**1. Introduction**

Global trade and integration are the main drivers of global economic growth. In the last decade, the global economy has faced a slowdown in economic growth and a decrease in the integration level, but global trade and integration have promoted a better flow of technology that ensures avoid gaps in economic development between developed and developing countries. Despite the fact that in the last 5 years the trend of globalization has changed to the trend of geoeconomic fragmentation, the issue of the effectiveness of creating economic unions has remained relevant, and only the

point of view has changed. The presence of synchronization between the economic cycles of the countries of a geoeconomic union is a generally accepted indicator to determine the presence of integration and the efficiency of a geoeconomic union [1–5].

The large emerging economies: Russia, India, China (hereinafter—the "LEE") and their geoeconomic alliance is the object of our study. Russia, India, and China are emerging market countries. The role of emerging markets has grown significantly over the past few decades, and they are playing a significant role in the global economy [6]. Restrictive measures in China due to the coronavirus pandemic, as well as the lifting of restrictions, cause surges in resource prices around the world and peak loads in the global logistics system [7]. Kremer et al. [8] note that the decline in medium-term global growth reflects a slower rate of change in the progress of improving living standards in countries such as China and Korea. As a result, since the previous global crisis in 2008, there has been a debate about the separation of the economic development of emerging markets from developed markets, the so-called "decoupling hypothesis" [6, 9–11]. Before the 2008 crisis, most of the literature supported the decoupling hypothesis [12, 13]. Since the 2008 crisis, there have been many studies showing a reduction or disappearance of its effect [14, 15]. The trade wars between the United States and China also contribute against support for the decoupling hypothesis.

The topic of economic growth in the context of high risks of fragmentation of the global economy has great relevance. A number of researchers support the existence of spillover effects arising from alliances [12, 16], while others find no such evidence [17, 18].

In this paper, we investigated the output gaps of large emerging economies: Russia, India, and China. We chose the output gap as an indicator of the economic growth efficiency of national economies. We used the Hodrik-Preskott filtering method to isolate the output gap. Next, we conducted a spectral analysis to determine the degree of synchronization of economic cycles. A similar approach was taken by Papageorgiou et al. [4], and Frankel and Rose [2], etc., against European Union countries.

In the second part, we investigated the output gaps of LEE, having isolated it by the statistical method of Hodrik-Preskott filtering rather than by calculation one. This method allows us to determine positive and negative gaps between real and potential gross domestic product (GDP). We calculated output gaps in US dollars at 2015 prices, in local currency at constant prices, in US dollars at current prices, and in local currency at current prices. This allowed us to identify the inflationary component and the component related to the exchange rate of national currencies. We applied spectral analysis to determine the degree of synchronization of business cycles.

In the third part, we discussed statistical results of the study, and in the fourth part, we tried to find explanations for these results and make conclusions.
