Finite-time singularities in the dynamics of hyperinflation in an economy
The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective "adaptive inflation expectations" with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r (t...
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todo:paper_15393755_v80_n2_p_Szybisz2023-10-03T16:22:29Z Finite-time singularities in the dynamics of hyperinflation in an economy Szybisz, M.A. Szybisz, L. Critical time Finite time singularity Initial time Linear feedback Logarithmic divergence Logarithmic singularity Nonlinear feedback Power law Singular solutions Theoretical approach Yugoslavia Zimbabwe Error analysis Time series Time series analysis The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective "adaptive inflation expectations" with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r (t), changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time tc. By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p (t). One is given by the already reported form p (t) (tc -t) -α (with α>0) and the other exhibits a logarithmic divergence, p (t)ln [1/ (tc -t)]. The singularity is a signature for an economic crash. In the present work we express p (t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r (t) and p (t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed. © 2009 The American Physical Society. Fil:Szybisz, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15393755_v80_n2_p_Szybisz |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Critical time Finite time singularity Initial time Linear feedback Logarithmic divergence Logarithmic singularity Nonlinear feedback Power law Singular solutions Theoretical approach Yugoslavia Zimbabwe Error analysis Time series Time series analysis |
| spellingShingle |
Critical time Finite time singularity Initial time Linear feedback Logarithmic divergence Logarithmic singularity Nonlinear feedback Power law Singular solutions Theoretical approach Yugoslavia Zimbabwe Error analysis Time series Time series analysis Szybisz, M.A. Szybisz, L. Finite-time singularities in the dynamics of hyperinflation in an economy |
| topic_facet |
Critical time Finite time singularity Initial time Linear feedback Logarithmic divergence Logarithmic singularity Nonlinear feedback Power law Singular solutions Theoretical approach Yugoslavia Zimbabwe Error analysis Time series Time series analysis |
| description |
The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective "adaptive inflation expectations" with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r (t), changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time tc. By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p (t). One is given by the already reported form p (t) (tc -t) -α (with α>0) and the other exhibits a logarithmic divergence, p (t)ln [1/ (tc -t)]. The singularity is a signature for an economic crash. In the present work we express p (t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r (t) and p (t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed. © 2009 The American Physical Society. |
| format |
JOUR |
| author |
Szybisz, M.A. Szybisz, L. |
| author_facet |
Szybisz, M.A. Szybisz, L. |
| author_sort |
Szybisz, M.A. |
| title |
Finite-time singularities in the dynamics of hyperinflation in an economy |
| title_short |
Finite-time singularities in the dynamics of hyperinflation in an economy |
| title_full |
Finite-time singularities in the dynamics of hyperinflation in an economy |
| title_fullStr |
Finite-time singularities in the dynamics of hyperinflation in an economy |
| title_full_unstemmed |
Finite-time singularities in the dynamics of hyperinflation in an economy |
| title_sort |
finite-time singularities in the dynamics of hyperinflation in an economy |
| url |
http://hdl.handle.net/20.500.12110/paper_15393755_v80_n2_p_Szybisz |
| work_keys_str_mv |
AT szybiszma finitetimesingularitiesinthedynamicsofhyperinflationinaneconomy AT szybiszl finitetimesingularitiesinthedynamicsofhyperinflationinaneconomy |
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1807323667527368704 |