Wavelet analysis of impact of renewable energy consumption and technological innovation on CO 2 emissions: evidence from Portugal

Abstract

This paper uncover a new perception of the dynamic interconnection between CO2 emission and economic growth, renewable energy use, trade openness, and technological innovation in the Portuguese economy utilizing innovative Morlet wavelet analysis. The research applied continuous wavelet transform, wavelet correlation, the multiple and partial wavelet coherence, and frequency domain causality analyses are applied on variables of investigation using dataset between 1980 and 2019. The result of these analyses disclosed that the interconnection among the indicators progresses over time and frequency. The present analysis finds notable wavelet coherence and significant lead and lag interconnections in the frequency domain, while conflicting relationships among the variables are found in the time domain. The wavelet analysis according to economic viewpoint affirms that renewable energy consumption helps to curb CO2 while trade openness, technological innovation, and economic growth contribute to CO2. The outcomes also proposed that renewable energy consumption decreases CO2 in medium and long run in Portugal. Therefore, policymakers in Portugal should stimulate investment in renewable energy sources, establish restrictive laws, and enhance energy innovation.

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Environmental Science and Pollution Research
https://doi.org/10.1007/s11356-021-17708-8
RESEARCH ARTICLE
Wavelet analysis ofimpact ofrenewable energy consumption
andtechnological innovation on CO2 emissions: evidence
fromPortugal
Tomiwa SundayAdebayo1 · Seun DamolaOladipupo2 · IbrahimAdeshola3 · HusamRjoub4
Received: 25 August 2021 / Accepted: 18 November 2021
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
Abstract
This paper uncover a new perception of the dynamic interconnection between CO2 emission and economic growth, renewable
energy use, trade openness, and technological innovation in the Portuguese economy utilizing innovative Morlet wavelet
analysis. The research applied continuous wavelet transform, wavelet correlation, the multiple and partial wavelet coherence,
and frequency domain causality analyses are applied on variables of investigation using dataset between 1980 and 2019.
The result of these analyses disclosed that the interconnection among the indicators progresses over time and frequency.
The present analysis finds notable wavelet coherence and significant lead and lag interconnections in the frequency domain,
while conflicting relationships among the variables are found in the time domain. The wavelet analysis according to economic
viewpoint affirms that renewable energy consumption helps to curb CO2 while trade openness, technological innovation,
and economic growth contribute to CO2. The outcomes also proposed that renewable energy consumption decreases CO2
in medium and long run in Portugal. Therefore, policymakers in Portugal should stimulate investment in renewable energy
sources, establish restrictive laws, and enhance energy innovation.
Keywords CO2 emissions· Economic growth· Renewable energy consumption· Technological innovation· Partial and
multiple wavelet coherence
Introduction
Climate change is one of the globe’s most pressing concerns
in recent years, owing to its destructive effects on proper-
ties and human lives. Greenhouse gas (GHGs) emissions
are a major contributor to global warming (Acheampong &
Boateng, 2019; Adebayo & Kirikkaleli 2021). CO2 emis-
sions have garnered considerable attention as a metric of
pollution in the literature over the years (Akadırı etal.,
2021; Zhang etal. 2021). The research focuses on connec-
tion between CO2 and technological innovation in Portugal.
As potential factors of CO2, trade openness (TO), renewable
energy usage (REC), and economic expansion (GDP) are
all given a prominent role. Over the last several decades,
economic expansion has been the dominant cause of CO2
emissions. A reversed U-shape relationship exists between
ecological deterioration and GDP (Grossman & Krueger
1991). Environmental Kuznets curve (EKC) is the name of
the idea. According to the EKC, emerging nations, in par-
ticular, are confronted with the issue of ecological deteriora-
tion at the early phase of growth (Adebayo & Acheampong
Responsible Editor: Ilhan Ozturk
* Tomiwa Sunday Adebayo
twaikline@gmail.com
Seun Damola Oladipupo
seunlad50@gmail.com
Ibrahim Adeshola
deshyengr@live.com
Husam Rjoub
hrjoub@ciu.edu.tr
1 Department ofBusiness Administration, Faculty
ofEconomics andAdministrative Science, Cyprus
International University, 99040Nicosia, Turkey
2 Department ofEarth Science, Faculty ofScience, Olabisi
Onabanjo University, Ago-Iwoye, OgunState, Nigeria
3 Department ofInformation Technology, School
ofComputing andTechnology, Eastern Mediterranean
University, NorthCyprus, Mersin10, Turkey
4 Department ofAccounting andFinance, Faculty
ofEconomics andAdministrative Sciences, Cyprus
International University, Mersin 10, 99040Haspolat, Turkey

Environmental Science and Pollution Research
1 3
2021; Gyamfi etal. 2021; Sarkodie & Adams 2018). This is
because, in the early stages of economic progress, nations
utilize resources that have the potential to harm the environ-
ment. This pattern continues until a higher income level is
reached, at which point the development structure is trans-
formed to incorporate ecologically friendly resources includ-
ing renewable energies and innovative production processes.
Renewable energy has been shown in the literature to help
restore energy security and address climate change issues
(Alola etal., 2021; Pata 2021; Shahbaz etal. 2021). In sev-
eral cases, renewable energy sources could meet nearly half
of global demand of energy by 2050, avoiding dangerous
human disruption of the climate structure (Adedoyin etal.,
2020; Baloch etal. 2021; Solarin etal. 2017). Nations must
rearrange their energy sectors in order to reduce emissions
and manage climate change (Adewale Alola etal., 2021;
Shahbaz etal. 2018). There is consensus that energy-use
strategies should be updated to upsurge the percentage
of renewable energy sources in order to reduce pollution
(Anwar etal. 2021). In this way, energy policy would not be
jeopardized by trade openness.
Trade openness (TO) boosts economic growth by allow-
ing nations to take use of their comparative advantages in
terms of resource transfer. Based on the channel via which it
comes, it has a diverse influence on the ecosystem (Gyamfi
etal. 2020; Rjoub etal. 2021). The negative impact is mostly
due to lax environmental rules, which continue to draw pol-
luting industries. On the flipside, trade could draw some
businesses to nations where knowledge spillovers boost
cleaner manufacturing and, as a consequence, a healthier
environment (Sarkodie & Strezov, 2019). Furthermore,
international interrelations between multinational firms
and nations have facilitated the dissemination of technology
advancement into developing economies, which has sup-
ported the ecosystem preservation in some way.
As a consequence of the growing relevance of environ-
mental issues, a growing number of scholars are looking
at the impacts of technology innovation (TI) on CO2. It is
well recognized that TI has a substantial impact on CO2
emission mitigation. CO2 emissions have been decreased,
and environmental quality has improved in host nations as
a result of technological innovation paired with ecological
conservation measures. Numerous studies have examined
the interconnectedness between TI and CO2 (Adebayo &
Kirikkaleli 2021; Zhao etal. 2021). For instance, the studies
of Kihombo etal., (2021) and Udemba etal., (2021) estab-
lished that technological innovation improves the quality
of the environment. Contrarily, some studies found posi-
tive/insignificant interconnection between CO2 and TI. For
instance, the studies of Kumar & Managi, (2009) and Ade-
bayo & Kirikkaleli, (2021) for emerging nations and Japan
established that technological innovation mitigates environ-
mental quality. In light of mixed findings in literature, the
current research assesses the effect of TI and REC on CO2
as well as the role of GDP and TOP in Portugal.
Why Portugal? In 2020, Portugal contributed for around
1.6% of EU CO2 emissions. Portugal’s energy and climate
policy aim toward carbon neutrality and rapidly expanding
generation of renewable power, as well as improving energy
efficiency (IEA, 2021b). Energy import reliance is being
reduced, while cheap energy availability is being main-
tained. Portugal, in the long term, wants hydrogen to play
a significant role in reaching carbon neutrality. Although
Portugal has made significant improvement in electricity
generation decarburization, fossil fuels still lead the coun-
try’s energy mix (IEA, 2021b). To reach Portugal’s targets
for growing the percentage of renewables, cutting demand
of energy, and decreasing emissions, the transportation,
industrial, and construction sectors all have a lot of work
ahead of them. In 2019, imported fossil fuels constituted
for 76% of primary energy supply in Portugal (24% natural
gas, 6% coal, and 43% oil). Portugals GHG emissions have
increased by 13% from 2014 to 2018, owing to the upsurge
in economic activity and a high share of fossil fuels in its
energy supply (see Fig.1) (IEA, 2021b).
The paper contributes to the ongoing literature in the fol-
lowing ways: First, this paper quantitatively examines the
nexus between CO2 and TO, GDP, REC, and TI. A compre-
hensive analysis of the nexus between CO2 and TO, GDP,
REC, and TI in Portugal is thus very important to understand
the associated questions: Does REC aid in abating environ-
mental degradation? Do GDP and TO contribute to CO2
emissions? And, does TI affect CO2? These are all intercon-
nected issues that will require extensive research over a long
timeframe. To the understanding of the authors, no research
has comprehensively examined all of these variables, par-
ticularly for Portugal. As a result, a thorough investigation
into the interconnectedness between CO2 and the regressors
is critical. Second, the vast majority of empirical investiga-
tions utilized approaches such as general method of moments
(GMM), dynamic ordinary least square (DOLS), ordinary
least square (OLS), autoregressive distributed lag model
(ARDL), vector error correction model (VECM) and many
more, which restrict the efficacy of environmental policy
information. As a result, the present research uses a wavelet
analysis framework to investigate data’s frequency domain
properties over time and identify time-localized informa-
tion (Aguiar-Conraria & Soares, 2011). Morlet wavelet is a
wavelet technique which “produces information on the phase
and amplitude, both vital to research synchronism between
different time-series” which “links the relationship of these
variables with each other and its progression over time”
(Sharif etal. 2019).
Wavelets’ capacity to expose hidden processes of devel-
oping cyclic trends, patterns, and non-stationarity, which are
typical of financial and economic time series, is one of its

Environmental Science and Pollution Research
1 3
main advantages. This method is also useful for simulating
economic processes in which economic agents have diverse
term (horizon) objectives (Mutascu, 2018). The wavelet
analysis provides a more insightful understanding of the
relationships between the variables under consideration,
such as whether they represent a short-term or long-term
reaction, whether the correlations are positive or negative,
and which indicators are leading or lagging. The wavelet
approach also allows for more exact timing of shocks that
produce shifts in rhythm of the cross-country business cycle.
This information has significant policy implications on how
to speed up the growth of renewable energy in Portugal by
creating and coordinating appropriate economic develop-
ment and trade openness policies.
The remainder of the paper is laid out as follows: “Syn-
opsis of related studies” section presents literature review
which is followed by methodology in “Data and methodol-
ogy” section. The findings are presented in “Data analysis
and discussion” section and “Conclusion and policy direc-
tion” section concludes the research.
Synopsis ofrelated studies
This section of the empirical analysis presents the summary
of studies on the effect of renewable energy consumption,
economic growth, technological innovation, and trade open-
ness on CO2 emissions.
Impact ofeconomic growth onCO2 emission
Over the years, significant studies have been conducted
regarding the association between CO2 and GDP. However,
mixed findings have surfaced based on techniques,
approaches, timeframe and country/countries of inves-
tigation. For example, the research of Akinsola etal.,
(2021) on the nexus between CO2 and economic growth
in Indonesia using the wavelet tools reported positive co-
movement between CO2 emissions and economic growth.
Similarly, Alola etal., (2021) examined the interconnect-
edness between GDP and CO2 in China using dataset from
1971 to 2016. Their outcomes utilizing the QQR technique
revealed that at all quantiles (0.1–0.95), the effect of eco-
nomic growth on CO2 emissions is positive suggesting
that economic expansion impedes environmental quality in
China. Likewise, using the novel dual gap approach, Kirik-
kaleli etal., (2021) scrutinized the nexus between CO2 and
growth in Turkey utilizing data stretching between 1971
and 2017, and their outcome revealed that environmen-
tal degradation in Turkey is caused by Turkey pro-growth
agenda. Furthermore, He etal., (2021) investigated the
association between GDP growth and CO2 emissions in
Mexico utilizing the novel dual gap and frequency domain
causality approaches from 1990 to 2018. Their finding dis-
closed that economic expansion leads to increase in envi-
ronmental deterioration in Mexico. Contrarily, some stud-
ies found negative interconnectedness between CO2 and
GDP. For instance using the novel quantile-on-quantile
approach, Rjoub etal., (2021) examined the interconnect-
edness between CO2 and GDP in Sweden between 1965
and 2019. Their empirical outcomes revealed that eco-
nomic growth reduces CO2 emissions suggesting that Swe-
den growth is sustainable. Similarly, the study of Usman
in the USA suing dataset from 1984Q1 to 2014Q4 and
ARDL approach reported that increase in GDP mitigates
CO2 in the USA.
Fig. 1 Trends in total energy
supply (TES) by source in Por-
tugal. Source: (IEA, 2021a)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1990 1995 2000 2005 2010 2015 2020
% of ecruosyb)SET(ylppusygrenelatoT
Coal Hydro Wind, solar, etc. Biofuels and waste Oil Natural gas

Environmental Science and Pollution Research
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Impact oftechnological innovation on CO2
emissions
Recently, technological innovation has been incorporated
as a new indicator into the growth-environment framework,
as it is recognized as an important component in the reduc-
tion of CO2 globally. For example, Kirikkaleli & Adebayo,
(2020) examined the nexus between technological innova-
tion and CO2 emissions within the global context from 1990
to 2018. The authors applied the DOLS and spectral cau-
sality approaches to examine this interconnectedness and
the outcome uncovered that TI curbs CO2. Similarly, Khan
etal., (2020) assessed the connection between technologi-
cal innovation and CO2 emissions in China using dataset
from 1970 to 2017. Using the ARDL approach, their find-
ing shows that TI abates CO2. Moreover, Kihombo etal.,
(2021) assessed the influence of TI on CO2 in West Asia
and Middle East nations from 1990 to 2017, and their find-
ing showed that TI decreases CO2. On the contrary, some
studies established positive/insignificant connection between
technological innovation and CO2 emissions. For example,
the study of Adebayo & Kirikkaleli, (2021) on the intercon-
nection between CO2 and technological innovation reported
that increase in technological innovation mitigates environ-
mental quality in Japan. Similarly, the research of Udemba
etal., (2021) reported that positive (negative) shifts in
technological innovation increase (decrease) technological
innovation using dataset from 1990 to 2018 and nonlinear
ARDL approach.
Impact ofrenewable energy consumption on CO2
emissions
Global CO2 is now related to several sectors of the econ-
omy. As a result, measuring environmental degradation in
the growth-energy-emission nexus has progressed beyond
just exploring the link between GDP and emissions. Renew-
able energy sources have long been recognized as having
the capacity to cut CO2 emissions and promote a more
environmentally friendly atmosphere, according to climate
change experts. Several studies in the literature have taken
renewable energy into account. For example, Kirikkaleli &
Adebayo, (2021) examined the nexus between REC and CO2
emissions in India using dataset from 1990 to 2018, and
their finding disclosed that increase in REC curbs CO2 in
India. Likewise, Pata, (2021) study on the interconnection
between REC and CO2 emissions in China with the EKC
framework from 1980 to 2016 revealed that REC plays a
crucial role in combating CO2 emissions suing the ARDL
approach. Similarly, Pata & Aydin, (2020) scrutinized the
influence of renewable energy on CO2 in the BRICS nations
from 1971 to 2016 using the Fourier ADL cointegration dis-
closed that renewable energy use curbs emissions of CO2 in
the selected nations. Radmehr etal., (2021), using dataset
from 1995 to 2014 GS2SLS method, explored the interrela-
tionship between REC and CO2 emissions, and their finding
showed that renewable energy Granger causes CO2 emis-
sions which infers that renewable energy can predict CO2
emissions. Likewise, using the novel QQ approach, Sharif
etal., (2021) assessed the connection between REC and
CO2 in the USA, and their findings unveiled that renewable
energy use abates CO2 emissions. Likewise, the research of
Yuping etal., (2021) in Argentina reported that renewable
energy use impacts CO2 emissions negatively.
Impact oftrade openness on CO2 emission
Trade openness is a new addition to the growth-emissions
relationship. After disaggregating trade into import and
export, Salman etal., (2019) discovered that export boosts
CO2 in various Asian nations. Moreover, Mutascu, (2018)
utilized disaggregated trade (import and export) to assess
the association between trade openness and CO2 emissions
in France between 1960 and 2016 using the wavelet tools.
The author finding disclosed that imports increase CO2
emissions while exports mitigate CO2 emissions. Moreo-
ver, Orhan etal., (2021) assessed the effect of trade open-
ness on CO2 emissions in India from 1960 to 2019 using the
wavelet tools, and their findings disclosed that trade open-
ness triggers CO2 emissions, thus, validating the pollution-
haven-hypothesis (PHH) for India. Moreover, the study
of Dauda etal., (2021) on the trade-CO2 nexus in Africa
reported that trade openness contributes to environmental
degradation. Contrarily, some studies established negative
relationship between CO2 emissions and trade openness.
For instance, Essandoh etal., (2020) pinpoint that trade
decreases CO2 emissions in advanced nations by assessing
the nexus between CO2 and trade openness in 52 advanced
and emerging nations between 1991 and 2014. According
to the research, knowledge spillover from trade reduces
emissions across nations. When absorption capacities are
built via human capital and other mechanisms to channel
it into the economy, nations can completely profit from the
spillover.
Theoretical framework
The environmental Kuznets curve (EKC) concept has been
used widely in the literature to investigate the relationship
between economic growth and ecological deterioration.
According to the EKC, the environment worsens as real
output rises until a certain level of economic expansion is
reached, at which point pollution begins to decline as per
capita GDP rises, resulting in an inverted U-shape connec-
tion (Grossman & Krueger 1991). This is due to people’s

Environmental Science and Pollution Research
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demands for governments to enact strict ecological rules in
effort to enhance a green environment. Individuals with a
higher income level are more worried about their health and,
as a result, want a better environment, which typically leads
to governmental actions to promote a healthy environment
and reduce emissions. Again, at a higher degree of develop-
ment, the economy’s composition shifts away from very pol-
luting industries and toward innovative and service-oriented
industry, which has lower pollution levels.
It is well recognized that TI has a significant impact on
CO2 reduction. CO2 emissions have been minimized, and
the quality of the environment in host nations has improved
as a result of technological innovation paired with environ-
mental conservation activities. Technological advancements
are critical in reducing emissions while also assisting in
energy conservation. Moreover, technological innovation is
required for the most efficient use of traditional and renew-
able energy sources. Renewable energy sources can also be
developed with the assistance of technological innovation.
Technological advancements also boost renewable energy
potential, increasing the probability that renewable energy
will be available to satisfy future energy demand. Because
of the rising need for energy, it is commonly believed that
renewable energy will become the most important source
of energy in the future, and it is also an ecologically benign
source of energy.
The impact of trade openness is broken down into three
categories: scale, composition, and technique (Farhani
etal., 2014). In general, the scale effect demonstrates that
increased trade volume has an influence on output, con-
sumption of energy, and, as a result, upsurge CO2. The
re-assignment of exchanged products or resources is part
of the composition stage. In terms of the technique effect,
trade openness usually leads to a healthier ecosystem as a
consequence of improved industrial processes as a result of
technical innovation and efficient energy use, both of which
are generally connected with cross-national trade. The envi-
ronment is affected in two ways by trade openness. When
polluting companies seek shelter in areas with low environ-
mental restrictions, their activities most often increase CO2
emissions, which is known as the pollution haven hypothesis
(PHH). When the host nation benefits from environmentally
friendly knowledge spillovers from trade, nevertheless, it
increases quality of the environmental. This scenario is
regarded as pollution halo hypothesis. The paper theoreti-
cal model is framed centered on the above discussions as
follows:
where, GDP, REC, CO2, TO, and TI stand for economic
growth, renewable energy use, CO2 emissions, trade open-
ness, and technological innovation respectively.
Data andmethodology
Data
The present study dataset is comprised of selected variables,
such as, carbon emissions (CO2), economic growth (GDP),
renewable energy use (REC), technological innovation (TI),
and trade openness (TO) in Portugal. The description of data
and source is depicted in Table1. The current research uti-
lized the quadratic match-sum method (Anwar etal. 2021;
Shahbaz etal. 2018) to convert annual data into quarter fre-
quency. As data is converted from low to high frequency,
this process adjusts for seasonal deviations by removing
point-by-point data deviations (Ozturk & Acaravci, 2016).
For empirical analysis, quarterly data of China has taken
over the period of 1980–2018. To obtain the return series,
the data is turned into a natural logarithmic difference series
in order to make our result more comparable (Awosusi etal.,
2021).
Methodology
Wavelet transform
To expand the boundaries of the Fourier transform, the
wavelet transform method was introduced. The Fourier
transform is constrained by the fact that the time series under
examination should be cyclic, and it presupposes that occur-
rences do not spread over distinct time intervals, among
(1)
𝐂𝐎2=𝐟(GDP,REC,TI,TO )
Table 1 Variable unit and
source
BP and WDI denote British Petroleum and World Development Indicator, respectively.
Indicators Description Units Source
CO2CO2 emissions Metric tons per capita BP
GDP
Economic growth GDP per capita (constant 2010 US$) WDI
REC
Renewable energy consumption Renewable energy consumption per capita (kWh) BP
TI
Technological innovation Total number of patent applications (registered by
residents and non-residents)
WDI
TO Trade openness Sum of exports and imports as a share of GDP WDI

Environmental Science and Pollution Research
1 3
other things (Ramsey & Lampart 1998). Wave-like oscil-
lations regularly change the arrangement of the bands from
top to bottom or bottom to top. This is due to the presence of
short time periods at a high rate, as well as progressive time
dilatation or wrapping, as opposed to a variety of iterations
in the attuned mode, which is produced by detaching the
interval phase into a succession of gradually short sectors.
Continuous wavelet transform (CWT)
This kind of wavelet transfiguration
Wx(m,n)
is initiated
by assessing a definite wavelet ψ (.) against the time series
x(t)∈L2(
ℝ
),
i.e.,
A crucial characteristics of the CWT is its capability to
decay and after that successively clearly rebuild a time series
x (t) ∈ L2 (ℝ):
Furthermore, the CWT retains the power of the time
series under consideration, and the equation is as follows:
The current study utilized the features to explain WTC,
which measures the extent of the intuitive connection
between two indicators.
Wavelet coherence (WTC)
Wavelet coherence (WC) is a bivariate model for studying
the connection between two time series. In support of a
proper description of WTC, the WTC can identify places in
the time and frequency gap where the studied time period
demonstrates instantaneous fluctuation but lacks a large
common control. The modified wavelet coherence coeffi-
cient model can be expressed as follows, according to Tor-
rence & Compo, (1998).
where the smoothing tool is depicted by R. The series of
coefficient in terms of wavelet coherence squared falls in
the range 0 ≤ R2(m, n) ≤ 1. Weak correlation is depicted by
values close to zero while value close to 1 depicts strong
(2)
W
x(m,n)=∫∞
∞
x(t)1

n
𝜑
−

t−m
N

dt
.
(3)
x
(t)=1
C
𝜑
∫
∞
0
[
∫
∝
−∞
Wx(m,n)𝜑m,n(t)dtu
]
dn
N2,N>
0.
(4)
∥
x∥2=1
C
𝜑
∫
∞
0
[
∫
∝
−∞
IWx(m,n)I2dm
]dn
N
2
(5)
R
2(m,n)=N

N−1Wxy(m,n)


2
N

N−1

Wx(m,n)

2

N

N−1

Wy(m,n)

2

correlation. As a result, squared wavelet coherence is
equal to the correlation coefficient squared in linear regres-
sion since it interacts via the indigenous linear connection
between stationary series of two variables at each scale.
Partial wavelet coherence (PWC)
PWC is a method that is similar to PC. PWC is analyzed
using the wavelet transfiguration method. The approach
identifies WC for x2 and x1 series after canceling the effect
of x3. The PWC is shown by the equations below:
The PWC is based on a linear relationship (by remov-
ing × 3 influence). The following is a representation of the
PWC;
When the influence of x3 is eliminated, as indicated by
(Mutascu, 2018), a low PWC indicates that series x2 has
little impact on x1..
Multiple wavelet coherence (MWC)
The MWC approach is sufficient for evaluating the coher-
ency of multiple indicators with another control indicators.
The MWC is shown in the equation below:
(6)
R
(x1,x2)=
S[W
(
x1,x2
)
]
√
S
[
W
(
x1
)]
,S[W
(
x2
)
]
;
(7)
R2(
x1,x2
)
=R
(
x1,x2
)
∙R
(
x1,x2
);
(8)
R
(x1,x3)=
S[W
(
x1,x2
)
]
√
S
[
W
(
x1
)]
,S[W
(
x3
)
]
;
(9)
R2(
x1,x3
)
=R
(
x1,x3
)
∙R
(
x1,x3
);
(10)
R
(x2,x3)=
S[W
(
x2,x2
)
]
√
S
[
W
(
x2
)]
,S[W
(
x3
)
]
;
(11)
R2(
x2,x3
)
=R
(
x2,x3
)
.R
(
x2,x3
);
(12)
RP
2
(
x1,x2,x3
)
=
|
|
|
R
(
x1,x2
)
−R
(
x1,x2
)
.R(x1,x2)∗
|
|
|
[1−R(x1
−
x3)]2[1−
(
x3−x2
)
]2
(13)
RM
2
(
x1,x2,x3
)
=
R
2(
x1,x2
)
+R
2(
x1,x3
)
−2Re[R
(
x1,x3
)
∗R(x3,x2)
∗]
1−R2(x
3
,x
2
)

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By employing two separate predictor time series x2 and
x3 at a time and frequency relationship, the overhead equa-
tion produces the results, squared wavelet coherence, that
describe the amount of wavelet power of the criteria times
series x1 that is comprehensible. The statistical significance
level of wavelet coherence, as well as multiple and partial
wavelet coherence, is calculated using the Monte Carlo
approach, as previously stated.
Frequency domain causality (FDC)
The paper also identifies the causal influence of TI, REC,
GDP, and TO on CO2 at various frequencies. Therefore, we
applied the Breitung & Candelon, (2006) frequency domain
causality. “The key distinction between the time domain
method and the frequency-domain method is: the ‘time-
domain’ method informs us where a particular change arises
inside a time series, while the ‘frequency-domain’ method
evaluates the extent of a specific variation in time series”
(Adebayo & Beton Kalmaz 2020). The frequency domain
causality test is illustrated as follows. The test is based on a
rebuilt VAR between x and y, denoted as follows:
The AIC is employed selection of lag
l
. The null hypoth-
esis (M) that
My
→
x(ω)=0
is centered on Geweke, (1982)
where
𝜔𝜀(0, 𝜋)
stands for the frequency, and the null Ho is
illustrated as follows:
The vector connected to the y coefficients is represented
by
𝛽
.
The Ho depicts that, X does not cause Y at all frequen-
cies. Furthermore, the 5% and 10% level of significance is
based on Breitung & Candelon, (2006) for all frequencies
in the interval (0,π). Frequency ω is associated to period t
as
t=2𝜋∕𝜔
.
Data analysis anddiscussion
Description ofData
This research tends to scrutinize the time–frequency cau-
sality between CO2 emissions and economic growth, trade
openness, renewable energy use, and technological innova-
tion. Descriptive statistics are used in prior empirical investi-
gations to examine and comprehend the univariate properties
of understudy parameters. Table2 unveils the descriptive
(14)
xt=θ
1xt−1+
⋯
+θ
1xt−1+
𝛽
1yt−1+
⋯
+β
lyt−1+
𝜀
t
(15)
H0∶R(𝜔)𝛽=0
(16)
R
(𝜔)=
cos(𝜔)cos(2𝜔)…cos(l𝜔)
sin(𝜔)sin(2𝜔)…sin(lw)
statistics outcomes, and it can be seen that the GDP mean
value is the highest which is followed by technological
innovation, trade openness, CO2 emissions, and renewable
energy. The standard deviation demonstrates how concen-
trated the data are around the mean; the smaller the stand-
ard deviation, the more concentrated the data are. Based on
this logic, trade openness is more concentrated around its
mean which is followed by economic growth, CO2 emis-
sions, renewable energy use, and technological innovation.
The Jarque–Bera test demonstrates that all of the variables
under investigation are non-normal. This suggests that non-
linear estimating, such as wavelet, is appropriate in this case
(Adebayo & Rjoub 2021; Odugbesan etal. 2021). Figure2
further depicts the descriptive statistics.
Wavelet transform
It can be deduced from the graph of the time series of these
five variables that the shape and trend are unpredictable,
with abrupt dips and spikes in time. With the naked eye, it
Table 2 Descriptive statistics
CO2GDP REC TI TO
Mean 1.5426 9.6976 1.2855 6.4198 4.1813
Median 1.6027 9.8245 1.2677 6.4910 4.1514
Maximum 1.9073 9.9869 2.1257 8.3501 4.4644
Minimum 0.9969 9.2800 0.3774 4.9599 3.9795
Std. dev 0.2760 0.2222 0.4634 1.0592 0.1324
Skewness − 0.7700 − 0.7679 0.1215 0.1335 0.6059
Kurtosis 2.3789 2.1527 2.1624 1.6356 2.4618
Jarque–Bera 18.385 20.509 5.0702 12.886 11.721
Probability 0.0001 0.0000 0.0792 0.0015 0.0028
-2
0
2
4
6
8
10
Mean
Median
Std. Dev. Skewness
Kurtosis
CO2 GDP RECTI TO
Fig. 2 Rader chart

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is difficult to study any evident cyclic or periodic tendency.
To investigate the concealed trends in these indicators, the
wavelet transform is applied. Wavelet transform’s built-in
multiresolution analysis aids in isolating and localizing
effects that might otherwise go unnoticed. The Morlet wave-
let transform outcomes for these five indicators are shown
individually below. Figure3 a–e illustrate the wavelet trans-
formation for CO2, GDP, TI, TO, and REC up to a level of
6. The graphs uncover meticulous coefficients as illustrated
by d1 to d6 and smooth element as shown by s6. The detail
parts are the high-frequency variations in the data which are
gathered and plotted overtime, while the smooth part is the
low-frequency variation in the original data. CO2.d1, GDP.
d1, TO.d1, TI.d1, and REC.d1 unveil the highest variations
of frequency in the original graph of CO2, GDP, TO, TI,
and REC data as shown in Fig.3a–e. It demonstrates those
discrepancies in CO2, GDP, TO, TI, and REC data over this
timeframe with the highest occurrence. Likewise, d2 to d6
uncover disparities of CO2, GDP, TO, TI, and REC values
with occurrence frequency getting halved with graphs. This
means that d2 depicts the temporal response of data with
an occurrence frequency half that of d1 and so on, all the
way to d6. It is worth noting that as we proceed from d1 to
d6, the changes of these parts in time get smoother, indicat-
ing that they show substantial patterns over time that can
be connected with other variables. The smooth part in the
Fig. 3 a CO2 emissions wavelet transform. b Economic growth wavelet transform. c Renewable energy consumption wavelet transform. d Tech-
nological innovation wavelet transform. e Trade openness wavelet transform

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underlying data is seen in CO2.s6, GDP.s6, TO.s6, TI.s6,
and REC.s6.
Wavelet correlation
The wavelet correlation between CO2 emissions and eco-
nomic growth, renewable energy usage, trade openness, and
technological innovation is shown in Fig.4a–d. The study
is carried out utilizing the Monte Carlo approach on four
distinct wavelet scales ranging between 1 and 16. If the
correlation value is close to zero, there is no dependence
between the variables under investigation. The closer the
value gets to 1, the stronger the correlation, indicating that
the two variables are linked. A negative correlation denotes
a dependency in the opposite direction. The analysis is car-
ried out for increasing wavelet scales, which extracts the
data’s underlying hidden information. The resolution of
analysis rises as the scale grows, implying that we evaluate
localized alterations in time. The following are some obser-
vations on the findings obtained for various correlations
between the variables. (i) There is indication of increas-
ing positive and significant correlation between CO2 and
economic growth as we move to higher scale. This implies
that these two variables are interdependent at dependent in
localized time periods. (ii) There is negative and significant
correlation between CO2 and renewable energy across all the
scales. This implies that these two variables move in oppo-
site direction. (iii) There is indication of decreasing positive
and significant correlation between CO2 and technological
innovation as we move to higher scale. (iv) There is a weak
ad positive correlation between CO2 and trade openness in
scales 1–8; however, in scales 8–16, there is weak evidence
of negative correlation between trade openness and CO2.
It can be claimed that CO2 and GDP, TO, TI, and REC all
show interdependency. Moreover, CO2 and TO, GDP, and
TI show positive and significant dependency while there is
evidence of negative dependency between CO2 and REC.
Continuous wavelet transform
The present research utilized the continuous wavelet trans-
form to capture the volatility in CO2 emission, economic
growth, technological innovation, and renewable energy
use. The 5% significance threshold is indicated by the black-
ringed area. Outside of the black contour, the region sur-
rounded by cone splits is weakened by edge effects. Blue
ab
cd
Fig. 4 a WC between CO2 and GDP. b WC between CO2 and REC. c WC between CO2 and TI. d WC between CO2 and TO

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denotes low power, whereas red denotes great power. The
frequency axis is on the Y-axis, while the time scale is on
the X-axis. The diagram depicts the edge effect as a lighter
shade. The continuous wavelet transform outcomes for these
five variables are shown in Fig.5a–e. A time–frequency
analysis of the indicators is depicted in the colored graph.
The x-axis represents the time or sample, while the y-axis
represents the period. The cone of influence is depicted in
the figure, demonstrating that the transform coefficients are
trustworthy throughout the region. The wavelet transform’s
scale is indicated on the right side. The variables’ time and
frequency localization are depicted in these graphs. The
major areas of importance are the yellow regions encircled
by a blue-yellow outline. These regions show the frequency
parts on the left-hand period scale and their presence in
the sample data on the right-hand x-axis scale. The areas
with dark red zones are surrounded in all of these figures
for GDP, CO2 emissions, technological innovation, trade
openness, and renewable energy. These circular circles also
demonstrate that these are the places where the data streams
have the most energy.
Figure5 a shows the wavelet power spectrum (WPS) for
CO2. In the 1985–1990 period of scales 8–32 quarterly, there
is volatility. Furthermore, the WPS of GDP is shown by
Fig.5b, and there is no significant volatility between the
periods of study. Moreover, Fig.5c unveiled the WPS of
REC. At period of scales 4–8 quarterly, between 1989 and
2019, there is proof of volatility. Figure5 d shows evidence
of volatility for TI at period of scales 4–16 from 1990 to
2015. Lastly, Fig.5c unveiled the WPS of TO. At period of
scales 16–32 quarterly, from 1989 to 1995 and from 2012 to
2016, there is proof of volatility. The continuous dependence
on nonrenewable energy may be attributed to this volatil-
ity. Portugal continues to rely on imported fossil fuels. For
instance, fossil fuel constitutes 76% of its primary energy
supply in 2019. On the other hand, over the years, Portugal
has also accomplished high shares of renewable energy. For
instance, in 2019, renewable energy comprises for 30.6%
of gross final energy demand (IEA 2020). According to the
United Nations Conference on Trade and Development, Por-
tugal is placed 32nd out of 158 nations in the Readiness for
Frontier Technologies Index.
Wavelet coherence
Figure6 a–d unveil the wavelet coherence (WTC) between
CO2 emissions and the regressors (economic growth, trade
openness, renewable energy use, and technological innova-
tion). The direction of coherence on the time–frequency
scale is shown, as well as the connection between the pairs
a
de
bc
Fig. 5 a WPS of CO2. b WPS of GDP. c WPS of REC. d WPS of TI. e WPS of TO

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of these variables. The rightward-up (leftward-down) arrows
show positive coherence with second variable leading while
rightward-down (leftward-up) arrows show negative coher-
ence with the first variable leading. Figure6 a presents the
WTC between CO2 and GDP. At period of scales 0–32 quar-
terly from 1981 to 1990, the majority of the arrows are right-
ward-up which suggest positive coherence between CO2 and
GDP with GDP leading. Furthermore, there is insignificant
coherence from 1995 to 2018. Figure6 b shows the WTC
between CO2 and REC. At period of scales 0–16 quarterly,
there is evidence of negative comovement between CO2 and
REC between 1985 and 2018, as disclosed by the leftward
arrows. Furthermore, the leftward-down arrows disclosed
that REC leads CO2 emissions. Figure6 c presents the WTC
between CO2 and TI. Between 1985 and 1988, at period of
scales 0–8 quarterly, the variables are out-of-phase (negative
correlation) with TI leading. Furthermore, between 1990 and
2015, at period of scales 0–16 quarterly, the arrows are right-
ward which suggests that the variables are in-phase (positive
coherency). Moreover, majority of the arrows are rightward-
up which implies that TI leads CO2. Lastly, Fig.6b presents
the WTC between CO2 and TO. Between 1990 at period of
scales 16–32 quarterly, the variables are in-phase (positive
coherence) from 1990 to 2000 are revealed by the rightward
arrows. Moreover, the rightward-up arrows show that TO
leads CO2.
Partial wavelet coherence
We proceed by applying the partial wavelet coherence
(PWC) as a robustness check for the wavelet coherence
(WTC). Figure7 a presents the PWC between CO2 and
GDP with the REC influence canceled. At period of scales
0–8 quarterly, there is significant coherence between CO2
and GDP with REC effected annulled. Furthermore, Fig.7b
presents the influence on GDP on CO2 with effect of TI dis-
regarded. Between 1985 and 1990 at period of scales 16–32,
there is strong coherence between CO2 and GDP with TI
influence canceled. Moreover, the effect of REC on CO2
with GDP canceled is presented by Fig.7c. At period of
scales 4–16 quarterly, between 1990 and 2018, we observed
significant coherence between CO2 and REC with GDP
effect neglected. Furthermore, Fig.7d presents the effect of
REC on CO2 with TI impact neglected. At period of scales
ab
cd
Fig. 6 a WCT CO2 and GDP. b WCT CO2 and REC. c WCT CO2 and TI. d WCT CO2 and TO

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0–16, from 1990 to 2018, we noticed a significant coherence
between CO2 and REC with TI influence neglected.
Figure7 e presents the PWC between CO2 and REC
with the TO influence canceled. At period of scales 0–16
quarterly, from 1990 to 2018, there is significant coher-
ence between CO2 and REC with TO effect annulled. Fur-
thermore, Fig.7f presents the influence on REC on CO2
with effect of GDP disregarded. From 1998 to 2002, and
2005–2010 at period of scales 0–16, there is strong coher-
ence between CO2 and TI with GDP influence canceled.
Moreover, Fig.7g presents the influence on TI on CO2 with
effect of REC disregarded. From 1981 to 1984, 1991–2000,
and 2004–2015, at period of scales 0–16, the influence of TI
on CO2 is strong with REC effect disregarded.
Additionally, the effect of TI on CO2 with TO influence
canceled is presented by Fig.7h, and the outcomes unveiled
significant coherence between TI and CO2 with TO effect
canceled from 1990 to 1994, and 2004–2008. Moreover, the
effect of TO on CO2 with GDP canceled is presented by
Fig.7i, and the outcomes unveiled insignificant coherence
between CO2 and TI with REC influence neglected. Moreo-
ver, the effect of TO on CO2 with GDP canceled is presented
by Fig.7j, and the outcomes unveiled insignificant coher-
ence between CO2 and TI with REC influence neglected.
At period of scale 32 quarterly, between 1990 and 1995, we
observed significant coherence between CO2 and TO with
REC effect neglected as depicted by Fig.4k. Furthermore,
Fig.4l presents the effect of TO on CO2 with TI impact
neglected. The outcomes unveiled insignificant coherence
between CO2 and TO with TI influence neglected.
Multiple wavelet coherence (MWC)
We also applied the multiple wavelet coherence to capture
the influence of x2 on x1 with the influence of x3 considered.
Figure8 a presents the effect of GDP on CO2 with the effect
of REC considered. At period of scales 0–32, the effect of
GDP on CO2 is significant with the effect of REC taken into
account from 1980 to 2018. Moreover, Fig.8b shows the
influence of GDP on CO2 with the TI influence taken into
consideration. At period of scales 0–32 quarterly, there is a
strong coherence between CO2 and GDP with TO impact
considered from 1980 to 2018 as revealed by Fig.8c. Fur-
thermore, Fig.8d presents the REC effect on CO2 with the
abc
def
Fig. 7 a PWC CO2-GDP-REC. b PWC CO2-GDP-TI. c PWC CO2-GDP-T0. d PWC CO2-REC-GDP. e PWC CO2-REC-TI. f PWC CO2-REC-
TO. g PWC CO2-TI-GDP. h PWC CO2-TI-REC. i PWC CO2-TI-TO. j PWC CO2-TO-GDP. k PWC CO2-TO-REC. l PWC CO2-TO-TI

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TI effect taking into account. At period of scales 0–32, there
is significant comovement between REC and CO2 with the
effect of TI considered. At period of scales 0–32 quarterly,
there is a strong coherence between CO2 and REC with TO
impact considered from 1980 to 2018 as revealed by Fig.8e.
Lastly, Fig.8f presents the effect of TO on CO2 with the
effect of TI considered. At period of scales 0–32, the effect
of TO on CO2 is significant with the effect of TI taken into
account from 1980 to 2018.
Frequency domain causality (FDC)
The present research applied the frequency domain causality
(FDC) suggested by Breitung & Candelon, (2006) to capture
the causal effect of renewable energy use, trade openness,
renewable energy use, and economic growth on CO2 emis-
sions. The outcomes of the FDC are presented in Fig.9a–d.
Figure9 a presents the causal effect of GDP on CO2 emis-
sions. In the long and medium term, the null hypothesis of
“no causality” is rejected at significance level of 5% and
10% respectively. Furthermore, the causal effect from renew-
able energy to CO2 emissions is presented in Fig.9b. The
outcome disclosed that in the long term, the failure to accept
the null hypothesis of “no causality” at significance level of
5% and 10% respectively. Also, Fig.9c presents the causal
interconnection from trade openness to CO2. We failed to
reject the null hypothesis of “no causality” from trade open-
ness to CO2. Lastly, Fig.9d presents the causal effect of
technological innovation on CO2 emissions, and we reject
the null hypothesis of “no causality” from technological
innovation in the medium and short term respectively.
Discussion offindings
This section of the paper presents discussion on the inter-
relationship between CO2 emission and economic growth,
technological innovation trade openness, and renewable
energy use in Portugal utilizing dataset from 1980 to 2019.
The study utilized batteries of wavelet tools-wavelet correla-
tion, wavelet coherence, continuous wavelet transformation,
partial wavelet, and multiple wavelet coherence approaches.
The outcomes of the wavelet transform revealed high dis-
crepancies in all the variables in the short term; however, as
we move into the medium and long term, the variables (CO2,
ghi
jkl
Fig. 7 (continued)

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GDP, TO, TI, and REC) become more stable. Moreover, we
applied the wavelet correlation test to assess the correlation
between CO2 and the independent variables (CO2, GDP, TO,
TI, and REC), and the outcomes show that at all scales, there
is evidence of positive correlation between CO2 emissions
and trade openness, economic growth, and technological
innovation while negative correlation was observed between
CO2 and renewable energy use at all scales. We proceed by
exploring the volatility in all the variables using the continu-
ous wavelet transformation, and the outcome shows evidence
of volatility in CO2 emissions from 1985 to 1990 at period
of scales 8–32 quarterly, renewable energy use from between
1989 and 2019 at period of scales 4–8 quarterly, technologi-
cal innovation from 1990 to 2015 at period of scales 4–16
quarterly, and trade openness from 1989 to 1995 and from
2012 to 2016 at period of scales 16–32 quarterly.
Furthermore, we applied the wavelet coherence (WTC) to
capture the causal interrelation and lead/lag relationship. The
outcomes of the WTC revealed that at all frequencies (short
and long term), there is negative coherence between CO2
emissions and renewable energy consumption. This finding
shows that renewable energy reduces emissions and hence
has the potential to contribute to a cleaner environment. As
a result, measures aimed at mitigating climate change should
primarily focus on renewable energy, which is ecologically
friendly. This outcome corroborates the studies of Yuping
etal., (2021) for Argentina, Pata (2021) for the USA, and
Solarin etal. (2017) who reported that renewable energy use
curbs CO2 emissions while the studies of Alola etal. (2021)
for China and Dauda etal. (2021) established that renewable
energy use aggravated environmental degradation. Moreo-
ver, we observed positive coherence between CO2 emissions
and economic growth at all frequencies between 1985 and
1995 suggesting that economic expansion caused increase
in CO2 emissions; however, from 2000 to 2019, there is
weak and insignificant coherence between CO2 emissions
and economic growth. This implies that growth drives CO2
emissions which complies with the studies of Awosusi etal.
(2021) for South Korea, Orhan etal. (2021) for India, and
Soylu etal. (2021) for China who reported negative comove-
ment between economic growth and CO2 emissions. In addi-
tion, we observed weak and positive coherence between
trade openness and CO2 emissions in the short and medium
term; however, in the long term, there is evidence of weak
coherence between CO2 emissions and trade openness. This
implies that in the short and medium term, trade openness
abc
def
Fig. 8 a MWC CO2-GDP-REC. b MWC CO2-GDP-TI. c MWC CO2-GDP-TO. d MWC CO2-REC-TI. e MWC CO2-REC-TO. f MWC CO2-
TO-T1

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contributes to environmental degradation while in the long
term, no significant association was observed between CO2
emissions and trade openness. This outcome corroborates
the studies of Orhan etal. (2021) for India and Mustacao
etal. (2018) for France who reported that in the short and
medium term, trade openness decreases environmental qual-
ity while in the long term, there is no significant connec-
tion between trade openness and CO2 emissions. Lastly, we
noticed positive coherence between technological innovation
and CO2 emissions in the short and medium term; however,
in the long term, there is insignificant coherence between
CO2 emissions and technological innovation. This implies
that in the short and medium term, trade openness contrib-
utes to environmental degradation while in the long term,
no significant association was observed between CO2 emis-
sions and technological innovation. This result affirmed the
outcome of Adebayo & Kirikkaleli (2021) in their study on
the interconnection between technological innovation and
CO2 emissions in Japan. However, the outcome contradicts
the study of Coeha etal. (2021) for South Korea, Kihombo
etal. (2021) for WEMA nations, and Khan etal. (2021) for
China who reported that technological innovation improves
the quality of the environment.
Furthermore, we applied the partial and multiple wavelet
coherence approaches as a robustness check to the wave-
let coherence, and the findings show that when the third
variable is considered, there is evidence of strong coherence
between the first and second variables. Moreover, we uti-
lized the frequency domain causality to capture the causal
linkages between CO2 emissions and renewable energy use,
technological innovation, and trade openness. The outcomes
unveiled that in the long term, both economic growth and
renewable energy consumption can predict CO2 emissions.
In addition, in the medium and short term, technological
innovation can predict CO2 emissions while no evidence of
causality was established between trade openness and CO2
emissions. These outcomes have significant policy implica-
tions for policymakers in Portugal.
Conclusion andpolicy direction
Conclusion
The research investigates the causality and sign of causal-
ity between carbon emissions (CO2), economic growth
(GDP), technological innovation (TI), renewable energy
use (REC), and trade openness (TO) for Portugal utilizing
dataset between 1980 and 2019. The present research lev-
erages several wavelet tools such as partial wavelet coher-
ence (PWC), wavelet coherence (WTC), and wavelet-based
Granger causality approaches to unearth these associations.
For various sub-periods and frequencies, detailed infor-
mation on this connection is provided, demonstrating the
Fig. 9 a Spectral causality
from economic growth to CO2
emissions. b Spectral causality
from renewable energy to CO2
emissions. c Spectral causality
from trade openness to CO2
emissions. d Spectral causality
from technological innovation
to CO2 emissions
024 6 8
0 1 2 3
frequency
Test Statistic5% C.V. 10% C.V.
024 6 8
0 1 2 3
frequency
Test Statistic5% C.V. 10% C.V.
0 2 4 6
0 1 2 3
frequency
Test Statistic5% C.V. 10% C.V.
0 2 4 6
0 1 2 3
frequency
Test Statistic5% C.V. 10% C.V.
ab
cd

Environmental Science and Pollution Research
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lead-lag linkage between variables under anti-cyclical and
cyclical influences.
The outcomes of the wavelet correlation disclosed that
there is a positive correlation at all scales between CO2 and
trade openness, economic growth, and technological inno-
vation while in at all scales, there is negative correlation
between renewable energy use and CO2 emissions. Moreo-
ver, the WTC outcomes show that at high and medium fre-
quencies from 1980 to 2019, renewable energy use drives
CO2 negatively. Moreover, at all frequencies, between 1980
and 2000, GDP drives CO2 positively, though no signifi-
cant comovement was observed between 2000 and 2018.
Furthermore, in the short and medium term, between 1980
and 2019, there is positive comovement between techno-
logical innovation and CO2. Lastly, at low frequency, the no
evidence of significant coherence between CO2 and trade
openness in the long term. Important consequences arise at
high and medium frequencies (i.e., medium and short term),
as indicated by disinflation process and economic crises.
From 1980 to 1995, trade openness caused CO2 emissions
driven by the business cycle at medium and high frequencies
(i.e., short and medium term), with the impact diminishing
from the beginning of 2000. The growth pattern of Portugal
boosted flow of international trade of “dirty goods” for both
exports and imports, implying the presence of composition
and scale effects. Luckily, the effect has a brief duration and
is mitigated, in part, by international conventions to which
Portugal has agreed. Moreover, the PWC and MWC tests
also provide supportive evidence of the wavelet coherence.
Lastly, the frequency domain causality test shows signifi-
cant causal association from economic growth, renewable
energy, and technological innovation to CO2 emissions wile
no significant causality was found from trade openness to
CO2 emissions.
Policy implications
In terms of policy consequences, policymakers should bear
in mind three key things: the time-horizon of intervention,
the resolution of the effect, and the economic features of
the targeted sub-period of time. At high, medium, and low
frequencies (short, middle, and long term), renewable energy
consumption aids in mitigating emissions of CO2. There-
fore, policymakers in Portugal should stimulate investment
in renewable energy sources, establish restrictive laws, and
enhance energy innovation. Consumption of renewable
energy improves well-being of people. Furthermore, energy
from economic expansion must be converted into renewable
energy sources, as well as a transition in technology, in order
to effectively balance CO2 emissions.
Furthermore, we observed positive comovement between
technological innovation and CO2 emissions in short and
medium term (high and medium frequencies); however,
in the long term (low frequency), no evidence of comove-
ment between technological innovation and CO2 emissions.
Therefore, in the short and medium term, environmental
technology should be linked to firm profits. As a result, the
capacity to promote a clean environment will not be an extra
cost, but rather a fantastic approach to generate high income
while also advancing sustainable growth. Furthermore, poli-
cymakers in Portugal should be aware of the environmental
impact of their actions by enhancing the creation of innova-
tions that promote a clean environment. The advantages of
political, global, and social issues should be utilized to sup-
port the transition of creative ideas that are both economi-
cally and ecologically sustainable.
Moreover, policy interventions are neutral at low fre-
quency because trade is not susceptible to CO2 and vice
versa, regardless of the economic environment. This dem-
onstrates that environmental policies or trade are not long-
term solutions. Ecological controls become essential in the
medium and short term, with a persistence of about 20years.
As a result, authorities should reduce CO2 emissions at
medium and high frequencies by regulating the activity of
“pollutant capacity” and the consumption of imported “dirty
products.” Such modifications are more appropriate in some
conditions, such as the absence of early ecological laws, eco-
nomic instabilities, and process of disinflation. Trade open-
ness performs an essential role in the long run, but only for
around 20years. As a consequence, policymakers should
decrease trade openness at low frequency and only during
the business cycle in order to minimize emissions as a con-
sequence of “dirty products” traded.
Caveat ofstudy
The limitation of the current research is that the empiri-
cal analysis concentrated on the impacts of technological
innovation, trade openness, renewable power, and economic
growth exclusively on CO2 emissions, as they are the only
measure of a country’s environmental quality. Future study
could be performed on a broader sample of nations with
additional drivers of CO2 emissions. Likewise, the research
might be improved by incorporating important factors into
the model, such as economic complexity, eco-innovation,
globalization, financial development, and information and
communications. Future research might expand on this
framework by incorporating additional indicators of envi-
ronmental deterioration, such as load factor and ecological
footprint.
Author contribution Tomiwa Sunday Adebayo and Rjoub Husam:
Conceptualization, Supervision, Writing—review and editing. Tomiwa
Sunday Adebayo: Methodology, Software. Ibrahim Adeshola and Seun
Damola Oladipupo: Conceptualization, Investigation, Resource, Writ-
ing—review and editing.

Environmental Science and Pollution Research
1 3
Data availability Data is readily available at the request from the cor-
responding author.
Declarations
Ethics approval. This research complies with internationally accepted
standards for research practice and reporting.
Consent to participate. Not applicable.
Consent for publication. Not applicable.
Competing interests The authors declare no competing interests.
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