This paper proposes a new procedure for analyzing volatility links between di®erent
markets based on a bivariate Markov switching model. An empirical application of this
procedure to three emerging markets is examined and discussed

Sola, M

Spagnolo, F

Spagnolo, N

English

Brunel University Research Archive

A Test for Volatility Spillovers¤martin solaa,b, fabio spagnoloa and nicola spagnolocaSchool of Economics, Mathematics and Statistics,Birkbeck College, University of London, UKbDepartment of Economics, Universidad Torcuato Di Tella, ArgentinacDepartment of Economics and Finance, Brunel University, UKJanuary 2002AbstractThis paper proposes a new procedure for analyzing volatility links between di®erentmarkets based on a bivariate Markov switching model. An empirical application of thisprocedure to three emerging markets is examined and discussed.Keywords : Markov switching, GARCH, Volatility, Financial crises.JEL Classi¯cation: C32, G151 IntroductionDuring recent years we have witnessed several ¯nancial crises which have originated in anemerging economy and have then, after a short period of time, spread across to other markets.The transmission mechanism could either be explained as the natural consequence of the realand ¯nancial interrelations between these economies, or (and) as a result of the action ofinstitutional investors which have long positions in emerging markets ¯nancial instrumentsand, whenever a crises takes place, want to reduce their portfolios' risk by selling their highreturn high risk positions (e.g. Kaminsky and Schmukler, 1999).A popular approach used to test the transmission of shocks across ¯nancial marketshas been based on generalized autoregressive conditionally heteroscedastic (GARCH) models(see Reinhart (2001) for a survey). Nevertheless, tests for contagion based on GARCHmodels do not allow us to distinguish whether the interaction takes place in periods of calm(low volatility) or crises (high volatility). These models are typically symmetric both inthe parameterization (an economy a®ects the other in the same way in periods of calm andin periods of crises) and in the temporal causality (an economy a®ects the other futurevolatility both in calm and in crises). In that respect, these models do not seem rich enoughto accommodate the economic and ¯nancial explanations of the crises presented above.¤The authors are grateful to Zacharias Psaradakis for useful comments and Melinda Borgen for assistance.Martin Sola and Fabio Spagnolo are grateful to the ESRC for support under grant L138251003. Correspondingauthor: Fabio Spagnolo, School of Economics, Mathematics and Statistics, Birkbeck College, 7-15 GresseStreet, London W1P 2LL, United Kingdom. Tel. +44 (0)20 76316452; fax: +44 (0)20 76316416. E-mail:fspagnolo@econ.bbk.ac.uk1This paper proposes an alternative way of detecting the transmission of high volatility pe-riods from one economy to another. We consider a parameterization of the Markov switchingmodel used in Phillips (1991) and Ravn and Sola (1995) which allows for four possible statesof nature (consisting of combinations of either low or high volatilities) and test whether acountry leads the other in and out of a period of crises (de¯ned as periods of high volatility).An attractive feature of this approach is that it accounts for the fact that a crises (and itstransmission) is better characterized as a sporadic event (which only take place a few timesin a sample), rather than a structural relationship between stock markets as in a multivariateGARCH.An empirical application of this procedure to three emerging markets recently a®ectedby severe ¯nancial crises is examined and discussed. For the Asian countries considered inthe paper, we cannot reject the hypothesis that Thailand leads South Korea and thereforethe volatility spillovers appear to be unidirectional following the onset of the crisis, runningfrom the markets in turmoil (Thailand) to the other (South Korea). Only weak evidence ofvolatility spillover was found between South Korea and Brazil.2 The ModelConsider the following model for the 2 £ 1 vector zt = [xt; yt]¶;zt = ¹ + ©stut, (1)where ¹ = [¹x; ¹y]0 and ut is a Gaussian process with zero mean and positive-de¯nite co-variance matrix §; fstg is modelled as a time-homogeneous Markov chain on f1; 2; 3; 4g,independent of futg, with st indicating the state that the system is in at date t. The timeseries fztg (the vector of stock market returns of country xt and yt) satis¯es therefore afour-state Markov processztj(st = s) » N(¹;-st), (2)for s = 1; 2; 3; 4; with -st = ©0st§©st . Accordingly, the variance-covariance matrices are:- =(-s=1 ="¾2xh ¾xh;yh¾yh;xh ¾2yh#; -s=2 ="¾2xh ¾xh;yl¾yl;xh ¾2yl#; (3)-s=3 ="¾2xl ¾xl;yh¾yh;xl ¾2yh#; -s=4 ="¾2xl ¾xl;yl¾yl;xl ¾2yl#);where the indices h and l refer to high or low volatility. In the general case the transitionmatrix will be given by a 4 £ 4 matrix, ¦ (with elements ¼ij = Pr(st = ijst¡1 = j),i; j = 1; 2; 3; 4), where each column sums to unity and all elements are nonnegative. Wecan impose various restrictions on the transition matrix to test particular hypotheses. Forexample, if the volatility of each country's return follows an independent regime-shiftingprocess, the four states transition matrix will be given by¦indep =0BBBB@¼xh¼yh ¼xh(1 ¡ ¼yl) (1 ¡ ¼xl)¼yh (1 ¡ ¼xl)(1 ¡ ¼yl)¼xh(1 ¡ ¼yh) ¼xh¼yl (1 ¡ ¼xl)(1 ¡ ¼yh) (1 ¡ ¼xl)¼yl(1 ¡ ¼xh)¼yh (1 ¡ ¼xh)(1 ¡ ¼yl) ¼xl¼yh ¼xl(1 ¡ ¼yl)(1 ¡ ¼xh)(1 ¡ ¼yl) (1 ¡ ¼xh)¼yl ¼xl(1 ¡ ¼yh) ¼xl¼yl1CCCCA .(4)2We can then test the validity of the restricted version by using a likelihood ratio (LR) testthat under the null hypothesis is distributed as Â2(8): We will refer to this as the hypothesisof independence (or no ¯nancial contagion) between x and y. Contagion, as opposed toindependence, occurs whenever one of the countries leads (or lags) the other one in and outperiods of high volatility. This would be the case, for example, if y is always in the samestate that x was one period before. The appropriateness of this hypothesis can be veri¯ed bytesting (using LR tests distributed as Â2(10)) if we can reduce the transition matrices to¦xly1 =0BBBB@¼xh ¼xh 0 00 0 (1 ¡ ¼xl) (1 ¡ ¼xl)(1 ¡ ¼xh) (1 ¡ ¼xh) 0 00 0 ¼xl ¼xl1CCCCA (5)where ¦xly1 indicates x leads y one period. It is also possible to allow for expected leads oflonger than one period; the matrix ¦xly2 below illustrates the case where the expected lead istwo periods:0BBBBBBBBBBBBBB@¼xh¼xh+(1 ¡ ¼xh)(1 ¡ ¼xl)¼xh¼xh+(1 ¡ ¼xh)(1 ¡ ¼xl) 0 00 0(1 ¡ ¼xl)¼xh+¼xl(1 ¡ ¼xl)(1 ¡ ¼xl)¼xh+¼xl(1 ¡ ¼xl)(1 ¡ ¼xh)¼xl+¼xh(1 ¡ ¼xh)(1 ¡ ¼xh)¼xl+¼xh(1 ¡ ¼xh) 0 00 0¼xl¼xl+(1 ¡ ¼xl)(1 ¡ ¼xh)¼xl¼xl+(1 ¡ ¼xl)(1 ¡ ¼xh)1CCCCCCCCCCCCCCA:(6)Similar matrices can be constructed for the case where y leads x.Whenever the results are inconclusive (say more than one of the restricted models pre-sented above is not rejected), the models can be compared using selection criteria whichweight ¯t, measured by the maximized log-likelihood, and complexity, measured by the num-ber of parameters. Two popular criteria, the Akaike Information Criterion (AIC) and theSchwarz Bayesian Criterion (SBC), are employed in the next section.3 Empirical ResultsAs an empirical illustration of the testing procedure outlined before, we investigate for thepresence of volatility spillovers across three emerging stock markets which have recently beenhit by a severe ¯nancial crises, namely Thailand, South Korea and Brazil. The popular viewis that the East Asian crisis began in Thailand during the late spring of 1997 with sustainedspeculative attacks on the local currency and as a result the Korean currency was attackedlater that year1. The crisis then spread to other emerging economies including Brazil.To assess the plausibility of the contagion interpretation of the crises, we apply ourmethodology to countries with similar fundamentals and economic links, such as Thailandand South Korea. Contagion for these economies is consistent with both the real interrelationand the portfolio interpretation transmission channel.1See Corsetti et al (1998) for a detailed review.3We also consider countries without substantial economic and direct ¯nancial linkages(such as South Korea and Brazil). For these countries, evidence of contagion running fromSouth Korea to Brazil would be supportive of the hypothesis that, as Asian markets tumbled,international investors had to liquidate positions in Brazil in order to balance their portfolio.Statistical inference in the context of Markov switching models described in the previoussection is carried out by making use of the non-linear algorithm of Hamilton (1994, Ch. 22).Figure 1 plots the logarithmic di®erences of stock market indices for Thailand and SouthKorea over the period 1980:I-2001:II and shows that the volatility has substantially increasedin both countries as a consequence of the 1997 crisis. Maximum likelihood estimates2 of thegeneral model for the two countries, reported in Table 1, provide evidence of the magnitude ofthe changes in volatility between periods calm and crisis. Figure 2 plots the ¯lter probabilitiesof being in each state of the four regimes from the general model. It is clear from the plot thatstate 4 (low volatility) is associated with the period 1980-1985, while state 1 (high volatility)is associated with 1987-1988 (in correspondence with the Black Wednesday) and 1997-2001(in correspondence to the Asian ¯nancial crisis). For (most of) the remaining of the sample,Thailand is characterized by periods of high volatility and Korea by periods of low volatility.Table 2 reports maximized log-likelihood values for the models described in the previoussection. The restriction of independence of the Markov processes which dictate the switchesof the volatilities in the two countries is rejected at the conventional level of 5%. While thehypothesis of volatility spillovers running from South Korea to Thailand is ¯rmly rejectedfrom the data, the test statistic for the hypothesis that Thailand leads South Korea by twoperiods is not rejected by the data at the 5% signi¯cant level. Furthermore, both the AICand the SBC favour Thailand leading South Korea by two periods.Turning to South Korea and Brazil, Figure 3 plots the logarithmic di®erences of stockmarket indices for 1984:II-2001:II. From Table 1, the estimated parameters show signi¯cantevidence of shifts between regimes, with the estimated volatility being on average ¯ve timeslarger in periods of crises than in periods of calm. The inferred ¯lter probabilities shownin Figure 4 identify the years 1986-1988 and 1998-2000 as associated with periods of crises(state 1), and 1994-1995 with periods of calm (state 4). Notice that the stock returns ofboth countries are highly volatile starting from the middle of 1998 in correspondence to thebeginning of the Brazilian crisis. In contrast with the case of Thailand and South Korea, theresults presented in Table 2 show little evidence in favor of the contagion hypothesis. Eventhough we do not reject the hypothesis that South Korea leads Brazil by two periods, this isnot strong evidence in favour of that hypothesis since we also cannot reject the hypothesisof independence. When we compare the restricted models, both AIC and the SBC criteriasuggest that the independent model is preferred to the contagion interpretation.4 SummaryThis paper has introduced a new method for testing volatility spillovers which characterizethe transmission of the crises as a sporadic event which typically involve a country goingfrom a period of low volatility to high volatility, and being followed by the other in the subse-2All the ¯tted models considered in this section have standardized residuals which exhibits no signs oflinear or nonlinear dependence.4quent(s) period. The appealing feature of our speci¯cation is that it enables us to identify theprobabilistic structure, the timing and the duration of the volatility transmission mechanismfrom one country to another. The potential applicability of the proposed procedure has beenillustrated through an analysis of Thailand, South Korea and Brazil data.References[1] Corsetti, G., P. Pesenti, and R. Roubini, 1998. What caused the Asian currency and¯nancial crises? Parts I and II. NBER Working Papers, No. 6833 and 6844.[2] Hamilton, J.D., 1994. Time Series Analysis. Princeton: Princeton University Press.[3] Kaminsky, G.L. and S.L. Schmukler, 1999. What triggers market jitters? A chronicle ofthe Asian crisis. Journal of International Money and Finance 18, 537-560.[4] Philips, K.L., 1991. A two-country model of stochastic output with changes in regimes.Journal of International Economics 31, 121-142.[5] Ravn, M.O. and M., Sola, 1995. Stylized facts and regime changes: Are prices procyclical?Journal of Monetary Economics 36, 497-526.[6] Reinhart, C.M., 2001. A summary of the empirical literature on contagion. Manuscript,School of Public A®airs and Department of Economics, University of Maryland.5Table 1. General ModelaThailand (x) South Korea (x)South Korea (y) Brazil (y)¹x ¡ 0:00501(0:01625)0:11688(0:03066)¹y 0:00182(0:01486)0:03202(0:01494)¾2xh 0:08324(0:026230:10152(0:03853)¾2xl 0:01143(0:00224)0:01596(0:00331)¾2yh 0:08153(0:03446)0:16253(0:04459)¾2yl 0:07554(0:02436)0:03252(0:01374)¾xh;yh 0:04815(0:02258)¡ 0:02718(0:05612)¾xh;yl ¡ 0:00367(0:00690)0:00826(0:00776)¾xl;yh 0:07687(0:02755)0:05200(0:02210)¾xl;yl 0:00228(0:00190)0:03673(0:00893)aFigures in parentheses are estimated standard errors.Table 2. Maximized Log-Likelihood and Complexity-Penalized Likelihood CriterionaThailand and South Korea South Korea and BrazilModel Log-L AIC SBC Log-L AIC SBCGeneral 234.18 -424.36 -370.62 133.61 -223.22 -174.40Independent 226.11 (*) -424.22 -390.02 129.63 -231.26 -200.19Korea leads Thailand (1Q) 209.49 (**) -394.98 -365.67Korea leads Thailand (2Q) 216.23 (**) -408.46 -379.15Thailand leads Korea (1Q) 216.67 (**) -409.34 -380.03Thailand leads Korea (2Q) 227.65 -431.30 -401.99Brazil leads Korea (1Q) 122.28 (*) -220.56 -193.92Brazil leads Korea (2Q) 123.55 (*) -223.10 -196.46Korea leads Brazil (1Q) 120.91 (**) -217.82 -191.18Korea leads Brazil (2Q) 125.02 -226.04 -199.41a(1Q) and (2Q) indicate leading by one and two quarters. (*) and (**) indicate signi¯cance at 5% and 1%respectively, on the basis of a LR test. AIC and SIC are de¯ned as -2logL+2k and -2logL+ln(T)k, respectively,where k is the number of estimated parameters, T is the sample size and logL is the maximized log-likelihood.6Figure 1: Quarterly Returns for Thailand and South Korea-.8-.6-.4-.2.0.2.4.6.880 82 84 86 88 90 92 94 96 98 00Thailand South KoreaFigure 2: Filter Probabilities for Each State in the General Model0.00.20.40.60.81.080 82 84 86 88 90 92 94 96 98 00Probabilities of State 10.00.20.40.60.81.080 82 84 86 88 90 92 94 96 98 00Probabilities of State 20.00.20.40.60.81.080 82 84 86 88 90 92 94 96 98 00Probabilities of State 30.00.20.40.60.81.080 82 84 86 88 90 92 94 96 98 00Probabilities of State 47Figure 3: Quarterly Returns for South Korea and Brazil-1.2-0.8-0.40.00.40.81.286 88 90 92 94 96 98 00South Korea BrazilFigure 4: Filter Probabilities for Each State in the General Model0.00.20.40.60.81.086 88 90 92 94 96 98 00Probabilities of State 10.00.20.40.60.81.086 88 90 92 94 96 98 00Probabilities of State 20.00.20.40.60.81.086 88 90 92 94 96 98 00Probabilities of State 30.00.20.40.60.81.086 88 90 92 94 96 98 00Probabilities of State 48

A test for volatility spillovers

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