Integration of macroeconomic fundamentals in the West African Monetary Zone: A multi scale perspective

Abstract A recently developed wavelet multiple correlations and cross correlations based on the maximal overlap discrete wavelet transform by Fernández-Macho is employed to analyse the interdependence of macroeconomic fundamentals among countries within the West African Monetary Zone for data from January 2000 to December 2018. We establish that the nature of interdependence among exchange rates, inflation, and interest rates vary across the countries. We document that the overall correlations of the three macroeconomic variables are weak in the short term, medium term, and long term. There is evidence of weaker integration at all frequencies for exchange rates, inflation, and interest rates.However, Ghana has the maximum wavelet multiple correlations at these times. The overall correlation of macroeconomic variables shows inconsistencies and may be accounted for by varying factors which often exert influence on market linkages over time. It is clear from the empirical evidence that the ex-ante conditionality for the introduction of the single currency in West African Monetary Zone will be difficult to achieve.


PUBLIC INTEREST STATEMENT
The present study holds significant public interest as it investigates the feasibility and challenges of establishing a monetary union within the West African Monetary Zone (WAMZ). With the increasing focus on regional economic integration and the success of currency unions like the Euro, it is crucial to understand the impediments that hinder the formation of a common currency in the WAMZ.By examining the behaviour of macroeconomic fundamentals across six WAMZ member countries, namely Ghana, Guinea, Gambia, Nigeria, Sierra Leone, and Liberia, the study provides valuable insights for policymakers, researchers, and stakeholders. Understanding the dynamics of these variables, such as interest rates, inflation rates, and exchange rates, is essential for effective decisionmaking and policy formulation. The findings shed light on the specific time periods, months, and countries that contribute to variations in macroeconomic variables, enabling policymakers to identify key drivers and potential areas for intervention. Moreover, the study uncovers the leading and lagging roles played by different countries in shaping the overall macroeconomic dynamics, emphasizing the need for coordinated efforts and cooperation among WAMZ members. By providing evidence on how to address the challenges and potential solutions for establishing a monetary union, this research has practical implications for policymakers seeking to enhance economic integration, stability, and financial cooperation within the WAMZ. Ultimately, this study serves the public interest by providing valuable insights into the feasibility of a monetary union in the WAMZ and offers guidance for policymakers in formulating effective strategies for regional economic integration in the West African region. By promoting stability, cooperation, and sustainable growth, the research contributes to the overall prosperity and development of the West African nations and their citizens.

Background
The West African Monetary Zone (WAMZ) is a sub-region in the Economic Community of West African States, which comprises eight countries in West Africa, including Nigeria, Ghana, Sierra Leone, Gambia, Guinea, Liberia, Guinea-Bissau, and Cape Verde. These countries have been struggling to integrate their economies and introduce a common currency, the eco. This is partly attributed to the diverse economic structures, the different exchange rate regimes, and the difficulty in ensuring a uniform or well-coordinated monetary policy framework. The lack of harmonisation among macroeconomic policies of member states has been identified as a significant challenge to achieving integration and optimal currency area (OCA) in the subregion. The convergence of macroeconomic fundamentals, such as exchange rates, inflation, and interest rates play a critical role in promoting economic stability and foster economic integration in the region. These variables are closely interconnected and have significant effects on each other (see Alagidede et al., 2008 for a discussion on these issues).
The WAMZ has implemented a series of policy reforms aimed at advancing the convergence of macroeconomic policies across member states. However, uncertainties have remained around the effectiveness of these conditionalities in achieving macroeconomic synchronisation and attain economic integration in the region (Mogaji, 2018). Some of the policies embarked on in recent years include the establishment of a regional surveillance mechanism to monitor macroeconomic indicators and the adoption of a common monetary policy framework in the region. These policies were envisioned to promote macroeconomic convergence, accomplish economic integration in the WAMZ, and propel the introduction of a single currency in the ECOWAS region. Recent arguments have bordered on the relevance of the African Continental Free Trade Agreement (AfCFTA) for the integration of macroeconomic fundamentals and trade integration in Africa. AfCFTA, headquartered in Accra (Ghana), is regarded as a momentous breakthrough in advancing regional economic integration in Africa. In line with its mandate, AfCFTA is to engender a single market for goods and services, stimulate free movement of people and investments, and enhance intra-African trade (African Union, 2018). It is envisaged that this agreement could have the potential to transform the economic landscape of the continent and promote sustainable economic growth and development.
However, despite these policy reforms, challenges remain in the integration of macroeconomic fundamentals in the WAMZ. The diverse economic structures of member states and the lack of political will to implement common policies continue to hinder progress towards macroeconomic convergence. Although there is anecdotal evidence of efforts to avert the abandonment of the eco agenda, the WAMZ still faces significant challenges in achieving macroeconomic convergence from both internal and external fronts. The internal factors include the persistence of structural imbalances, weak institutional frameworks, and lack of fiscal space, which have evolved into the limited capacity of member states to implement coordinated macroeconomic policies. On the external front, shocks emerging from economic policy uncertainties, global pandemics such as COVID-19, and commodity price deviations have exposed the vulnerabilities of member state economies and underscored the imperative for enhanced synchronisation of macroeconomic policies in the region. Most recent arguments have also cantered on how the COVID-19 pandemic has exacerbated the existing challenges in the African continent, leading to significant economic disruptions in the region.
According to a report by Reuters, ECOWAS issued a statement through Mr. Jean-Claude Brou (who is the current president of the ECOWAS Commission) and announced a new target date of 2027.This was primarily influenced by the COVID-19 pandemic, which exacerbated existing problems and introduced new obstacles (Reuters, 2021). Political issues have also complicated the currency unification process. The pandemic had a profound impact on economies worldwide. It not only exacerbated existing problems but also added new obstacles to the currency unification process. In response to the havoc caused by the pandemic, ECOWAS, under the leadership of its president, cited the COVID-19 pandemic as the primary reason for the recent postponement and the subsequent shift of the target date to 2027. In addition to the pandemic, other political issues have further complicated the process of currency unification in the sub-region. These factors, combined with the ongoing challenges faced by ECOWAS, have contributed to the delays and setbacks in achieving the goal of introducing a common currency. Although there are impediments that have occasioned several postponements, ECOWAS has remained committed to pursuing the introduction of a single currency to attain economic integration and facilitate trade and financial stability within the region. There is a need to address the existing problems, such as vulnerabilities to external shocks and other political issues within the bloc, and pave way for the successful implementation of the common currency in ECOWAS.
In this article, we advance the ongoing debate on the synchronisation of macroeconomic policies in the region, and how that promotes regional economic integration in Africa. This would provide evidence on the progress made so far towards the integration of macroeconomic fundamentals in the WAMZ and evaluate the effectiveness of policy measures adopted to achieve macroeconomic convergence. By understanding these, we would be able to highlight the challenges and opportunities that lie ahead. The insights into the coordination of macroeconomic policy in the WAMZ would yield recommendations for future policy actions to advance the proper harmonisation of macroeconomic policies in the region. The article takes a multi-scale perspective to examine the integration of exchange rates, inflation, and interest rates. The multiscale angle of the analysis supports a deeper understanding of the complex cohesion existing among macroeconomic policies and their effect on economic outcomes in the WAMZ. This provides a proper understanding of the prospects of macroeconomic integration in the sub-region.
The application of the wavelet correlation and wavelet cross-correlation to study the relationship between variables (either using discrete or continuous wavelet transforms) has been gaining popularity since these statistical tools are able to handle multiscale analysis and nonstationarity (see, Fernández-Macho, 2012;Polanco-Martínez & Fernández-Macho, 2014). There have been several methods for analysing the co-movement of financial time series such as the vector autoregression and error correction models. However, the wavelets methodology has assumed an enviable place in research since it is able to explore the interconnectedness of financial time series, thanks to its ability to simultaneously accommodate time and frequency domains (Rua, 2010). Tweneboah (2019) argues that the proponents of multivariate wavelets technique have contended that the multiple wavelets framework is more suitable than the conventional techniques in several ways. According to the author, the overall correlations within the multivariate set of different time scales can be shown in two plots of wavelet multiple correlation (WMC) and wavelet multiple cross-correlation (WMCC). Again, there is protection against spurious correlation within the estimation tool.

Motivation and contributions
We analyse the co-movement of exchange rates, inflation, and interest rates independently and simultaneously across the WAMZ for the period January 2000 to December 2018. We provide a detailed analysis of the interrelationships among these macroeconomic variables independently and simultaneously. The motivation for this study springs from the imperative to provide further evidence on the economic integration of the African continent. Following the approval of heads of states of ECOWAS in 2000 for the non-CFA countries to form a second monetary zone which will eventually merge with the CFA zone to create a single currency for the region; it has become a strenuous agenda for the participating countries to meet the convergence criteria. The main objective of WAMZ was to foster the rapid integration of the six economies with a view to ultimately integrating with the WAEMU, a group of Francophone ECOWAS members. The introduction of a common currency was envisaged to promote trade among the member countries and strengthen their bond as well as diminish the vulnerability of the sub-region against external shocks.
Despite the considerable attempts to study convergence of macroeconomic variables in the region, the evidence is far from being conclusive. There is no consensus on what drives interdependence of macroeconomic fundamentals or how the whole mechanism of synchronisation evolves. We contribute to the extant literature by exploring the relationships among exchange rates, inflation, and interest rates in the WAMZ using wavelet methodology. The empirical tool considers both time and frequency domains and supports the simultaneous analysis of the interlinkages among the variables at different frequencies and how these relationships evolve over time. It is clear from the empirical evidence that the ex-ante conditionality for the introduction of the single currency in ECOWAShas been difficult to achieve (Harvey, 2012). This has offered credence to arguments that the WAMZ countries should consider the possibility to achieve convergence conditions ex post (see, Tweneboah et al., 2016, for a similar argument).
The paper provides evidence and contributes to the debate by using the wavelet-based measure of co-movement is a unified framework, which allows analysis into the degree of relationship between two or more variables and how they move together over time and across frequencies. Rua (2010) argues that this tool constitutes a refinement to previous approaches that makes itpossible to capture the time and frequency varying features of co-movement. We employ two statistical tools recently developed by Fernández-Macho (2012) to analyse the interdependence of macroeconomic variables in the WAMZ (Owusu Junior et al., 2017). By employing the WMC and WMCCtechniques, this study aims to provide a detailed analysis of the interconnections between exchange rates, inflation, and interest rates in the WAMZ. The use of this approach allows for a nuanced understanding of how these variables interact across various frequencies and time scales, shedding light on the dynamics of interdependence and contagion within the region. To the best of our knowledge, there has been limited attempt to assess the feasibility of the single currency for the WAMZ by examining the degree of relationships that exist among exchange rates, inflation, and interest rates, independently and simultaneously. A study by Adam et al (2012) came close to using the three macroeconomic variables to assess the feasibility of the single currency for the WAMZ. Their study used inflation and exchange rates. They investigate macroeconomic convergence in the WAMZ by using monthly data from January 1990 to May 2010. The study documents no evidence of convergence in inflation in the WAMZ and little support for convergence in exchange rates. Based on this evidence, the authors argued that the WAMZ was not ready for a single currency and lent support to the decision to postpone the introduction of the eco to 2015 as a step in the right direction. According to their arguments, the possibility of introducing the eco requires a change of macroeconomic policy direction of member countries due to the evidence of divergence in inflation and non-convergence across the region.
Our main research objective is to contribute to the empirical literature on comovement or synchronization of exchange rates, inflation, and interest rates in the WAMZ using wavelets. The wavelets technique can clearly examine the time-frequency domain dynamics, lead/lag switches, and overall correlation within a multivariate framework. It also contributes to the literature on currency union in the WAMZ, by assessing the preparedness or the extent of convergence of the macroeconomic variables to achieve the eco by the new date in 2027 after several postponements.
The remainder of the article is structured as follows. Section 1 covers the status of the convergence criteria and empirical evidence. We present the wavelet estimation technique and a description of the data and statistical properties in Section 2. Section 3 captures the results and analysis of the interdependence of exchange rates, inflation, and interest rates, and the last section presents the conclusions and policy recommendations.

Status of convergence in the WAMZ
The formation of a common currency entails addressing various issues and criteria for creating an optimal currency area. These include promoting high levels of trade among member countries, ensuring labour mobility, establishing mechanisms for fiscal transfers, and achieving a high degree of synchronization in business cycles. These criteria have been discussed in works by Mundell (1961), McKinnon (1963), and Kenen (1969). In addition to these general considerations, the specific challenges faced by the proposed common currency, the eco, need to be addressed. The member states of the WAMZ have established a convergence framework that outlines certain requirements. For instance, member countries are expected to achieve single-digit inflation rates and maintain a budget deficit of less than 3 percent of GDP. Central bank financing of budget deficits should be limited to 10 percent of the previous year's tax revenue, and the debt position should not exceed 70 percent of GDP. Furthermore, member countries are expected to manage the variability of their nominal exchange rates within a range of ±10 percent.These convergence requirements are essential for ensuring the effective functioning of a common currency.
The convergence framework of the WAMZ and ECOWAS has taken the form of convergence framework of some successful integration stories such as the Euro Monetary Union, also known as Euro Area or eurozone. Before the euro was introduced, policies and conditionalities were established and imposed to ensure that member states converged their national policies to achieve economic integration through what is commonly known as the Maastricht criteria. European Union member states agreed to these requirements in the Maastricht Treaty in 1991, to measure their preparedness to adopt the euro as a single or common currency. The set of macroeconomic indicators hinged on price stability, sound or sustainable public finances, exchange rates stability, and stability of long-term interest rates (European Union, 1992). Both the Maastricht Treaty and ECOWAS criteria have focused on macroeconomic indicators such as price stability, sound public finances, exchange rate stability, and stability of long-term interest rates that are relevant to the promotion of economic stability and sustainability. Member states were required to demonstrate their ability to maintain low inflation rates and control price levels, as well as ensure responsible fiscal policies and sustainable public debt. Furthermore, exchange rates were expected to be stable, and long-term interest rates should exhibit a level of stability.
The purpose of these convergence criteria was to create a foundation of economic stability and align national policies to foster a harmonized economic environment within the eurozone. Similarly, the WAMZ and ECOWAS have also adopted a convergence framework that aims to achieve economic convergence among member states. This framework involves establishing policies and conditions related to price stability, fiscal discipline, exchange rate stability, and interest rate stability. By emulating the convergence criteria of successful integration stories like the eurozone, the WAMZ and ECOWAS aim to promote economic integration, facilitate trade, and enhance regional financial stability. Through the convergence framework, member states strive to align their policies and promote economic cooperation to achieve sustainable and inclusive economic growth in the region.
Given the importance of convergence of macroeconomic fundamentals to monetary unions, much research has been conducted on the topic, some on the larger ECOWAS and the WAMZ itself. The research conducted by Owusu Junior et al. (2017) focused on examining the interdependence of exchange rates within the WAMZ. The study utilized the Continuous Morlet Wavelet Transform to analyse the lead-lag relationships in the frequency-time domain for the member countries' real US dollar exchange rates and their absolute log returns. The findings of the study indicated that lead-lag connections varied across countries and there was no single country that consistently led in terms of both real and absolute returns of the exchange rates. This lack of convergence in exchange rates aligns with other evidence that suggests non-convergence within the monetary zone, which poses challenges to the implementation of a single currency in the ECOWAS region.
Available data on the WAMZ from 2015 to 2020, highlighted that no member state has been able to meet all the primary and secondary criteria consistently, as required by the Macroeconomic Convergence and Stability Pact. This presents a significant obstacle to the realization of a single currency in the WAMZ. In 2020, Nigeria and Guinea were able to meet five out of the ten criteria, while the rest of the countries attained four criteria in both the primary and secondary categories. This indicates that achieving convergence before the introduction of the eco currency is a challenging task. However, the endogeneity of the OCA theory, proposed by Frankel and Rose (1998), suggests that monetary integration can be achieved post facto, meaning that convergence can be pursued after the introduction of a common currency.

Empirical evidence
The issue of co-movement has garnered significant attention; particularly regarding stock returns (refer to Boako & Alagidede, 2017;Brooks & Del Negro, 2004). However, there has been relatively less focus on major macroeconomic variables such as interest rates, inflation rates, and exchange rates across countries, particularly within the WAMZ. While there exists a wealth of research on the European Union in this regard, studies examining the integration process of the ECOWAS are scarce. Empirical investigations into the co-movements of macroeconomic variables, including exchange rates, have employed various methodologies.
Another study by Frimpong (2022) focused on investigating the interconnectedness of countrylevel macroeconomic variables within the WAMZ. The macroeconomic variables studied included inflation, nominal effective exchange rate (NEER), exchange rate, and global economic policy uncertainty. The study analysed monthly data spanning from February 1997 to May 2019 and employed wavelet techniques such as vector wavelet and wavelet multiple, along with the TVP-VAR (time-varying parameter vector autoregression) as a robustness check. The findings of this study revealed significant co-movements between the macroeconomic dynamics of the selected economies in the time-frequency domain. Specifically, the research identified evidence of strong co-movements between the macroeconomic conditions of certain countries in the long term. Additionally, the NEER was found to be highly exposed to external shocks due to periodic swings such as inflation, making it more susceptible to such shocks. Furthermore, the study observed a high interdependence among macroeconomic variables in the long term, except for the exchange rate. Lastly, it was noted that global economic policy uncertainty exhibited long-term lags within the interdependencies of inflation and the NEER, but not the exchange rate.
Conducted a study focusing on analysing business cycles within individual countries under the COWAS using GDP data from 1980 to 2015. The researchers detrended the data using the Hodrick-Prescott filter and employed covariance analysis on the computed z-scores to assess the level of synchronization of regional business cycles, the symmetry of regional macroeconomic policies, and the symmetry of regional trade flows. The findings of the study indicated an overall increase in business cycle synchronization and symmetry in macroeconomic policies among the ECOWAS countries. However, the intensity of these phenomena was higher within the WAEMU compared to the WAMZ. This suggests that the countries within the WAEMU exhibited greater alignment in terms of their business cycles and macroeconomic policies compared to those within the WAMZ.
In a study by Mogaji (2019), the author investigated the homogeneity in inflation patterns across the WAMZ. The countries examined were The Gambia, Ghana, Liberia, Nigeria, and Sierra Leone. One major focus was on examining the feasibility of exchange fixation within the monetary zone. This was done by measuring absolute inflation rate differentials, which were derived from the deviations of individual member countries' inflation rates from various benchmarks. These benchmarks included: (i) the inflation rates of the US and the Eurozone, (ii) the convergence criterion policy inflation target rate of 5%, and (iii) the WAMZ's average inflation rate over a convergence 12-year period. The empirical findings of the study suggested that shocks to inflationary trends within the WAMZ would have permanent and long-lasting effects on inflation rates within the zone. The analysis indicated that inflation rates may not return to the trend path over time. This implies that inflationary shocks could have persistent impacts on inflation rates in the WAMZ, suggesting the presence of structural factors affecting inflation dynamics in the region.
Another study by Seraphin (2019) used data from 30 May 2010 to 31 December 2016 and reported a transmission of volatility among the cedi, naira, and franc CFA. This suggests that changes in volatility in one currency tend to affect the other currencies in the sample. The findings of the study provide support for the creation of a monetary zone within the ECOWAS region, indicating the potential benefits of increased monetary integration and coordination among member countries. Abayomi and Olaronke (2015) examined the pattern of exchange rate fluctuations in currencies within the WAMZ for the period spanning from 1960 to 2011. The findings of the study indicated that the Ghanaian cedi exhibited the highest level of volatility among the currencies in the region. Additionally, the study concluded that leverage existed for the Gambian Dalasi but not for the Nigerian naira, while the findings were inconclusive for the other countries. Furthermore, the impact of central bank intervention on exchange rate volatility varied across the countries studied. The study found inconclusive evidence regarding the effect of central bank intervention on exchange rate volatility in Ghana, Guinea, and Liberia. However, the findings indicated that central bank interventions reduced the level of volatility persistence in the Gambia and Nigeria. In contrast, central bank interventions increased the level of volatility persistence in Sierra Leone during the period under review. The study provided insights into the exchange rate fluctuations in WAMZ currencies and highlighted the varying impacts of central bank interventions on volatility in different countries within the region.
Tule, Ajilore, and Ujunwa (2019) conducted a study using quarterly time series data from Nigeria, Ghana, The Gambia, and Sierra Leone with data spanning the period 1980 to 2016. The objective was to investigate whether monetary policy shocks originating from Nigeria have a significant impact on macroeconomic fluctuations in the WAMZ economies. The researchers employed the Global Vector Autoregressive (VAR) method with Diebold-Yilmaz connectedness weights computation for their analysis.The findings of the study revealed that unanticipated monetary policy shocks in Nigeria have various effects in different WAMZ countries. In Nigeria itself, such shocks lead to a depreciation of the Nigeria-USA exchange rate, stimulate economic growth, reduce inflation, and expand the money supply in the short run. In Ghana, similar shocks from Nigeria cause a depreciation of the exchange rate, a slowdown in economic growth, and a high inflationary impact in the short term. In the Gambia, unanticipated shocks from Nigeria result in a strengthening of the Gambia-USA exchange rate, a decrease in economic growth, and inflationary pressures. Sierra Leone experiences an appreciation of its currency, like the Gambia, along with economic expansion and rising inflation. Moreover, the money supply also increases to accommodate the growing demand.These findings support previous research indicating significant geographical linkages within the WAMZ region through which macroeconomic fluctuations are transmitted. From a policy perspective, it is crucial for monetary authorities in the region to collectively address the challenge of stabilizing their economies in response to monetary policy shocks originating from Nigeria.
Ndiaye (2021) examined inflation behaviour in ECOWAS. The study observed that WAEMU countries generally have lower inflation rates compared to WAMZ nations. The findings indicated that exchange rate pass-through effects experienced by the WAMZ countries explain this difference. Statistical exercises conducted in the study suggested that differences in money supply and output growth do not account for the higher inflation in WAMZ countries, but exchange-rate passthrough does. Alagidede, Coleman, and Cuestas (2010) investigated the dynamics of inflation in five WAMZ nations. They employed panel unit root tests to analyze the stationarity properties of inflation rates. The study applied different methods and found mixed results regarding the presence of a unit root. While some tests indicated stationarity, others suggested the presence of a unit root. The study also revealed long memory behaviour in inflation rates across all countries, indicating persistent inflation trends.Another study by Alagidede et al. (2008) examined the convergence of exchange rates and prices in the WAMZ. They analysed quarterly data from 1974 to 2007 and found that real exchange rates in The Gambia, Ghana, Nigeria, and Sierra Leone followed a random walk, while nominal exchange rates and nominal prices adjusted at different speeds to achieve long-run purchasing power parity (PPP). Another study by Ogunkola (2005) suggested that the region was moving closer to a monetary union based on the modelling of the real exchange rate. Balogun (2009) assessed the determinants of inflation differentials in the WAMZ. Using macroeconomic convergence as a benchmark, the study found that regional inflation rates were often above a single-digit target and varied widely among the countries. The pursuit of distorted interest rates, exchange rate overvaluation, and expansionary monetary policies were identified as major factors contributing to inflationary divergence. Also, Balogun (2007) examined the feasibility of a single currency in the WAMZ. By analysing monetary and macroeconomic stability, the study concluded that independent monetary and exchange rate policies had limited effectiveness in influencing domestic activities, GDP, and inflation. The study suggested that members of the WAMZ would benefit from surrendering some policy instruments to a planned regional body under appropriate monetary union arrangements.
In conclusion, there is limited literature on the simultaneous co-movement of exchange rates, interest rates, and inflation rates in the context of ECOWAS monetary integration. The motivation for further research lies in the lack of literature on the macroeconomic variables used to assess the integration of ECOWAS economies. Most studies have focused on other variables related to business cycle synchronization. Additionally, this research aims to make a methodological contribution by examining co-movement within the time-frequency domain. This approach provides valuable insights into the dynamics of spillover transmissions and interdependence structures among the variables. This research addresses the existing research gap, contributes to the understanding of macroeconomic dynamics in the WAMZ, and offers valuable insights for policymakers and researchers interested in the integration of ECOWAS economies. The methodological contributions, particularly the exploration of co-movement within the time-frequency domain, add depth and nuance to the analysis of spillover effects and interdependencies among exchange rates, interest rates, and inflation rates.

WMC and WMCC framework
This paper utilized the WMC and WMCC techniques to investigate the interdependence of exchange rates, inflation, and interest rates independently and simultaneously within the WAMZ. The chosen approach, proposed by Fernández-Macho (2012), was selected for its capability to capture both the co-movement and contagion effects across different time scales and at the frequency level. This methodology allows for a comprehensive analysis of the interrelationships among these variables. The authors adopted the classification of contagion and interdependence based on the strength of wavelet coherence at different frequencies.On the other hand, interdependence is detected when strong wavelet coherence is found at lower frequencies, suggesting a synchronized behaviour of variables over longer time horizons. This classification approach is consistent with previous studies such as Saiti et al. (2016), Dewandaru et al. (2015), Bodart and Candelon (2009), Vincent and Bertrand (2005), and aligns with the understanding of contagion and interdependence in the literature.
The WMC and WMCCbegin with the Maximal Overlap Discrete Wavelet Transform MODWT (see; Fernández-Macho, 2012;Gençay et al., 2001;Percival & Walden, 2000). The MODWT is defined as follows: Let X t ¼ x 1t; x 2t; ; . . . ; x nt be a multivariate random process and W jt ¼ w 1jt; w 2jt; ; . . . ; w njt represent their respective scale λ j wavelet coefficients calculated by adopting the MODWT. The wavelet multiple correlations ðWMCÞψXðλ j Þ can be expressed as a single set of multiscale correlations from Equation 1 subsequently. ψXðλ j Þ ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi For each λ j the square roots of the coefficients of determination of the regression formed by the linear combination of w ijt; i ¼ 1; 2; . . . ; n variables for which such coefficient of determination is maximum. From literature, it is understood that for regression of a regressandz t on a set of predictors z t z k; k�i � � a coefficient of determination can be procured as diagonal element of the inverse of the complete correlation matrix P:where P j is the ðn � nÞ correlation matrix of W jt ¼ w 1jt; w 2jt; ; . . . ; w njt and maxdiagð:Þ elects the maximum element in the diagonal argument.
From the regression theory; the fitted values of z i as ẑ i WMC can also be expressed as Equation 2, where w ij is chosen to maximize ψXðλ j Þ and ŵ ijt are the fitted values in the regression of w ij on the rest of the wavelet coefficients at scale λ j ; ψXðλ j Þ ¼ Corrðw ijt ;ŵ ijt ÞCovðw ijt ;ŵ ijt Þ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi The WMCC in equation (2) is generated by allowing a lag τbetween observed and fitted values of the variables at each scale λ j ; ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Confidence intervals (CI) from WMC are computed using the Fisher (1915)

Data and statistical properties
The sample covers the period from 1 January 2000 to 31 December 2018, encompassing 227 observations for interest rates, inflation rates, and exchange rates series across the WAMZ. The mean values of the macroeconomic variables are generally negative, except for the exchange rate in Ghana, which has a positive mean. Regarding volatility or risk, interest rates exhibit relatively lower degrees of volatility across the WAMZ markets, with values ranging from 0.99 (for Ghana) to 3.29 (for Guinea). In contrast, both inflation rates and exchange rates show similar and high degrees of volatility, with values ranging from 30.86 (for Gambia) to 2494.4 (for Guinea) for inflation rates. However, concerning exchange rates, Ghana and Gambia have lower volatility, with values of 0.028 and 9.56, respectively. The skewness of the returns is mostly negative for all countries, indicating a leftward or negative asymmetry in the distributions, except for Guinea, which shows positive skewness in relation to the exchange rate. When considering kurtosis, some macroeconomic variables exhibit positive kurtosis, indicating heavy tails, while others show negative kurtosis. The coefficient of variation, which is the ratio of the standard deviation to the mean, suggests a generally low variability or high degree of stability in all countries across the WAMZ. This implies that the relative variability of the macroeconomic variables is low compared to their means, indicating a degree of stability in the region.
The Shapiro-Wilk statistic, a test for normality, rejects the null hypothesis of Gaussian (normal) distribution in all the series for monthly frequencies across all countries. This suggests that the data for interest rates, inflation rates, and exchange rates do not follow a normal distribution in the WAMZ countries. The rejection of the null hypothesis indicates that the data may have a nonnormal distribution, potentially exhibiting skewness, kurtosis, or other departures from normality. Table 1 shown below is the description of the summary statistics of the countries understudy

Co-movement of macroeconomic fundamentals
This paper examines the co-movement of interest rates, inflation rates, and exchange rates in the WAMZ using time series data from 2000 to 2018. The analysis employs the wavelet multiple correlations and wavelet multiple cross-correlations techniques to explore the relationships between these macroeconomic variables at different time scales. The study considers bivariate correlations at four wavelet scales, representing Ghana (C1), Guinea (C2), Gambia (C3), Nigeria (C4), Sierra Leone (C5), and Liberia (C6). The data is decomposed into multiple time scales using the W2CWM2C approach with the MODWT method and Daubechies Least asymmetric wavelet.
The paper introduces new visualized plots of the wavelet multiple cross-correlations for different time scales, specifically focusing on a 30-day lag. The classical plot highlights the symmetry of the wavelet multiple correlations, while the visualized plot illustrates the strength of the crosscorrelations. By combining the four plots into a single visualization, the results become easier to interpret. The long-dashed vertical lines indicate the time lag at which the strongest wavelet correlation values are localized. Furthermore, the confidence interval is examined to determine if it spans zero. An important feature of the wavelet multiple cross-correlations is the ability to identify the variable that maximizes the cross-correlations against a linear combination of the remaining variables. This information is displayed on the right side of each wavelet scale. The analysis encompasses different frequencies or wavelet scales and includes leads and lags up to 30 trading days. Within each wavelet correlation, the wavelet coefficients are estimated with a 95% confidence interval. The portions of the interval that span zero are depicted in white, while the coefficients falling outside this range are considered statistically significant. Figure 1 presents the wavelet correlation matrix for interest rates among the WAMZ countries from 2000 to 2018. The findings reveal various levels of correlation between the countries. Ghana tends to have an inverse correlation or lower levels of correlation with several countries, including Sierra Leone, Guinea, and Liberia, with average correlations ranging from −0.001 to −0.08. On the other hand, Ghana and Nigeria exhibit the highest degrees of correlation, with coefficients ranging from 0.34 to 0.56 at different time scales, averaging 0.32. Gambia and Sierra Leone demonstrate an average correlation of 0.13 (ranging from −0.01 to 0.56). In the short term, the bivariate correlation between countries is generally weak. For example, Ghana shows negative or inverse correlations with Nigeria, Guinea, Sierra Leone, and Liberia, with correlations ranging from −0.05 to −0.17. In the medium term (around scale 4), Ghana has a high correlation with Nigeria and Liberia, at 0.41 and 0.36, respectively, while the rest of the countries still exhibit low levels of correlation. In the long term, at lower frequencies (higher scales, such as scale 8), Ghana and Nigeria (C1, C4) have the highest correlation of 0.56. Gambia and Sierra Leone (C3, C5) follow with a correlation of 0.52. However, Ghana and Liberia, which have a correlation of 0.36 in the medium term, exhibit an inverse or negative correlation of −0.38 in the long term.  Figure 2 and 3 represent the WMC and WMCC respectively for interest rate across the WAMZ. From Figure 2, it is evident that the highest correlation of interest rates among the WAMZ countries occurs in the long run, reaching approximately 80% at scale 8. The multiple correlation is initially low at the highest frequency (lowest scale), around 0.40, but steadily increases to around 0.50 at the monthly scale. There is a temporary downtrend in multiple correlation as the markets move from scales 4 to 8, indicating lower correlation at lower frequencies (higher scales). At the scale of 2-4, the correlation is slightly above 0.5, and it generally increases, reaching a value of around 0.8 at the scale of 4-8. This suggests that in the short run, about 50% of the fluctuations in a particular market can be explained by the overall market behaviour, while in the long run, almost the entire movement of a market can be explained by the behaviour of other markets (Kumar, 2019). Figure 3 presents the results of the WMCC for interest rate returns at different frequencies (wavelet scales) and time lags, up to 30 days. It is evident that as one moves from the highest to the lowest scale, the correlation weakens. Integration is observed to be relatively weak between the WAMZ interest rates, especially in the short term (at higher frequencies below wavelet scale 2). The study identifies cross-correlations above 0.53 in the medium term (between wavelet scale 2-4). At the lowest scale, there is clear evidence of significantly weaker correlations, with Sierra Leone potentially lagging the other interest rates at time 23. The correlation steadily increases from around 0.36 to approximately 0.71 at the intermediate scales. Ghana and Guinea's interest rates show greater prospects of lagging the WAMZ interest rates during these periods. However,  for the highest scale (lowest frequency), wavelet correlations exhibit significant coefficients across all time lags, with Ghana's interest rate potentially leading or following at this period. This suggests that any shocks that affect the Ghanaian market may be transmitted to other WAMZ interest rates.

Interdependence of interest rates within the WAMZ
In terms of actual lead/lag, the paper finds that Ghana leads at time −1 and lags at time 5. This indicates that Ghana has the maximum wavelet multiple correlations during these times. The study also observes that short-term transmissions are slow and persistent, as they do not occur at high frequencies. Guinea and Sierra Leone, on the other hand, have the potential to lag in the short term (at times 24 and 23, respectively). These findings suggest that Ghana's stability and lack of political interference contribute to its leadership position, while Guinea and Sierra Leone exhibit potential delays in the short term. Figure 4 presents the wavelet bivariate correlation for inflation rates across the four scales. Like the interest rate series, there is variability in the degree of correlation across different timescales. In terms of magnitude, the correlation between Guinea and Nigeria demonstrates the highest degrees of correlation, with coefficients varying from 0.03 to 0.47 at different timescales, averaging 0.17. Sierra Leone and Liberia follow with an average correlation of 0.16, ranging from 0.11 to 0.42. On the other hand, Gambia (C3) exhibits negative or relatively lower levels of correlation with most countries, namely Nigeria, Sierra Leone, and Ghana, with an average correlation of approximately −0.01, −0.04, and −0.13, respectively.

Interdependence of inflation within the WAMZ
In the medium term (at a scale of 2-4), most countries exhibit negative or inverse correlation. For example, Sierra Leone (C5) and Liberia (C6) have a correlation of −0.2, while Gambia (C3) demonstrates inverse or negative correlation with Nigeria, Sierra Leone, and Ghana, with correlation values of −0.03, −0.22, and −0.3, respectively. This weaker correlation continues into the long term at scale 8, which represents lower frequencies. In the long term, most countries still exhibit very weak correlation. Guinea (C2) and Liberia (C6) show a strong correlation of 0.41, followed by Ghana and Nigeria with a correlation of 0.15.  Figure 5 presents graphical results of the WMC for the inflation rate returns in the WAMZ at four different timescales. The highest correlation among the WAMZ inflation rates appears to occur in the medium term, just below 60%, at scale 4. The multiple correlation is significantly low (0.40) at the highest frequency (lowest scale), which is around 1-2 months. However, in the long term, at scale 8, the correlation among the WAMZ inflation rates starts to decline to around 50%. At the scale of 2-4 months, the correlation is approximately 60%, and it decreases overall, reaching a value around 50% at the scale of 4-8. This suggests that in the short run, around 50% of the fluctuation in a particular market can be explained through the overall market behaviour. In the long run, almost the entire return movement of a market can be explained through the behaviour of other markets (Kumar, 2019). Figure 6 illustrates the wavelet multiple cross-correlations for the inflation rates at different frequencies and across leads and lags up to 30 days. In the short term, at a scale of 1-2, there is minimal correlation among the inflation rates of the WAMZ countries. The correlation is only around 19%. However, as we move to the medium term (scale 2-4), the correlation among the countries' inflation rates starts to increase. In the medium term, the correlation ranges from 36% to 69%.
In the long term, at scale 4-8, the correlation of inflation rates among the countries becomes more significant, reaching a rate of 86%. This indicates a high correlation at lower frequencies (higher scales). Conversely, at higher frequencies (lower scales), the correlation among the countries appears to be low but begins to rise in the medium term. Regarding leading or lagging behaviour, in the short term (higher frequency), Ghana has the potential to lead at time −10. In the medium term, Liberia has the potential to lead at time −14, but as we approach the end of the  medium term, Nigeria has the potential to lead at time −17. In the long term (lower frequency), Liberia has the potential to lag at time 11. Figure 7 presents the wavelet bivariate correlation for exchange rates across the four scales. Like the interest rate and inflation rate series, there is variability in the degree of correlation across different timescales. In terms of magnitude, Gambia and Nigeria demonstrate the highest degrees of correlation, with coefficients ranging from 0.5 to 0.58 at different timescales, averaging 0.36. This is followed by Nigeria and Liberia, with an average correlation of 0.07 (ranging from 0.02 to 0.25). Liberia generally shows relatively lower levels of correlation with all the other exchange rates. The average correlations with Ghana, Guinea, and Gambia are −0.035, −0.1025, and −0.1, respectively. In the medium term, at a scale of 2-4, the overall correlation ranges from −0.12 to 0.25, indicating that the exchange rate correlation among the countries is around 25% during this period. Only Gambia and Nigeria, represented by C3 and C4, exhibit a high correlation of 0.57, which is 57% in the medium term. Weaker correlations are observed in the long run (lower  frequency), with only Gambia and Nigeria showing a higher correlation of around 58%. Some countries even exhibit inverse or negative correlation with each other. Figure 8 presents the graphical results of the WMC for the exchange rate returns among the WAMZ countries at four different timescales. The highest correlation of exchange rates among the WAMZ countries is observed in the medium term, with a correlation of around 70% at a scale of 2. Towards the end of the medium term, at scale 4, the correlation declines slightly to around 61%. In contrast, the multiple correlations are significantly low at the highest frequency (lowest scale) of 1-2, with a value of 0.20. However, in the long term, at around scale 8, the correlation among the WAMZ exchange rates increases to around 70%. At the scale of 2-4, the correlation declines from 61% to approximately 60%, and overall, it increases, reaching a value around 70% at the scale of 8. This indicates that in the short run, approximately 20% of the fluctuation in a particular market can be explained by the overall market behaviour. In the long run, however, almost the entire return movement of a market can be explained through the behaviour of other markets. Figure 9 presents the wavelet multiple cross-correlations for the exchange rates among the WAMZ countries at different frequencies and across leads and lags up to 30 days. In the short term, which is at a scale of 1-2, there is not much correlation observed among the exchange rates of the WAMZ countries. The correlation at this scale is approximately 35%. However, as we move towards the end of the medium term, at scale 4, the correlation among the countries' exchange rates begins to increase to around 69%, indicating a stronger correlation.

Interdependence of exchange rates within the WAMZ
In the long term, at scale 8, the correlation of exchange rates among the countries becomes even stronger, reaching a level of approximately 86%. This suggests that at a lower frequency (higher scale), the correlation of exchange rates among the WAMZ countries is high. On the other hand, at a higher frequency (lower scale), the correlation among the countries appears to be low but starts to rise in the medium term. Regarding leading or lagging behaviour, in the short term, Nigeria has the potential to lag (at time 0.1). In the medium term, Nigeria again has the potential to lead or lag (at times 0 and 3). In the long term, which is at a lower frequency, Ghana has the potential to lead (at a time of −3).

Conclusions and policy recommendations
This study makes a valuable contribution to the existing literature on the interdependence of macroeconomic fundamentals within the WAMZ by employing a recently developed technique called wavelet multiple correlation and wavelet multiple cross-correlations. This approach allows for the assessment of integration levels and spill-over effects among interest rates, inflation rates, and exchange rates across the WAMZ.Regarding the interdependence of interest rates, the findings reveal that the degree of correlation varies across different timescales. In the short run, the co-movement of interest rates among the WAMZ countries is weak. However, as the time horizon increases, multiple correlations show a gradual increase, transitioning from pockets of weaker correlations in the short run to moderate and stronger correlations in the medium to long run.
Specifically, Ghana and Nigeria exhibit the highest correlation from the short to the medium term, while Gambia and Sierra Leone demonstrate a higher correlation in the long term. However, during the short term, the correlation among the six countries is generally very weak. Additionally, even in the long run, the overall correlation remains low for most countries, with Ghana's interest rate showing the potential to lead or lag in the medium to long term. It is noteworthy that Ghana displays an inverse correlation with Sierra Leone, Guinea, and Liberia in the short run, indicating weak co-movement of interest rates among these countries.Moving to inflation rate interdependence among the WAMZ countries, the results once again indicate variations in correlation across different timescales. In the short run, the co-movement of inflation rates among the countries is very weak, except for Guinea and Nigeria, which exhibit a higher correlation of 0.47. Similarly, Sierra Leone and Liberia show a correlation of 0.42 at the end of the short term. The findings highlight the weak co-movement of inflation rates among the WAMZ countries, with only a few instances of higher correlations. This suggests limited synchronization of inflation dynamics within the region, particularly in the short term.
The study further reveals that even in the long term, the correlation of inflation rates among the countries of the WAMZ remains very weak, except for Guinea and Liberia which exhibit a higher correlation in the long term. Generally, the correlation of inflation rates among the six countries is not encouraging across the short term, medium term, and long term. Graphical representation of the overall correlation of inflation rates confirms the same pattern observed in the bivariate pairwise correlation analysis, indicating a consistently weak correlation of inflation rates within the WAMZ across all timescales. However, it is worth noting that Liberia and Ghana show the potential for leading or lagging in the short to medium term, while Nigeria and Liberia exhibit similar potential in the medium to long term.
The study examines the exchange rate interdependence among the countries of the WAMZ and finds that the degree of correlation varies across different timescales. The results indicate that exchange rate correlation within the WAMZ is generally very weak, both in the short term, medium term, and long term. This weak correlation is evident in the fact that most countries exhibit negative or inverse correlation across all timescales. However, it is worth noting that Gambia and Nigeria demonstrate a relatively higher correlation of approximately 0.58 from the medium term to the long term.
The results of this study indicate a lack of progress in economic integration among the countries of the WAMZ over time. These findings support other evidence showing a lack of convergence in macroeconomic variables within the region, which poses challenges to the eventual implementation of a common currency. The behaviour of macroeconomic variables in the WAMZ exhibits distinct patterns, making it difficult to use interest rates, inflation rates, and exchange rates in one market to explain the returns observed in other WAMZ markets. The significant disparities between interest rates, inflation rates, and exchange rates suggest a more divergent dynamics in these markets in the long run.To strengthen and expedite the integration process in the sub-region, it is crucial for member countries to commit to credible macroeconomic policies aimed at achieving convergence benchmarks. Furthermore, participating countries should consistently strive to implement suitable monetary and fiscal policies, as well as establish robust structural and institutional measures. Given Africa's history of excessive spending, weakened fiscal positions, undue political pressures, and compromised governance institutions, it is authoritative to address these challenges to meet convergence benchmarks.
The paper recommends that to make a common currency a viable option, it is important to ensure that member states commit to the implementation of sound and credible fiscal and monetary policies. Also, WAMZ countries should strengthen the fiscal, monetary, and exchange rate policies of all the WAMZ countries involved in the integration process. Countries are encouraged to embark on rigorous structural and institutional reforms to support the emerging dictates of the ECOWAS integration agenda. Additionally, we emphasise the imperative for strict enforcement of regional agreements like the ECOWAS trade liberalization scheme. The key stakeholders should take a realistic and pragmatic measures that incorporate the complexities and challenges associated with ECOWAS integration and ensure the success of the monetary union.

Funding
The authors received no direct funding for this research.

Disclosure statement
No potential conflict of interest was reported by the authors.