1. Introduction

This chapter is devoted to the substantiation of methods of statistical assessment and modeling of macroeconomic business cycles on the basis of their understanding as an integrated effect of changing business phases in different sectors, as well as the impact of synchronization and harmonization of business cycles in both the economy of one country and the intercountry levels.

The main directions of quantitative research of business cycles based on the econometric approach, which are widely presented in the literature, fall into two main groups. The first of these is the identification of stable cyclic components in the dynamics of macroeconomic

indicators. In most cases, the authors of scientific publications use the real GDP (gross domestic product), as an indicator for investigation of macroeconomic business cycle. The development of this direction is the study of the interplay of the "total" business cycles identified in the GDP dynamics by countries. The second direction is the definition and quantitative description of the cyclic components in the dynamics of indicators characterizing the processes in individual sectors or spheres of the economy. The "specific cycles" thus estimated are the basis for the identification and quantification of the so-called common cycle using cluster analysis methods. In this case, the "common" (or as it is also called the "reference") cycle is represented as a multivariate value of the actual reaction of individual industries or economic subsystems, e.g., financial, investment, labor market, etc., observed with the help of statistical indicators. This chapter proposes a method for identifying and quantifying the common business cycle as a directly unmeasurable phenomenon, which manifests itself in fluctuations in the dynamics of the specific indicators of industries and economic systems, but has an objective and independent economic nature. In the author's opinion, specific cycles, even if they have a leading character with respect to the general cycle, are its economic consequence. The chapter suggests methods and their applications for identifying and quantifying the macroeconomic business cycle as a latent system-wide phenomenon, as well as methods for estimating intercountry synchronization and harmonization of common cycles. At the same time, the author gives her own definition of these forms of the interaction of business cycles. This approach is different to the view expressed in many publications about the identity of the concepts of synchronization, harmonization, concordance, and correlation of business cycles.

2. A literature review of the definition of a business cycle and methods

Statistical Methodology for Evaluating Business Cycles with the Conditions of Their Synchronization…

http://dx.doi.org/10.5772/intechopen.75580

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The number of scientific papers devoted to the theory and methods of quantifying business cycles is measured in hundreds. Nevertheless, there is a basis for their distribution into two large parts. This basis is the definition of the concept of fluctuations in economic activity. This determines the choice of mathematical and statistical methods used to determine business cycles (Kijek [20]). The first part includes the papers which are based on Burns and Mitchell's definition of a cycle [3]. According to them, a business cycle represents the four distinct phases of "aggregate economic activity" development that evolve from one into another: expansion, recession,

The second part is the works based on a different view of business cycles, which was presented by Lucas [23], who does not interpret cycles as inevitable transitions between different phases of the cycle. He sees the business cycle as a process of oscillation of GNP around a long-term trend. Some authors define the business cycle in accordance with Burns and Mitchell and then continue to measure the fluctuations of the macroeconomic aggregate values (GNP, GDP,

This approach cannot be adopted without a preliminary study confirming that the observed cyclicality of the national economy is a violation of macroeconomic equilibrium rather than synchronous periodic fluctuations of various economic activities without changing of their balance.

The two basic approaches to the definition of the concept of a business cycle, mentioned above,

Harding and Pagan [17] define three directions ("traditions") in the deviation of approaches presented in the literature on the development of cycle indicators from information available in

The main idea of the first direction is changing of the initial time series (yt) by a series of binary random variable St, which includes turning points. In this case, peaks (troughs) are considered as local maxima (minima) in the series yt, and they are taking the value unity and zero otherwise:

<sup>∨</sup> <sup>t</sup> <sup>¼</sup> <sup>1</sup> yt <sup>&</sup>lt; yt�<sup>1</sup> <sup>≤</sup> <sup>j</sup> <sup>≤</sup> <sup>k</sup> ;

where ∨t (∧t) are binary variables and k is the length of period for local maxima (minima)

Harding and Pagan [18] show that for Burns and Mitchell's specific cycle dating procedures it is necessary to set k = 5 for monthly data or k = 2 for quarterly data, but it is not the single variant. Mathematics and IT providing of extracting and estimation of turning points in

<sup>∧</sup> <sup>t</sup> <sup>¼</sup> <sup>1</sup> yt <sup>&</sup>lt; yt�<sup>1</sup> <sup>≤</sup> <sup>j</sup> <sup>≤</sup> <sup>k</sup> : (1)

industrial production, investment, and so on) relatively to the long-term trend.

were the basis for developing analytical tools for recognizing cycles.

structure of economic time series have been actively developing.

a time-continuous random variable (yt).

estimation.

for extracting cyclic components

depression, and revival.

The chapter in addition to this introduction includes two main sections and a conclusion. The first section is devoted to the review of scientific publications that disclose the concept of the "business cycle," and also this section presents the author's systematization of the methods outlined in a number of publications for identifying cyclic components in the dynamics of macroeconomic indicators. In the second section of the chapter, an algorithm for quantifying the overall business cycle based on the principal component method is proposed, and methods for estimating synchronization and harmonizing business cycles are substantiated. The conclusion of the chapter contains a concentrated expression of scientific novelty of the author's methodological proposals of the business cycle quantification and the features of the algorithms for evaluating their synchronization and harmonization at the macroeconomic level.

The proof of the concept proposed in this chapter and the approbation of the corresponding algorithm were realized on the basis of statistics of Eurostat and Rosstat. Most of the examples in this chapter are compiled from the results of calculations for Germany and Russia, which allows a comparative analysis provided that there is a significant difference in the duration and stages of the history of the market economy that have a significant impact on the formation of sustainable multi-year business cycles.

Approbation of the proposed algorithm can be based on R-packages or the "STATISTICA" program.
