1. Introduction
Brazil is an emerging country and historically played a major role in fulfilling its climate commitments with the global summit. The country started to monitor deforestation in the Amazon in 1985. Since this year, more than half a million square kilometers of forest have been destroyed for land occupation, logging, pastures, agricultural crops, mining, and among others [
1]. Between 2004 and 2012, Brazil reduced the deforestation rate in the Amazon by 83% [
2]. The effective application of national environmental laws, the creation of large protected areas, the introduction of commitments in the soy and beef production chains, the restrictions on access to credit for rural producers that do not comply with environmental regulations, and the use of real-time satellite imagery to monitor and locate illegal logging were very important initiatives that contributed to that success [
3]. Nonetheless, after 2012, several misguided measures and budget reductions for environmental enforcement agencies were implemented. Consequently, the rate of deforestation increased again [
4,
5].
Indeed, a dramatic increase occurred in 2019, when deforestation increased 85%, according to the National Institute for Space Research (INPE) [
6]. From January to December 2019, a total of 9174 were deforested, compared to 4951 in the same period in 2018 [
6]. Nonetheless, deforestation is not the only driver that can lead to fires. Fire can either be used in a farm-fallow context to prepare the area for agriculture using the cyclic slash-and-burn system and also as means of pasture management in cattle ranches. Moreover, climate changes and climatic extremes can lead to uncontrolled fire on open lands or in the forest [
7,
8,
9].
Accordingly to the Paris Agreement on Climate Change, Brazil has committed to end illegal deforestation by 2030 [
10]. Considering its own National Policy on Climate Change, Brazil had also committed to reduce deforestation in the Amazon to less than 3925 square kilometers per year by 2020 [
11]. However, from January to July 2020, deforestation was recorded at 4739.92 square kilometers. This area not only considerably exceeded the limit that Brazil included in its climate commitments for the entire year 2020 but also is larger than the area deforested in the same period in 2019 [
11]. For the same period of 2021, the Legal Amazon suffered a deforestation of 5026.52 square kilometers, thus showing a growth of 6% in one year.
The destruction of Brazilian vegetation, especially in the Amazon, has consequences that go far beyond Brazil. Forests act as natural carbon storage areas, absorbing and storing it over time. When a forest burns, it can release hundreds of years of stored carbon in the form of carbon dioxide, one of the main greenhouse gases driving climate change, into the atmosphere in a matter of hours [
12]. The Amazon plays an exceptional role against climate change, storing approximately 100 billion tons of carbon—an amount equivalent to ten years of global greenhouse gas emissions, having 2018 as the reference year—and removes approximately 600 million of tons per year of the atmosphere [
13,
14].
Fires do not occur naturally in the humid ecosystem of the Amazon basin. In fact, they are started by people who complete the deforestation process when the most valuable trees have already been removed, often illegally.
Fire can also spread from newly deforested areas and old grasslands to forested areas. Fires, caused by natural ignition, like lightning, are extremely rare in the rainforest and are estimated to occur only every 500 years or more [
15].
Accordingly, the development of new technologies, methods and models able to contribute to mitigate the occurrence of fires is very important. Acknowledging the factors that contribute to igniting fires is becoming extremely necessary for not only planning control and suppression but also to avoid social and economic losses in the upcoming years [
5]. In this context, a fire risk model was constructed by Zhao et al. [
16] with Geographic Information System (GIS) and a multi-layer hierarchical analysis allowing for evaluating the impact of various factors on fire occurrence in a more precise manner.
In turn, Zhang at. al. [
17] proposed a new firefighting distance criterion (FFDC) to evaluate the actual firefighting coverage of the road network improving the ability and shortening the response time of firefighting activities.
Methods, analysis and modelling using statistics applicable to the fires phenomena have also been developed. As an example, in order to improve statistical approaches for near real-time land cover change detection in non Gaussian time series (TS) data, Anees et al. [
18] proposed a supervised land cover change detection framework in which a TS is modeled as a triply modulated cosine function using the extended Kalman filter, and the trend parameter of the triply modulated cosine function is used to derive repeated sequential probability ratio test (RSPRT) statistics.
Scientists warn that the government’s failure to contain the accelerating pace of forest loss could push the Amazon to a ’tipping point’, when vegetation can be replaced by a type closer to a savanna. In this case, huge amounts of greenhouse gases would be released into the atmosphere and could have catastrophic consequences for the Brazilian economy and for the global efforts to mitigate climate change [
19].
It is well known that the advances related to Brazil’s environmental agenda projected until the year 2012 fell short of expectations. Nonetheless, the national public policy agenda remained aligned with the declared commitment to international policies, and the country’s leading role can be measured by the international reference that the Rio+20 meeting [
20] in 2012 assumed before the international community. After 2014, an imbalance in relation to environmental policy in Brazil allows for pointing to an initial crisis in this sector that began with the impeachment in August 2016 and deepened after 2019 [
21]. According to Araújo [
22], there is evidence of the gravity of the destruction of environmental protection policy that has taken and continues to take place in Brazil by changing non-statutory rules and cutting budgets.
The aforementioned moving towards the relaxation of environmental policy may have contributed to increase fires justifying this investigation and the introduction of a structural break in the fires TS.
The most recent adoption of environmental policies that generate doubtful or unsatisfactory results affects the Brazil’s credibility and may contribute to increasing the risk aversion of external and even internal investments, especially long-term ones. Moreover, this theme also concerns the international community due to the related environmental aspects and, therefore, has a global reach.
The main goal of this work is to investigate possible cross-relations and contagion between the level of fires in Brazil versus the evolution of some time series (TS) that represent some variables of interest that can be impacted by the fires, such as the agricultural planted area (AGR), ethanol (ETH) production, rainfall in the midwest region (RMW) and gross domestic product (GDP). For this purpose, we adopt the detrended cross-correlation analysis (DCCA) method [
23,
24,
25].
Stemming this ideas, the remaining sections are organized as follows; in
Section 2, the selected TS are described and the necessary mathematical and computational methods are introduced. In
Section 3, the results obtained are discussed. Finally, in
Section 4, the main conclusions are outlined.
3. Results and Discussion
As previously stated, this study adopts the DCCA cross-correlation coefficient and the rolling window approach to assess the relationships between the TS that represents fires and those TS related to the other four key variables of interest for the Brazil’s economic growth. We highlight that the rolling window approach strengthens the results, i.e., it provides robustness to the achieved results since it involves an analysis with explicit time variation.
Figure 3a,b and point out the
coefficient for periods
and
, respectively. One can observe that the cross-correlation strengthened for
in comparison to
but could not overpass the 0.7 threshold.
Similarly, from
Figure 3c,d, it is possible to note a non-correlated pattern between
pair later in the last decade (
). However, as the period approaches the impeachment date, we note a rapid increase of cross-correlation that is also sustained for
. Most of Brazil’s ethanol production is predominantly concentrated in the southeast region (mainly from sugarcane in Sao Paulo state), and, therefore, relatively distant from the Amazon forest zone. One of the reasons that can explain the increase of cross-correlation in later
and succeeded by
is due to an increase of ethanol corn-based production in the midwest region, which has been intensively supported by the Brazilian government in both periods. Secondly, as fires data include all the biomes in Brazil, another possible relation between fires and ETH is due to the application of fires in sugarcane harvest in some regions [
28]. One may also note that this pattern weakened by the end of
, but it can easily be explained by COVID-19 outbreak’s impact on fuel demand, which forced a decrease in the fuel supply in Brazil. Therefore, on a regular basis, one can expect that the co-movement between
is likely positive, but it reversed in an extreme fuel market condition. It can indicate that fires dynamics are not dependent on ETH. In other words, ETH production does not cause most of the movement in fires.
On the other hand, the
showed a weak cross-correlation during
, but this pattern shifted for
, where a negative cross-correlation for most parts of the period can be observed. This pattern is only expected for the case where the lack of rainfall (drought) in the midwest, which is an Amazon forest zone, could cause an increase in fires.
Figure 4 reinforces this conclusion since the periods showed a predominant difference, i.e.,
for every applied time scales (
n). Moreover, it is also possible to note that the
pair only showed a significant cross-correlation during the periods close to the impeachment process, i.e., in the five months prior to the event and the subsequent five months. However, it is possible to note that, during this short time span, it reverted from a positive cross-correlation to a negative pattern. The lack of evidence of a clear pattern might indicate that this is not a causation relation, since it is expected that the
variable shows a pattern similar to the
, considering the vast influence of agricultural scope to the Brazilian GDP.
Table 3 summarizes the descriptive statistics for the
distributions as a function of
n with the different sizes of
W (18, 24, 30 and 36 months). Differently from expected and observed by some authors [
25,
38], the distributions’ mean values are not close to zero and the standard deviation (SD) does not decrease for greater
W sizes. In addition, mostly skewness and kurtosis diverged from values observed from normal distributions, i.e.,
and
for different combinations of
n and
W. Multiple pieces of evidence tend to affect the normality of the distributions. For this reason, the D’Agostino and Pearson’s normality test [
51,
52] is conducted, and the results are shown in
Table 4. For the ones that reject the null hypothesis of normality (marked in
Table 4), the contagion test must be conducted by different statistical approaches such as a non-parametrical test.
Hence, the contagion hypothesis can be tested for each
distribution.
Table 5 depicts the significance test, where the
t-test is applied to parametric (normal) distributions and the Wilcoxon signed-rank test for non-parametric (non-normal) distributions. In general, there is evidence of a contagion, i.e., differences for
and
, for every set of pairs. Combining the specific data in
Table 5 illustrates that the
has more expressive contagion in the mid-term—as pointed by
and
—than in the long-term (
and
). The fact that the
was shown to have impacted the fires in the long term of
as much as in
might indicate that the agricultural impact on fires has not been influenced by any particular policy. Differently, the
and
revealed a contagion for every window size. Therefore, these factors presented the most relevant shift in pattern for the post-impeachment period (
). Some factors such as the
are not controlled by any sort of government policy but have a clear causation aspect. On the other hand, as pointed earlier, the
variable might be influenced by the Brazilian energy downstream policies, which have been intensively incentivizing the production of the ethanol corn-based.