstable in Europe and the US in the current regime.
Oglend et al. (2015) reveal that the shale gas kindly provides
a natural experiment to assess the impact of a significant and
persistent supply shock on the LPG-oil relationship. Authors
also determine that there exists a bidirectional causal association
between the Propane, Butane prices, and oil prices. Ramberg and
Parsons (2012) have similar outcomes that crude oil and natural
gas prices are cointegrated at short investment horizons.
and PMB, PCPS, PAFEI prices. This reveals that an increase or
decrease in crude oil prices might cause a more considerable rise
or drop in the propane markets in three different locations and vice
versa. Because propane is often used as a petrochemical feedstock
in the petrochemical industry and naphtha exists as its substitute,
a dramatic drop in crude oil prices may make naphtha more cost-
competitive in comparison with propane, hence further dampens
the propane demand in the petrochemical use (Bai and Lam, 2019).
The implications of the economic connectedness are significant
on a practical perspective for the design of portfolios, asset
pricing, and risk management because they identify the profits of
diversification, the growth of asset pricing model, optimal time-
varying hedge ratios. Traders would use the indicated associations
to build up profitable trading strategies, whereas hedgers are able
to observe the commodity futures markets to conduct freight risk
management. Policymakers should take into account the dynamics
of return and volatility spillovers between crude oil and propane
markets to create sound policy based on a clear comprehension of
the transmission between these markets. For academics, it opens a
new research path to tag on investment opportunities and financing
decisions. It then allows for comparison with other markets as well
as different future energies that serve as investment instruments.
5. CONCLUSION AND RESEARCH
IMPLICATIONS
This paper investigates time-frequency connectedness between
crude oil prices and propane series in different locations. We have
employed MODWT, wavelet covariance, wavelet correlation,
continuous wavelet power spectrum, wavelet coherence spectrum,
and wavelet-based Granger causality test using the weekly data
from the period of 2006 to 2018, which allows us to examine co-
movement, volatility and lead-lag interdependency for different
investment horizons.
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