*2.2. Methodology*

This study employed the Event Study Methodology followed by Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) analysis. The event study is commonly used in the literature regarding the stock market in order to examine the impact of newly published information on the stock rates. The present research adapts it to the area of macroeconomics and investigates whether and how the exchange rate is affected by the publication of announcements concerning NG in Israel.

For each event, the expected return was estimated by calculating the average exchange rate return over the estimation period. The expected return was used as the benchmark return in the normal situation to compare with the actual exchange rate return during the event window. The benchmark return represents the return that was not related to the event of interest. Next, we calculated the abnormal exchange rate return, which represents the difference between the actual return and the expected return. Afterwards, we calculated the average abnormal exchange rate return and aggregated the result. Then, the mean adjusted return (MAR) methodology was applied to analyze whether the announcement causes a statistically significant abnormal return.

In the present research, the estimation window begins 300 days before the publication of the article, and ends 17 days prior to its publication. The event window is defined from 16 days before publication of the article until 16 days subsequent to its publication. In the event study methodology, there is no universal rule on the lengths of the event windows. Over the years, many articles used the event study methodology and changed the size of the event window according to the research needs [20–25].

In addition, in the present method, the "event day" is defined as day zero: the day on which the announcement is published (Figure 2).

**Figure 2.** Estimation window (L1) for the period of time preceding the event (L2).

The development of the method used today began in the classic articles of [20,21]. They examined the publications of reports that focused on the influence of share splits, after taking into consideration the influence of a concurrently increased dividend. In order to study the influence, they compared the actual stock returns surrounding the date of the notice of the split to the expected return without the event. The role of the event study method in the present paper is to examine whether the rate of change in the ILS to USD exchange rate surrounding the publication of the announcement is identical to the normally expected return without the publication. The study follows the mean adjusted return (MAR) method based upon statistical expectations during the estimation period [22,26,27], so that the average exchange rate that will be obtained will also continue in the event window, and any change from the calculated rate will be called the abnormal real exchange rate.

The underlying hypothesis is that the expected change in the real exchange rate is equivalent to the actual real exchange rate. The present research tests the hypothesis using the t-test. The methodology in the present research is based on [28] and adapted to the calculation of the abnormal return of the real exchange rate. The detailed mathematical notation is presented in Appendix A.

Empirical work indicates that exchange-rate volatility behaves according to a GARCH )Generalized Auto-Regressive Conditional Heteroscedasticity) model that was developed by [29].According to the model, fluctuations in the exchange rate during a given period depend on fluctuations in the exchange rate in the preceding periods [30–33].

Recent studies confirmed that the GARCH(1,1) model is the most appropriate measure of exchange-rate volatility [34,35]. Additionally, research by [36] revealed that the exchange-rate series exhibits empirical regularities such as clustering volatility, non-stationarity, non-normality, and serial correlation, which justify the application of the GARCH methodology. Another recent study by [37] that used GARCH(1,1) found that exchange rate volatility affects both international trade and foreign direct investment (FDI) significantly but negatively in countries engaged in OBOR (One Belt One Road is a global development strategy adopted by the Chinese governmen<sup>t</sup> involving infrastructure development and investments in 152 countries and international organizations in Asia, Europe, Africa, the Middle East, and the Americas). [38] showed that the GARCH(1,1) model was more effective than other complicated GARCH models when they took 330 ARCH-type specifications into consideration. Therefore, the GARCH(1,1) was utilized for the volatility measurement of exchange rate in the present study.

Then, the abnormal return for the real exchange rate *Aei*,*<sup>t</sup>* of an announcement i on day t is defined as the difference between the actual return and the normal one.

$$A e\_{i,t} = e\_{i,t} - E(e\_{i,t} | I\_{i,t}) \tag{1}$$

where:

*Aeit*—The abnormal return for real exchange rate of an announcement *i* on day *t. eit*—The actually return for real exchange rate of an announcement *i* on day *t.*

*E*(*eit*|*It*)—The expected normal return for exchange rate of an announcement *i*, given information *I* known at time *t*.

The expected normal return for exchange rate and its volatility <sup>σ</sup>2*i*,*<sup>t</sup>* are presented in equations (2) and (3) as follows:

$$E(e\_{i,t}|I\_{i,t}) = \alpha\_0 + \alpha\_1 e\_{i,t-1} + \varepsilon\_{i,t} \tag{2}$$

$$
\sigma^2 \sigma^2 \, \_{i,t} = \beta\_0 + \beta\_1 \varepsilon^2 \, \_{i,t-1} + \gamma\_1 \sigma^2 \, \_{i,t-1}, \; AAe\_t \sim \mathcal{N}\left(0, \sigma^2 \, \_{i,t}\right) \tag{3}
$$

where β0 is the constant term, <sup>ε</sup>*i*,*<sup>t</sup>* is the error term, β1 is the coefficient for the lagged squared error at lag 1, and γ1 is the coefficient for the lagged conditional variance at lag 1.
