key: cord-304490-q9ab1pji
authors: Iqbal, Najaf; Fareed, Zeeshan; Shahzad, Farrukh; He, Xin; Shahzad, Umer; Lina, Ma
title: Nexus between COVID-19, temperature and exchange rate in Wuhan City: New findings from Partial and Multiple Wavelet Coherence
date: 2020-04-22
journal: Sci Total Environ
DOI: 10.1016/j.scitotenv.2020.138916
sha: 
doc_id: 304490
cord_uid: q9ab1pji

Abstract This study attempts to document the nexus between weather, covid-19 outbreak in Wuhan and the Chinese economy. We employ 24-h daily average temperature, daily new confirmed cases of a covid-19 in Wuhan, and RMB exchange rate to represent the weather, covid-19 outbreak, and Chinese economy, respectively. The methodology of Wavelet Transform Coherence (WTC), Partial Wavelet Coherence (PWC), and Multiple Wavelet Coherence (MWC) is used to analyze the daily data collected from 21st January 2020 to 31st March 2020. Results reveal significant coherence between series at different time-frequency combinations. Overall results show the insignificance of an increase in temperature to contain new covid-19 infections. The Renminbi exchange rate showed a negative coherence at specific time-frequency spots suggesting a negative but limited impact of the covid-19 outbreak in Wuhan on the Chinese export economy. Our results are contrary to many earlier studies, which show a significant impact of increased temperature in slowing down covid-19 spread. These results can have important implications for economic and containment policy making regarding the covid-19 outbreak.

The world is passing through an unprecedented situation as novel corona-virus (covid-19) is sweeping across -massive population of the world recently. The first case was reported in China's Wuhan during December 2019, and a statement from WHO confirmed the novel nature of the virus on 9 th January 2020 (Zhu et al., 2020) . Within the same month, WHO declared public health emergency of international concern (PHEIC) on 29 th January 2020, citing concerns for the response capacity of countries with weaker health systems (Sohrabi et al., 2020) . Due to the highly contagious nature of covid-19 (R 0 =2-5) and an ever-increasing number of cases in other parts of the world, soon it became a pandemic (Liu, Gayle, Wilder-Smith, & Rocklöv, 2020) . The total number of confirmed cases and deaths worldwide amount to 2,127,873 and 141,454 respectively at 04:33 hours Beijing time on 17 th April 2020, according to data from Johns Hopkins University. A recent study in Madrid suggests that covid-19 may become more contagious along time, implying that R 0 may increase (Garcia-Iglesias & de Cos Juez, 2020) . The health impact is severe enough to put more than half of the world's total population under some form of restric tion, while the economic impact is being called worse than the 2008-09 global financial crisis and compared with the Great Depression of 1930. Stock markets around the world have seen a worse decline for decades (Baker et al., 2020) . Researchers across the globe are struggling to document the nascent knowledge acquired through primary J o u r n a l P r e -p r o o f observation and experience of the situation. Efforts on a global scale are being made to know more about this virus and to slow down and ultimately stop the spread of this menace. Figure 1 shows the daily time trend of new confirmed cases in Wuhan city.

[ INSERT FIGURE 1 HERE] A sudden huge increase in new cases on 13 th February 2020 is due to the inclusion of new criterion (Clinical Symptoms) in detecting confirmed covid-19 cases. Figure 2 showing the map where the coronavirus originated.

Novel corona-virus belongs to the family of severe-acute-respiratory-syndrome (SARS) and bears flu like symptoms. Since the weather is a key variable in predicting flu, hence it is likely to be an important factor for covid-19 too (Sajadi et al., 2020) . Since severe cold, wind speed and rain (Weather variables) are expected to contribute to flu, cold, fever, cough and pneumonia etc. all of which are possible symptoms of covid-19, it is imperative to know how weather is associated with daily new confirmed infections of covid-19 in Wuhan during this outbreak. Figure 3 displays the 24-hourly daily average temperature of Wuhan city.

Covid-19 has severely restricted peoples' mobility and disturbed routine-life-activities of almost more than half of the world population. In this scenario, the negative economic impact of this disease is imminent, especially in the country where it was reported first (China) and which is also amongst the worst affected (82,341infected and 3,352 dead till 17 th April 2020). As China is a production house of the world and a major portion of its Gross Domestic Product (GDP) depends on exports, the Renminbi (RMB, Chinese currency) exchange rate is expected to be also affected (Feng, Li, & Swenson, 2016) . Due to lockdown in Hubei (Central Chinese province of which Wuhan is the capital), the movement of people and goods to and from this place was completely halted. Due to the novel nature of covid-19, it became difficult to ascertain if the virus could be spread through goods transport or not. In this uncertainty, other countries felt reluctant to allow Chinese made products to enter their borders. Production had already suffered due to complete lockdown in a whole province and then reduced demand overseas added further to declining exports in China. All these factors can affect the exchange rate of RMB, which is primarily linked to foreign trade flows (Li, Ma, & Xu, 2015) . In such a scenario, it is interesting to know how the Chinese RMB exchange rate moved with the emerging situation of the covid-19 outbreak, explicitly speaking the number of new daily confirmed cases in Wuhan during this period. Figure 4 shows the daily time trend of the RMB exchange rate against USD. This study attempts to document the relationship between local weather (Temperature), economy (Exchange rate of RMB), and covid-19 outbreak (Daily number of new confirmed covid-19 cases) in the Chinese city of Wuhan where it was first reported, using wavelet analysis. As it is an emerging situation, the research on different aspects of this global outbreak is still naive at the moment.

Soon after reporting of early cases of covid-19, it is established that human-to-human transmission is taking place Lai, Shih, Ko, Tang, & Hsueh, 2020) . Temperature is an important factor in infectivity reduction of the human coronavirus (Lamarre & Talbot, 1989) . Experience with SARS had demonstrated that the disease disappeared in warm weather during late July (Wallis & Nerlich, 2005) . Similar behavior has been expected by some in the case of covid-19, also due to its relationship with the same family i.e., corona-virus (Wilder-Smith, Chiew, & Lee, 2020). Temperature and humidity is an important factor in the survival of coronavirus on metal and other surfaces (Casanova, Jeon, Rutala, Weber, & Sobsey, 2010) . Higher humidity, lower temperature and tropical areas were found to be more feasible for the coronavirus spread during SARS outbreak (Chan et al., 2011) . A recent study finds an association between meteorological factors, air pollutants and number of deaths in Wuhan during covid-19 outbreak using the Generalized Additive Model (Ma et al., 2020) . Weather is found to be associated with the daily number of covid-19 cases in the Indonesian capital city of Jakarta also (Tosepu et al., 2020) . Research studies on the SARS outbreak found that daily infections could increase as higher as 18.18 times at low temperatures as compared to high temperatures (Merlo et al., 2006) . A study involving 429 cities around the world suggests that temperature may be an important factor in covid-19 infection and transmission and regions with similar weather conditions as of Wuhan should be extra cautious in preventing an outbreak . The same study suggests that there may be the best temperature for covid-19 transmission and low temperature is more feasible for this infection and transmission. Another research, including data from all cities of China suggests that increase in temperature leads to increase in doubling time of covid-19. This implies that high temperatures may reduce the speed of transmission of covid-19. Although the model from this study explains only 18% of the variation in doubling time of covid-19 cases, it still provides an important insight into how temperature can play a role in the containment of this outbreak (Oliveiros, Caramelo, Ferreira, & Caramelo, 2020 ). While the above mentioned studies suggest a decisive role of increased temperature in reducing covid-19 spread, the current spread around southern hemisphere suggests there may be only little if any role of temperature in this regard. According to research on global scale, high temperature does not seem to slow down the covid-19 spread (Jamil, Alam, Gojobori, & Duarte, 2020) . Another study on community outbreaks J o u r n a l P r e -p r o o f throughout the world suggests that covid-19 is a seasonal respiratory virus, spreading along similar latitude (Sajadi et al., 2020) .

In this uncertain situation where literature is inconclusive about the role of temperature in the covid-19 spread, we attempt to analyze the number of daily new covid-19 cases and average daily temperature in this regard. A better-modeled association helps to understand the behavior of this disease in varying weather conditions which can ultimately help to save precious human lives by taking preventive measures. What has happened in Wuhan is important for the rest of the world to know to enable them to making informed and better decisions related to covid-19 containment. A recent study cited measures taken in Wuhan as a model to contain the covid-19 elsewhere in the world (M. .

A few recent studies confirmed the negative impact of the covid-19 outbreak on the Chinese economy during its early stages (Al-Awadhi, Al-Saifi, Al-Awadhi, & Alhamadi, 2020; McKibbin & Fernando, 2020) . The Chinese economy is export-oriented, and significant changes in exports due to covid-19 can affect its exchange rate. A lot of research is available on the relationship between the exchange rate and exports of a country, especially in the case of China (Burdekin & Willett, 2019; Taylor, 2016) . A lot of studies conclude a positive relationship between the depreciation of RMB and Chinese exports (Park, Yang, Shi, & Jiang, 2010) while others are inconclusive (Cheung, Chinn, & Qian, 2012) . However, the current situation may be different as compared with the classical exchange-rate-exports relationship due to its novel nature. In the ongoing scenario, the RMB exchange rate is expected to show some coherence with the covid-19 outbreak, both directly and indirectly.

Weather is represented by "average daily temperature" in Wuhan and calculated by taking 24-hourly local observations and then averaging throughout every day. Covid-19 outbreak is represented by the "number of daily new confirmed infections" of covid-19 and the numbers are taken from National health commission of China's official website. Data on Chinese exchange rate v/s US dollar is taken from IMF website. All data values are collected on daily basis from 21 st January 2020 (Lockdown start date of Wuhan city) to 31 st March, 2020.

We have employed Continuous Wavelet Transform (CWT), Wavelet Transform Coherence (WTC), Partial Wavelet Coherence (PWC) and Multiple Wavelet Coherence (MWC) to analyze the association between the average daily temperature of Wuhan, number of daily new confirmed covid-19 cases in Wuhan city and RMB exchange rate. Wavelet methodology is used mostly in Geophysics and recently J o u r n a l P r e -p r o o f getting footprints in weather, environment, economics, and finance studies also (Afshan, Sharif, Loganathan, & Jammazi, 2018; Ng & Chan, 2012 ; Wu, Tan, Guo, Li, & Chen, 2019) . It can capture non-linear association between multiple series of data (Benhmad, 2012) . Such methodology has not been employed in any studies related to covid-19 up to the best of our knowledge till now.

There are several advantages of using wavelet methodology in multiple time series analysis; 1) Assumption of stationarity can be relaxed. 2) A series with non-normal distribution can be used. 3) Events localized in time can be captured efficiently. 4) Analysis is done from a time-frequency perspective. 5) Its very efficient in capturing non-linear relationships (which is the case most frequently in real world scenarios). 6) It can determine strength and direction of association and distinguish between short, medium and long term relationships at the same time. 7) Different types of wavelet functions can be used depending upon the nature of data which allows more efficient and accurate tracking of the association. 8) It can capture bi-directional (lead-lag) relationship at the same time at different time-frequency domains between two time series (Grinsted, Moore, & Jevrejeva, 2004; Ng & Chan, 2012; Vacha & Barunik, 2012) .

The mathematical equation for wavelet transforms coherence is presented below; (1)

The wavelet coherence ranges from 2 0 ( , ) 1 R m n  .

Zero means no coherence at all and one means perfect coherence. The method of Monte Carlo simulation is employed.

In this methodology, the coherence is studied between two variables while controlling for the common effects of third variable. The mathematical representation of this method is given as under; 

The simplest way of understanding multiple wavelet coherence to compare it with multiple correlation. In this method, coherence is studied between one dependent variable Y and the combination of two other X1 and X2 variables. The mathematical representations of MWC is shown below; ;

Descriptive statistics show that average number of daily cases of covid-19 is 704.31, ranging from minimum "0" to maximum 12,523 during our observation period. Average daily temperature is 10.7 degree Celsius, ranging from a minimum of 3 degree to a maximum of 21 degree centigrade. Exchange rate average is RMB 6.99 per USD fluctuating between 6.90 and 7.115 which shows limited variation (maximum 3%) during this period. Correlation between all three variables is positive and significant at the 1% level. Coefficient for correlation is 0.61 between covid-19 and temperature, 0.56 between covid-19 and exchange rate and 0.53 between temperature and exchange rate respectively. inside from the light ones outside is called "cone of influence" and represents essential "edge effects" along its borders.

Figure 5(b) shows the significant variations in temperature that can be seen in frequency bands of 0-4, 4-8 and 8-16 during 3 rd , 3 rd -4 th and 8 th , and 3 rd -6 th weeks of observation respectively represented by an "L" and a long oval shaped dark red contours. can be interpreted as a correlation that is loca lized in time-frequency domain in simple terms but possesses many advantages as compared to simple correlation (Grinsted et al., 2004) .

The direction of clusters of small arrows observed in the figure 6(b), represents the direction of association between covid-19 and temperature while the colored bar on the right side tells us the strength of this association. Arrows pointing towards right side mean a positive association (in phase) between these variables while negative (out phase) towards the left. Arrows inside the circle (contour) mean a significant association. Rightward direction of arrows inside the contour represents positive association between temperature and covid-19 in frequency band of 8-16 periods during third week of observation. Red color inside the circle matches with a correlation of almost 0.80 which is shown on the colored bar on the right side representing a strong association. Black cone shape lining from top to bottom on both sides is called "cone of influence" and represents significance level.

Temperature and exchange rate are in phase as shown by the arrows point ing towards right in the circle shown on the base of the figure 6(c) inside the cone of influence. Red color inside is matching with almost 0.80 shown on the colored bar on the right which means a strong association in the frequency range of 16 and onwards during 4 th and 5 th week of observation. There are notable edge effects also in the same frequency band before and after 4 th and 5 th week. There is another very small cluster of arrows J o u r n a l P r e -p r o o f pointing left and downwards in the frequency range of 0-4 periods during 2 nd week which implies an out-phase association running from exchange rate to temperature.

Figure 7a-1 shows result of Partial Wavelet Coherence (PWC) involving covid-19, temperature and exchange rate. It shows wavelet coherence between covid-19 and temperature while controlling for exchange rate. One small and the other large red colored contour can be observed in frequency domain of 0-4 and 8-16 periods respectively showing short and long term coherence within the given time period. Short term coherence is observed during 1st week while long term between 2nd and 3rd week of the observation. Red color inside contour matches with almost 0.80 on the colored bar on the right side of the figure showing a strong association. If we compare this result with WTC result of covid-19 and temperature from figure 6a, both are almost same. This implies that exchange rate has no significant impact on the relationship between covid-19 and temperature and results of WTC show true coherence between covid-19 and temperature. MWC shows how good the linear combination of independent variables co-moves with a dependent variable. Figure 7a -2 presents result of MWC involving covid-19 as dependent while temperature and exchange rate as independents. Linear combination of both independent variables explains variation (Small and large red circles with black outlining) in covid-19 in almost all frequency bands including 0-4, 4-8, 8-16 and 16 to onwards during 1 st , 3 rd -4 th , 2 nd -3 rd and 4 th -5 th weeks of observation respectively.

Figure 7b-2 shows MWC results of temperature as dependent while exchange rate and covid-19 as independent variables. Here also red colored islands with black outline can be observed in all frequency bands including 0-4, 4-8, 8-16 and onwards during 1 st -2 nd and 9 th , 3 rd , 3 rd -4 th and 5 th week of observation respectively. These small and large red colored contours show the strength of combination of exchange rate and J o u r n a l P r e -p r o o f covid-19 in predicting temperature. The more red the color, the more the variation can be explained in temperature by the combination of exchange rate and covid-19.

Figure 7c-2 shows MWC results involving exchange rate as dependent while temperature and covid-19 as independent variables. Two small circles can be observed in the frequency band of 0-4 during 2 nd and last week of observation respectively while a large red circle in frequency band of 16 and above during 4 th and 5 th week of observation. These red areas show the association between exchange rate and a linear combination of temperature and covid-19 in that particular time-frequency space.

Average daily temperature of Wuhan shows a positive (in phase) coherence with daily new number of covid-19 cases in medium term considering the given observation time period. This suggests that increase in temperature did not play any significant role in reducing the covid-19 spread in Wuhan. This result is contrary to a lot of other studies suggesting that increase in temperature may help to contain covid-19 spread. Our results are applicable for a temperature range between 3 degree and 21 degree centigrade which is the minimum and maximum temperature observed during the observation period. Although exchange rate and covid-19 show a significant negative (out phase) coherence for a short period of time during 4 th and 5 th weeks of observation, the impact of covid-19 on RMB exchange rate is not very large. The MWC results downplay any huge combined impact of covid-19 and temperature on RMB exchange rate suggesting little impact on Chinese exports during the observation period. Overall results show a significant co movement and coherence between covid-19, exchange rate and weather in Wuhan.

Although wavelet analysis is relatively new and better than correlation and many other time series techniques from many aspects as stated above in methodology section, results from this approach still need a caution in interpretation while talking about causality. In absence of any sound economic/scientific/social theory, there may not be any causation and data may show correlation and co-movements merely. 

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