Recurrence quantification analysis of business cycles
Introduction
Burns and Mitchell [12] define business cycles as a type of fluctuation which “consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle”. Imperfections may be intended as those perturbations of the equilibrium that can lead to recessions or to expansions.
Recurrence is defined as the ability of a dynamical system to return to the proximity of the initial point in phase space, and recurrence quantification analysis (RQA) was developed in order to understand the behaviour of the phase space trajectory of dynamical systems.
There is a debate in the literature whether economy is chaotic or stochastic and whether shocks are endogenous or exogenous. Most studies concentrated on financial time series (e.g. stock indices) because of accessibility of data, frequency and length. The current work, with an extensive analysis on macroeconomic data (i.e. consumption, investment, capital and income), aims to investigate: i. The applications of recurrence plots (RPs), and their quantitative description provided by RQA, to dynamical regimes of business time series, ii. Whether RQA can give some indications on the nature of trade cycles as well as on the nature of macroeconomic variables and the economy.
The rest of the paper is organized as follows. The first Section is a brief review of the literature on business cycles, recurrence quantification analysis and its applications to economics and finance. The second Section features material and methods and includes the description of both the dataset and the RQA methodology. The third Section shows the analysis performed and the results obtained. The final section draws some conclusions and makes suggestions for future research.
Section snippets
Literature review
RQA applications to economics and finance are not widespread and started later than in other fields [14], [18], [32], [44], [66]. The interest in RQA by economists stemmed from the world financial crisis of 2007–2010 which was not anticipated by a large part of economic literature [34]. In fact, the majority of economists, basing their models on standard equilibrium, implicitly assumed that “economies are inherently stable and that they only temporarily get off track” Colander et al. [16].
Material and methods
The variables under investigation are Capital (K), Consumption (C), Investment (I) and Income (Y) (see Appendix A). Cyclical swings of an economy, Fig. 1, are typically analysed in terms of the duration or the amplitude between a peak and the succeeding trough [11]. The Peak-Trough-Peak (PTP) cycle can be caused by various factors such as negative shocks in demand, in supply, in price and in credit (i.e. when “financial distress produces sharp discontinuities in flows of funds and spending and
Results and analysis
In this Section we show that, in some cases, early warning signals of dramatic changes (downturns/expansions) can be seen by computing recurrence variables within a moving window (epoch) shifted by a given number of points (delay) throughout the whole sample (i.e. the so called Recurrence Quantification Epoch (RQE) 4.1.3). Finally we demonstrate that RQA is a valid technique of investigation as it is able to distinguish between real and nominal data as well as between net and gross time series
Conclusions
So far, the literature has not been able to determine whether the economy is chaotic or not. This work concerns the application of recurrence plots and their quantitative description provided by recurrence quantification analysis (RQA) to appreciate subtle but essentially relevant changes in the dynamical regime of business time series. RQA aims at a direct and quantitative appreciation of the amount of deterministic structure of time series, and has been shown to be an efficient and relatively
Acknowledgements
The authors are grateful to the editor, the referees and to their colleagues at the School of Science and Technologies - University of Camerino and at the Department of Economics and Finance - University of Bari. Special thanks go to Alessando Giuliani at Istituto Superiore di Sanità, Laboratory of Comparative Toxicology and Ecotoxicology - Rome, Nicola Basile and Mario Sportelli at the Department of Mathematics - University of Bari for their comments and helpful discussions.
References (69)
- et al.
Nonlinear dynamics and recurrence plots for detecting financial crisis
North Am J Econ Finance
(2013) - et al.
Controlling the equilibria of nonlinear stochastic systems based on noisy data
J Franklin Inst
(2017) Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series
Physica A
(2011)- et al.
Periodic properties of interpolated time series
Econ Lett
(1994) - et al.
Correlations, risk and crisis: from physiology to finance
Physica A
(2010) - et al.
Controlling chaotic dynamical systems
Systems & Control Letters
(1997) Shock persistence and the measurement of prewar output series
Econ Lett
(1990)Expectations and the neutrality of money
J Econ Theory
(1972)A discrete mathematical model for chaotic dynamics in economics: kaldor’s model on business cycle
Math Comput Simul
(2016)- et al.
Recurrence quantification analysis and state space divergence reconstruction for financial time series analysis
Physica A
(2007)
Harrod’S ’knife-edge’ reconsidered: an application of the hopf bifurcation theorem and numerical simulations
J Macroecon
The foundations of factor analysis
Biometrika
Controlling stochastic sensitivity by the dynamic regulators
AIP Conference Proceedings
Method of stochastic sensitivity synthesis in a stabilisation problem for nonlinear discrete systems with incomplete information
Int J Control
Recurrence quantification analysis of financial markets
Chaos and complexity theory for management: Nonlinear Dynamics
The macroeconomics of the great depression: A comparative approach
Tech. Rep
Introduction to ’an essay in dynamic theory’: 1938 draft by roy f. harrod
Hist Polit Econ
Standard business cycle analysis of economic time series
Cyclical Analysis of Time Series: Selected Procedures and Computer Programs
Measuring business cycles
National Bureau of Economic Research
Fuzzy control of chaos
Int J Bifurcation Chaos
The financial crisis and the systemic failure of the economics profession
Critical Review
Frontiers of business cycle research
A new approach to analyzing convergence and synchronicity in growth and business cycles: cross recurrence plots and quantification analysis
Bank of Finland Research Discussion Paper
Recurrence plots of dynamical systems
EPL (Europhysics Letters)
The mechanisms of the business cycle in the postwar era
The American business cycle: Continuity and change
Monetary theory and the trade cycle
Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. examples from financial market indices
Int J Modern Phys
The debt-deflation theory of great depressions
Econometrica
Deterministic and stochastic optimal control
Stochastic distribution control system design: a convex optimization approach
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