A univariate representation

Nelson (1991) has proposed an exponential GARCH in order to overcome weaknesses of the general GARCH. In particular, he allows an asymmetric effect in

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volatilities from the positive and negative shocks of a financial series, including weighted innovation. A possible specification of the EGARCH (1,1) model, for example, could be: and is a conditional variance. The standardized residuals, zi,t, are from the set of information available in the previous period and ψ(.) is a conditional density function with v being a vector of parameters, specifying the probability distribution. The variance equation is a function of four parameters, where ci is a constant term, the estimated parameter αi is a symmetric effect of the model, γi is a parameter showing whether the model has an asymmetric effect, and βi is a parameter that measures the persistence in conditional volatility.

The presence of leverage effects in the model can be tested by the hypothesis that parameter γi is less than 0. In such a case, positive shocks in the market generate less volatility than negative shocks. In the case where γi is greater than 0, positive news destabilizes market volatility more than negative news. If γi is equal to 0 the model is symmetric with no significant either positive nor negative shocks.

The univariate EGARCH (1,1) methodology is applied to analyze the reaction of stock markets to local macroeconomic news releases. This model is utilized with a Gaussian normal distribution of errors to study the effect of macroeconomic announcement. The mean (Equation 7) and the conditional variance (Equation 10) are

2 ,t

i

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extended with parameters of macroeconomic announcements and stock market returns:

(11) _{, , , ,} ,

(12) _, ^,

,

,

, , ,,

where ri,t is the daily return at time t for an emerging stock market i. is a 2×1 vector of lagged stock market returns for the United States (US) and emerging Europe (EE). is an 1×2 vector of parameters, which represent the autoregressive effects in returns of US and EE markets and presumably capture information that extends beyond macroeconomic announcements alone. The parameter _, is an 3×1 vector lagged stock market returns for all the other sample countries in the study (i.e., ).

is an 1×3 vector of parameters, which represent autoregressive effects of emerging stock markets. The parameter _, is a dummy for macroeconomic announcements that originate in each local market; each of these dummies takes a value of 1 on announcement days and 0 otherwise. Thus, the estimated coefficients λi and ηi are the contemporaneous effects of local macroeconomic news on domestic stock markets and on the volatilities of these markets, respectively.

To study the dependence of news on the type of release, local macroeconomic news are segregated into ten sectoral categories. At this step, mean and variance equations are replaced with the following equations:

(13) Model 1: _{, , , ,}.

Model 2: _{, , , ,} .

(14) Model 1: _, ^,

,

,

, , ,.

Model 2: _, ^,

,

,

, , ,.

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Two models for each market are tested. In the mean equation for Model 1, _,is a c×1 vector of dummies for macroeconomic announcements taking place in category c at time t; each of these dummies takes a value of 1 on announcement days for a particular news category and takes a value of 0 otherwise. In the variance equation of Model 1, _, is a dummy for macroeconomic announcements; dummy takes a value of 1 on announcement days and 0 otherwise. In the mean equation of Model 2, _, is a dummy for macroeconomic announcements; again, the dummies take a value of 1 on announcement days and 0 otherwise. In the variance equation of Model 2, _, is a c×1 vector of dummies for macroeconomic announcements; each of these dummies takes a value of 1 on announcement days for a particular news category and 0 otherwise. The dummies _, are specific for each category even though for some categories the dummies are the same at particular time t. The estimated coefficients λi

and ηi capture the contemporaneous effects of local macroeconomic news from different categories on domestic stock markets and on the volatilities of these markets, respectively.

For the effect on domestic stock markets of foreign macroeconomic news that is released in foreign countries, the mean and variance equations are estimated as follows:

(15) Model 1: _{, , , ,}.

Model 2: _{, , , ,} .

(16) Model 1: _, ^,

,

,

, , ,.

Model 2: _, ^,

,

,

, , ,.

Two models are estimated for each local market. In the mean equation of Model 1, the parameter _, is a 3×1 vector of dummies for foreign macroeconomic announcements; each of these dummies takes a value of 1 on announcement days for

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a particular country and 0 otherwise. In the variance equation of Model 1, _, is a dummy for local macroeconomic announcements; the dummy takes a value of 1 on announcement days and 0 otherwise. In the mean equation of Model 2, the parameter

,is a dummy for local macroeconomic announcements; the dummy takes a value of 1 on announcement days and 0 otherwise. In the variance equation of Model 2, _, is a 3×1 vector of dummies for foreign macroeconomic announcements; each of these dummies takes a value of 1 on announcement days for a particular country and 0 otherwise. The _, , _,, _, and _, are specific for each country even though for some countries the dummies are the same. The estimated coefficients λi, λj, ηi and ηj

capture the contemporaneous effects of local and foreign macroeconomic news on domestic stock markets and on the volatilities of these stock markets, respectively.

The variance-covariance matrices may be optimized with the Berndt, Hall, Hall, and Hausman (1974) algorithm (Engle and Kroner, 1995). The BHHH is based on the determination of the first derivatives of the log-likelihood function with respect to the parameter values at each iteration. The BHHH method utilizes only first derivatives, but approximations to second derivatives are calculated.

From Equations (9), (11), and (13), the conditional log-likelihood functions, L(), is obtained for a sample of T observations:

(17) ∑ ,

(18) 2 1/2 | | 1/2 ,

where  represents the vector of all the unknown parameters. A numerical maximization of Equations (17) and (18) yields the maximum likelihood estimates with asymptotic standard errors.

The EGARCH models are F-tested to determine if they are correctly specified. Under the null hypothesis with normally distributed errors, the statistic should have an F-distribution with k-1 numerator degrees of freedom and T-k denominator degrees of freedom, where k is the number of explanatory variables.