Volatility Spillovers Across South American Currency Markets Finance Essay
This document explores return and volatility spillovers across South American currency markets using the recently developed Diebold-Yilmaz framework combined with a Bayesian approach to address the uncertainty surrounding the true extent of the phenomenon. The resulting spillover indices reveal that spillovers in volatility dynamics are generally higher and vary more sharply than spillovers in currency returns. Moreover, the pattern of interdependencies over time indicates that spillovers intensified during the recent financial crisis, which is consistent with the academic literature and with previous applications of the Diebold-Yilmaz framework to other asset classes and episodes of financial distress.
This document explores the dynamics of South American currency markets with the objective of identifying and measuring potential return and volatility spillovers.
The presence of spillover effects can be regarded as a consequence of financial and economic integration within the region, but it may also hint contagion dynamics or herding behaviour among investors. However, irrespective of the origin of this phenomenon, it is clear that a correct measurement of the spillovers is a valuable input to portfolio and risk management decisions, relevant both to local and foreign investors. Indeed, an adequate identification of spillover effects should provide insights on the way shocks are transmitted from one market to another and should therefore contribute to more efficient outcomes in terms of risk diversification. It should also aid hedging decisions in companies with cross-border investments in South America. Finally, the characterization of each market’s reaction to currency developments in the rest of the region should also prove relevant from a policymaking perspective.
The identification and measurement of spillovers is based on the spillover index recently proposed by Diebold and Yilmaz (2009a), which builds from the forecast error variance decomposition of vector autoregressive models fit to both return and volatility time series. Although this approach does not provide a forecasting tool, it has the virtue of aggregating cross-country spillovers into a single figure that can be compared to findings in other markets and, most importantly, that can be traced to explore the pattern of market interdependencies over time.
Moreover, this study innovates on the Diebold-Yilmaz framework in the sense that it assesses the uncertainty around the spillover estimates by incorporating a Bayesian perspective, which allows the construction of confidence intervals using a Monte Carlo exercise.
The estimated spillover indices indicate that over the past seven years (in which countries in the sample have had floating currency arrangements) the spillover effects have been significant, with the Diebold-Yilmaz index averaging 10% in the case of returns and 23% in the case of volatility. In line with Diebold and Yilmaz’s findings in previous applications to other assets, return spillovers tended to be more stable over time, while spillovers in volatility dynamics showed more abrupt variations over the sample period and, in particular, displayed a sizeable increase amid the global financial crisis of 2007-2008. Finally, it should be noted that the confidence bands constructed through the Monte Carlo exercise suggest a relatively tight distribution, indicating that the reported indices should be an accurate representation of the true magnitudes.
The rest of the document is organised as follows. Section II provides a brief review of relevant academic literature. Section III presents the methodological approach, explaining the Diebold-Yilmaz framework used to measure the spillovers across the currency markets and introducing a Bayesian perspective to assess uncertainty. Section IV characterises the time series used in this study. Section V presents the main findings and Section VI contains some concluding remarks.
The interdependence across currency markets has been a recurrent topic in economic literature. However, a great proportion of the body of literature is concerned with long-run settings (with a focus on the existence of different versions of the purchasing power parity and generally carried out using cointegration techniques), while studies of the short-term interrelations are relatively scarcer.
These later studies have been mostly concerned with exploring spillover effects in volatility dynamics, given that in developed countries exchange rates have been widely documented to follow a martingale process with not autocorrelation at returns level  . Engle, Ito and Lin (1990) studied the US dollar / Japanese yen exchange rate dynamics in both the Tokyo and the New York market and found evidence of “meteor shower”-type of volatility clustering as opposed to “heat wave”-type, implying that the major sources of disturbances were not changes in country-specific fundamentals and that shocks tended to increase conditional volatility in both markets. However, the question of whether the “meteor shower” resulted from correlated fundamental news or failure of market efficiency remained unanswered. Baillie and Bollerslev (1991) found evidence in the same direction considering the British pound, the Deutsch mark, the Swiss franc and the Japanese yen vis-a-vis the US Dollar. Since then, numerous studies have obtained similar conclusions in various applications  .
These research papers provide the theoretical background for the search of volatility spillovers across South American currency markets. However, it must be noted that in these markets there is also evidence of autocorrelation in exchange rate daily variations, motivating the specification of a VAR model for the respective means. While much of the recent literature has focused on volatility, this approach, together with an additional exploration of eventual spillovers in return dynamics, is not unprecedented either. Indeed, in this sense it is very similar to that adopted by Elyasiani, Kocagil and Mansur (2007) in an application of generalized variance decomposition analysis to the dynamics of the British pound, the Deutsche marc, the Swiss franc and the Japanese yen. It is also in line with previous applications of the Diebold-Yilmaz framework to other asset classes, including the exploration of the interdependencies across American equity markets (Diebold and Yilmaz, 2009b), East Asian equity markets (Yilmaz, 2010), global equity markets (Diebold and Yilmaz, 2009a) and different euro rates (McMillan and Speight, 2010).
The academic literature on the short-term dynamics of the South American currencies is very limited. This could be related to the fact that most countries in the region have a long history of currency arrangements that implied some sort of peg, so that daily movements (if any) where mostly governed by official interventions and not by market forces. In this context, most of the studies that have been undertaken over the past few years focus on convergence and the long-run behaviour of the currency markets (de Mello and Carneiro, 1997, Diamandis, 2003, Diamandis and Drakos, 2005), overlooking the patterns in daily variations.
Perhaps the most relevant reference regarding short-term dynamics and cross-country relationships is Ruiz (2009). The empirical research considered most Latin American currencies and applied a factor ARCH model to test for common volatility process in the foreign exchange markets. Ruiz concluded that in general exchange rates in Latin America do not share a common volatility process, but from the perspective of the present study it is worth noting that most of the countries that passed the test of common volatility were indeed South American countries. Ruiz attributed this result to the fact that South American economies have become more highly integrated than those in Central America, both financially and in terms of trade. Ruiz also pointed out that most countries in the region have followed similar macroeconomic policies in the past decades, including a shift towards inflation targeting regimes.
As noted in Elyasiani, Kocagil and Mansur (2007), interdependence may result from markets being simultaneously affected by public announcement of certain news, from agents in one market attempting to extract information about other markets by observing trade patterns in those markets or from governments quickly reacting to measures of other governments. In any case, the existence of spillovers is clearly consistent with increasing financial and economic integration, in line with Ruiz’s conclusions.
However, as noted by Pramor and Tamirisa (2006), the presence of “meteor showers” also implies a greater likelihood of bandwagon effects and contagion across financial markets. Considering the characterisation presented by Gelos and Sahay (2000), elements such as margin calls, herd behaviour (with possible rationalisations through informational models or models based on incentive structures) and psychological features involving imperfect recall of past events could have acted as very relevant mechanisms of contagion in South America in the past. Nevertheless, it must be noted that the Diebold-Yilmaz framework adopted in this study provides a measure of the magnitude and a description of the dynamics of spillovers over time, but it does not provide sufficient elements to formally distinguish between the notions of “interdependence” and “contagion” (see, for example, Forbes and Rigobon, 2002). Therefore, despite being a relevant dimension to gain a full understanding of the spillovers phenomena, the interpretation of the causes from that perspective lies beyond the scope of this study and remains as a future line of research.
The Diebold-Yilmaz spillover index
As previously noted, the spillover index proposed by Diebold and Yilmaz (2009a) is based on the variance decomposition of vector autoregressive (hereinafter VAR) models.
In VAR models, each variable can potentially depend on its own lags and also on the lags of all the other variables included in the model. Following Hamilton (1994), a -order -variable VAR model can be written as:
where is the vector collecting the time series whose dynamics are to be analysed (in this case either the return or the volatilities of the different currencies), denotes an vector of constants, denotes an matrix of autoregressive coefficients for and is the vector of error terms, which is assumed to follow a multivariate normal distribution. Moreover, when the time series are covariance-stationary, there is an equivalent moving average representation of the VAR model, in which is expressed as a convergent sum of the history of :
where is the mean process defined as = and the operator satisfies .
In this framework, Hamilton shows that the mean squared error of forecasting periods into the future can be expressed as:
where and .
To interpret the in a way that is economically meaningful, one would like to decompose it and identify the contribution of innovations attributable to the different components of the system. With this objective in mind, the so-called “identification” of the VAR model becomes a central issue. Indeed, the VAR model presented above can be thought of as a “reduced form” of a more general dynamic “structural” model, which allows for contemporaneous as well as lagged dependence between variables.
In the case of South American currencies, it is not difficult to conceive that the daily return and volatility in one country can be dependent not only on the lagged developments in other countries but also on what happens in the other markets during the same day. Consequently, the error terms of the reduced-form VAR are likely to be contemporaneously correlated, which obscures the identification of the various system shocks. The calculation of the variance decomposition, in turn, requires the definition of orthogonal (uncorrelated) innovations, which can be unequivocally associated with “new” information about each of the variables .
Orthogonal innovations can be obtained either by imposing restrictions on the “structural” system or by resorting to a Cholesky decomposition of the matrix . In the case of this analysis, there weren’t clear economic justifications to characterise the “structural” system  , so the Cholesky decomposition was used to obtain the lower triangular matrix such that . The vector of orthogonalised disturbances is therefore defined as , with .
Denoting , the forecast error can be rewritten as:
From this expression the notion of variance decomposition is straightforward. Considering the system as a whole, Diebold and Yilmaz define the “own variance shares” as the fraction of the -step-ahead error variances in forecasting due to shocks to , for . Denoting the elements of as , the sum of the “own variance shares” for all the variables corresponds to . In turn, the “cross-variance shares” or “spillovers” are the fraction of the -step-ahead error variances in forecasting that can be attributed to shocks in , for and . Accordingly, the sum of the “spillovers” considering all potential interactions between the variables can be calculated as . Finally, the total forecast error variance can be represented as and it is, of course, the sum of the “own variance shares” and the “cross variance shares” defined above. Based on these conventions, the spillover index is then defined as the sum of the “spillovers” relative to the total forecast error variation:
As highlighted by Diebold and Yilmaz, this spillover index has the virtue of aggregating cross-country spillovers into a single figure that can be traced over time using a rolling estimation of the VAR model that originates it. Moreover, it is a standard calculation that enables a comparison of the magnitudes of the spillovers in applications to different markets and assets.
Assessing uncertainty with a Bayesian perspective
The spillover index is a highly non-linear function of the parameters of the VAR model, which complicates the construction of confidence intervals in a purely frequentist framework. However, uncertainty around the estimated spillover indices can be introduced by analysing the VAR model with a Bayesian approach, using a Monte Carlo exercise.
This is an innovation from the original Diebold and Yilmaz framework, but it provides useful insights about the accuracy of the estimates and, from a theoretical point of view, it easily follows when building on the posterior conditional distribution of the VAR coefficients and the variance-covariance matrix of the error term.
Indeed, the VAR model presented in section III.i fits into the class of linear regression models with normally distributed errors. By grouping the vector of constants and the lagged variables into a matrix it can be written as:
Under a diffuse prior, Bauwens, Lubrano and Richard (1999) show that the posterior distribution of the estimated VAR can be factorised as the product of a conditional multivariate normal distribution and an inverse-Wishart distribution:
where is the number of observations, is the number of estimated parameters and indicates the Kronecker product.
Using these observations, confidence bands for the spillover index can be constructed by taking successive draws of the parameters and repeating the calculations on section III.i. More precisely, the Monte Carlo exercise proceeds as follows:
Draw a covariance matrix from the inverse Wishart distribution with parameters and .
Conditional on , draw a vector of coefficients for the VAR, , from .
Use and to get new matrices and new , so as to compute new matrices . Using , calculate and store the value of the spillover index.
Iterate. From a Bayesian perspective, the confidence intervals are the corresponding percentiles of the Monte Carlo iterations.
This procedure has been used in various financial applications, with Brunnermeier and Julliard (2008) being a pertinent example. As pointed out in that study, it should be noted that the factorisation of the posterior given above holds exactly under normality and the Jeffreys’ prior  , but it can also be obtained, under regularity conditions, as an asymptotic approximation around the posterior MLE. Moreover, it should also be noted that in the present application to South American currency markets there is firm evidence in favour of stationarity of all the returns and volatility series (see section IV), but this Bayesian approach would also be robust in case the covariance stationarity condition was not met.
In this study, 10,000 draws were taken for the return and the volatility VAR models, both when estimated for the whole sample and when computed using a rolling estimation window. The figures included in the tables and charts presented in this document correspond to the median value of the spillover indices obtained for each of those 10,000 draws. Confidence intervals are reported using the 5% and the 95% percentiles.
The Monte Carlo exercise and the calculations were implemented with a programme coded in R.
Descriptive statistics of recent currency developments in South America
The data set was collected from Bloomberg’s database and consists of daily observations of closing exchange rates ranging from January 1st, 2003 to February 11th, 2010 (making a total of 1,858 observations). The sample contains the currencies of Argentina (ARG), Brazil (BRA), Chile (CHI), Colombia (COL), Paraguay (PAR), Peru (PER) and Uruguay (URU). All the nominal exchange rates are expressed in foreign currency received per one US dollar. Unlike in other studies of dynamic dependence across markets, there was no need to adjust the data to take into account significant differences in trading hours.
Daily returns in each market were calculated as , where is the exchange rate in day . Proxies of the true volatility processes were constructed using the squared residuals of the returns dynamics. The residuals correspond to the estimated errors of models fit to each of the return series, to make a proper treatment of the mean process. The “optimal” model in each case was selected using the Schwarz’s Bayesian Information Criterion (BIC), allowing and to potentially vary between 0 and 6. The results of the model selection procedure are summarised in Table IV.1.
Despite currency quotes are available for a much longer period, this study considered only the past seven years to assess the exchange rate dynamics on a period of floating currency regimes. Indeed, most South American countries had some kind of currency peg in the previous decade but opted to move to a more flexible exchange rate arrangement in the aftermath of the financial crises that hit the region in the late 1990s and early 2000s. It is worth noting that Bolivia, Ecuador and Venezuela still hold currency arrangements that imply different sorts of pegs  and were therefore excluded from the study. In this way, all the countries considered in the sample had a floating exchange rate regime in the analysed period, although it must be noted that in some of them official intervention in the currency market is not unusual.
Tables IV.2 and IV.3 present summary statistics on the recent behaviour of the South American currencies. Over the sample period most currencies showed a moderate nominal appreciation, consistent with some degree of market correction following the sharp devaluations that took place in the region in the late 1990s and early 2000s but also with the abundant capital inflows registered in the past few years. The only country with a positive daily mean in the return series is Argentina, but it should be noted that it is also the country with the highest rates of domestic inflation over the analysed period.
In line with the usual features of daily financial data, in all countries the mean of the returns and volatility series is clearly dominated by a larger standard deviation and there is evidence of non-Gaussian behaviour. The Ljung-Box statistics for 10 lags indicate the presence of autocorrelation in the returns and the variance of all the currencies. Finally, the results of the unit root tests using the Augmented Dickey-Fuller and the Philips-Perron procedure suggest stationarity of all the returns and volatility series, which allows for the specification of VAR models  .
All the results presented in the following subsections were derived using a VAR(1) model for the returns and a VAR(4) model for the volatilities. In each case, the number of lags was selected using the BIC criterion. Moreover, the forecast error variance decompositions needed to calculate the corresponding spillover indices were derived using 10-days-ahead forecasts.
As previously noted, one of the central research interests of this study was to track the behaviour of spillovers over time, under the hypothesis that the pattern presumably changed over the period under analysis due to changes in the regional and international context.
However, the estimation of the spillover indices over the full sample provides some interesting insights. Intuitively, the results obtained when applying the methodology described in sections III.i and III.ii to the full sample provide a representation of the “average” magnitude of the spillovers over the period under study.
As can be seen in the figures V.1 and V.2, the distribution of the return and volatility spillover indices over the 10,000 draws of the Monte Carlo exercise is quite tight. The spillover index corresponding to currency returns has a median of 10.1% and a standard deviation of 0.5%. The estimates for the volatility dynamics indicate that in that case the spillover effect is much more significant, denoted by a median value of the spillover index of 23.4%. Finally, it is worth noting that in both cases the results reveal a positive skewness, indicating that higher values were relatively more frequent.
Moreover, the full-sample perspective provides a good starting point to analyse the individual contributions of the different countries to the overall magnitude of the spillovers in the region. While it is true that those contributions could also be traced over time (and under the same argument as before they have probably shown significant fluctuations in the sample period), the analysis of the rolling estimation of these figures rapidly becomes very complex, as it implies studying the pattern of too many possible interactions over time  . In this sense, it can be argued that the static, full-sample analysis is a first characterisation of the incidence of innovations in each market in a way that is tractable and simpler to present.
The main findings in this regard are reported using the so-called “spillover tables” suggested by Diebold and Yilmaz (2009a). The th value of each matrix corresponds to the estimated contribution to the variance of the 10-days ahead forecast error of country coming from innovations in country . Hence, the diagonal elements can be identified with the “own variance shares” defined in section III.i, while the off-diagonal terms are the essence of the quantification of spillovers. However, it should be noted that as the reported figures correspond to the median estimates of 10,000 draws in the Monte Carlo exercise, the spillover indices presented in the lower-right corner of the tables do not exactly coincide with ratio of the sum of off-diagonal terms over the sum of all the figures in each matrix.
Tables V.1 and V.2 show that Brazil was by far the country with the highest “contribution to others”, both in the case of innovations in the returns and of innovations in the volatility. This is consistent with the fact that Brazil is the biggest economy of the region and that it has significant financial and trade interlinkages with all the countries in the area. On the other hand, Colombia and Chile appear as the countries that receive the greatest “contribution from others” in the return dynamics of their foreign exchange markets, while in the other countries that figure is well below 10% (indicating than less than 10% of the error variance in forecasting 10-days returns can be explained by the innovations in other markets). In turn, in the case of volatility the “contribution from others” is higher in all countries, reaching 58% in the case of Peru.
While the implications of these findings are reasonable and quite intuitive, some key limitations of the methodological approach should also be considered. In particular and as explained in section III.i, the results described above can be dependent on the order of the variables, because the Diebold-Yilmaz framework relies on the Cholesky-factor identification of the VAR models. The robustness of the overall spillover patterns to VAR ordering is addressed in section V.iv, but it should be noted that the directional spillovers commented before could also vary significantly. In a more recent research paper (Diebold and Yilmaz, 2010) the authors tackle this issue by proposing an order invariant measure which relies on the generalized VAR framework of Koop, Pesaran and Potter (1996) and Pesaran and Shin (1998). As previously noted, Elyasiani, Kocagil and Mansur (2007) also resort to a generalized variance decomposition approach to analyse the degree interdependence among European currencies and the Japanese yen in the period 1985-2005. Testing the robustness of the directional spillovers in South American currency markets using such framework was beyond the scope of the present study, but it remains as a possible direction for future research.
Variation of spillovers over time
As expected, the rolling estimation of the spillover indices revealed that the intensity of the spillovers across South American currency markets varied over time and, in particular, that it increased substantially during the global financial turmoil of 2007-2008.
The Diebold-Yilmaz index for spillovers in returns doubled with the first signs of financial distress in July 2007, jumping from around 10% to slightly more than 20%. Our estimates indicate that it declined moderately in the beginning of 2008, but then bounced back to a maximum of 25% in October, amidst the collapse of commodity and equity markets worldwide. The rolling estimates show that the index experienced a downward correction since then, but in the end of the sample period it remained high at around 18.5%.
As shown in figure V.3, the fluctuations in volatility spillovers were sharper. The behaviour between 2003 and 2006 had already been more volatile (with the average standard deviation of the spillover index at 4.9% versus 2.3% in the case of spillovers in returns), but the difference became even more acute during the crisis period. The Diebold-Yilmaz index rose from around 20% to 85% in July 2007. As in the case of returns, the spillover index edged downwards from these record readings during the second half of 2007 and the beginning of 2008, but it spiked again when world markets collapsed in late 2008. As shown in the chart, the index remained high during the subsequent year, but by the end of the sample period it stood relatively in line with pre-crisis levels (slightly below 25%).
Comparison with previous studies
The pattern presented in the previous section is broadly consistent with the empirical findings of previous applications of the same methodological approach to other financial assets, which suggest that spillovers in volatility tend to show larger fluctuations than spillovers in returns.
Indeed, Diebold and Yilmaz (2009a) show that over 1997-2007 volatility spillovers in global equity markets presented sharp movements which coincided with “readily-identified crisis events”, whereas return spillovers displayed a more stable pattern. By the same token, the results of Diebold and Yilmaz (2009b) indicate that between 1992 and 2008 American equity markets showed sizeable spillover effects, but spillovers in volatility exhibited larger fluctuations than spillovers in returns. In particular, the authors found that the spillover indices increased at times of financial distress worldwide, including the Mexican, the Asian and the Russian crisis in the 1990s. Similarly, Yilmaz (2010) analysed the behaviour of East Asian equity markets between 1992 and 2009 and concluded that “while the return spillovers moved rather smoothly over time with occasional fluctuations during major crises, the volatility spillover index moves up and down as the data pertaining to major financial shocks are included in the rolling sub-sample window”.
The magnitudes of the spillover effects, however, differ from those found in previous studies. On the one hand, the 10.1% estimate for the “average” spillover index for currency returns reported in section V.i is below the 35.5% found by Diebold and Yilmaz (2009a) for global equity markets, the 18.6% reported by Diebold and Yilmaz (2009b) for equity markets in the Americas and the 31.6% reported by Yilmaz (2010) for East Asian equity markets. On the other hand, our “average” volatility spillover of 23.4% is broadly in line with Diebold and Yilmaz (2009b) finding for equity markets in the Americas (24.9%), but is still significantly lower than the 39.5% and the 77.7% figures reported by Diebold and Yilmaz (2009a) and Yilmaz (2010) for global and East Asian equity markets respectively.
These discrepancies could be partially explained by methodological differences, such as the horizon used to calculate the forecast error variance decomposition or the volatility proxy adopted on each study. However, they could also be related to the fact that the three studies show that the 1990s and early 2000s were characterised by higher spillover effects than the 2003-2006 period, which was in fact a period of very low spillovers in absence of major episodes of financial distress worldwide. The fact that the analysis of South American currency markets starts in 2003 could therefore contribute to explain why the full-sample spillover indices were lower than those reported in other studies. Finally, the differences with previous applications could also signal different dynamics in currency and equity markets. Unfortunately, the Diebold-Yilmaz framework has not yet been applied to other currency markets in a way that it yields comparable results  .
Robustness to VAR ordering
As previously noted, the Cholesky factorisation of the variance-covariance matrix of the VAR residuals provided a way of obtaining orthogonalised errors (which are central to the calculation of the variance decompositions and therefore of the spillover indices) without specifying a particular set of restrictions to the “structural” model. However, it can be argued that this approach is indeed implicitly imposing restrictions among the variables, in the sense that it implies that the first variable in the system will respond contemporaneously only to its own structural shock, the second variable will respond contemporaneously to its own shock and to the structural shock of the first variable, and so on (Hamilton, 1994).
The spillover indices reported in this study were based on a Cholesky decomposition that ordered the currency markets according to the size of the GDP of the respective countries, implicitly assuming that the currencies of the bigger economies were less likely to be affected by contemporaneous currency developments in other countries than the currencies of the smaller countries (for example, the dynamics of the Uruguayan Peso are more likely to be affected by movements in the Brazilian Real than vice versa).
The robustness of the results to that particular assumption was assessed by recalculating the spillover indices using alternative VAR orderings. Ideally, one would like to verify that results are robust to any particular order of the variables, but working with 7 currency markets that would imply evaluating more than 5,000 possibilities. Consequently, considering computational restrictions and following Diebold and Yilmaz (2009a) procedure, the robustness of the findings was explored by using six additional “rotated” orderings. Each of these “rotated” orderings implied moving the first market of the previous ordering to last position, keeping the rest unchanged.
Figures V.4 and V.5 present the results of that exploration, plotting the lowest and the highest values obtained at each point in time  , together with the maximum difference (in absolute value) between the results of the original order and the most extreme results obtained with rotated orders . The charts indicate that the range of variation is relatively narrow and that the alternative spillover indices reveal the same pattern over time, both in the case of return and of volatility series.
The application of the Diebold-Yilmaz framework to South American currency markets revealed the presence of spillover effects in both the returns and the volatility dynamics, meaning that a fraction of the daily developments in each country can actually be attributed to shocks in other markets. The Diebold-Yilmaz spillover indices, which formalise this notion using the forecast error variance decomposition of VAR models, were estimated at 10.1% and 23.4% for returns and volatility respectively. At a country level, Brazil was by far the country with the highest “contribution to others”, which is consistent with the fact that it is the biggest economy of the region and that it has significant financial and trade interlinkages with all the countries in the area.
The full-sample estimates of the spillover indices were lower than those obtained in previous applications of the same methodological framework to other asset classes. However, the rolling estimation of the spillover indices yielded a pattern over time that was very similar to that found in previous studies. In particular, our findings indicate that spillovers in currency volatility displayed sharper fluctuations than spillovers in returns, but both increased significantly amid the 2007-2008 global financial turmoil.
As previously noted, the Diebold-Yilmaz framework does not provide elements to formally distinguish between the notions of “interdependence” and “contagion”, but the pattern of the rolling estimates could be interpreted as hinting that investors might have treated the South American markets indiscriminately during the recent turbulence. The greater intensity of spillover effects in times of crisis is broadly consistent with the academic literature on bandwagon effects and contagion presented in section II and is highly in line with previous empirical applications to other asset classes and to other crisis episodes.
From a methodological point of view, it is worth noting that the present study innovated on the Diebold-Yilmaz framework by adopting a Bayesian perspective. In this way, the full-sample spillover indices were reported in the context of the distribution of 10,000 draws, allowing for a characterisation of the range of uncertainty. Moreover, the rolling estimations were presented together with confidence bands built from the Monte Carlo exercise, giving objective elements to assess the significance of the fluctuations over time.
Finally, while the economic implications of the findings are quite straightforward and give relevant insights from risk management and policy-making perspectives, it is important to acknowledge the limitations inherent to the methodological approach. These are, at the same time, interesting avenues for future research. The sensitivity of the results to the order of the variables is a central issue. The robustness of the overall spillover patterns was tested by using alternative orders, but it would be convenient to adopt an order-invariant forecast error variance decomposition in the spirit of Pesaran and Shin (1998), as done in the most recent research paper of Diebold and Yilmaz (2010). This approach would also provide sounder grounds to assess the robustness of country specific dynamics and, more generally, of directional spillovers across currency markets. Moreover, as noted in Diebold and Yilmaz (2009b), the VAR models could be enriched by allowing for time-varying coefficients or factor structure with regime switching. Such extensions could be useful to explore if government interventions in the foreign exchange markets (which are not infrequent in these countries) have an impact on the magnitude of return and volatility spillovers. On top of this, it should be borne in mind that the Diebold-Yilmaz approach does not provide a forecasting tool, but merely a framework to identify spillovers and trace their behaviour over time. The integration of spillovers in a model built for forecasting purposes was beyond the scope of the present study but should be an interesting line of future research. Finally, future studies could also incorporate high frequency data to explore the speed of spillover dynamics.
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