12 research outputs found
Scale invariant properties of public debt growth
Public debt is one of the important economic variables that quantitatively
describes a nation's economy. Because bankruptcy is a risk faced even by
institutions as large as governments (e.g. Iceland), national debt should be
strictly controlled with respect to national wealth. Also, the problem of
eliminating extreme poverty in the world is closely connected to the study of
extremely poor debtor nations. We analyze the time evolution of national public
debt and find "convergence": initially less-indebted countries increase their
debt more quickly than initially more-indebted countries. We also analyze the
public debt-to-GDP ratio R, a proxy for default risk, and approximate the
probability density function P(R) with a Gamma distribution, which can be used
to establish thresholds for sustainable debt. We also observe "convergence" in
R: countries with initially small R increase their R more quickly than
countries with initially large R. The scaling relationships for debt and R have
practical applications, e.g. the Maastricht Treaty requires members of the
European Monetary Union to maintain R < 0.6.Comment: 9 pages, 8 figure
The competitiveness versus the wealth of a country
Politicians world-wide frequently promise a better life for their citizens.
We find that the probability that a country will increase its {\it per capita}
GDP ({\it gdp}) rank within a decade follows an exponential distribution with
decay constant . We use the Corruption Perceptions Index (CPI)
and the Global Competitiveness Index (GCI) and find that the distribution of
change in CPI (GCI) rank follows exponential functions with approximately the
same exponent as , suggesting that the dynamics of {\it gdp}, CPI, and
GCI may share the same origin. Using the GCI, we develop a new measure, which
we call relative competitiveness, to evaluate an economy's competitiveness
relative to its {\it gdp}. For all European and EU countries during the
2008-2011 economic downturn we find that the drop in {\it gdp} in more
competitive countries relative to {\it gdp} was substantially smaller than in
relatively less competitive countries, which is valuable information for
policymakers.Comment: 11 pages, 7 figures, accepted for publication in Nature Scientific
Report
Cross-correlations between volume change and price change
In finance, one usually deals not with prices but with growth rates ,
defined as the difference in logarithm between two consecutive prices. Here we
consider not the trading volume, but rather the volume growth rate ,
the difference in logarithm between two consecutive values of trading volume.
To this end, we use several methods to analyze the properties of volume changes
, and their relationship to price changes . We analyze
daily recordings of the S\&P 500 index over the 59-year period
1950--2009, and find power-law {\it cross-correlations\/} between and
using detrended cross-correlation analysis (DCCA). We introduce a
joint stochastic process that models these cross-correlations. Motivated by the
relationship between and , we estimate the tail exponent
of the probability density function for both the S\&P 500 index as well as the
collection of 1819 constituents of the New York Stock Exchange Composite index
on 17 July 2009. As a new method to estimate , we calculate the
time intervals between events where . We demonstrate that
, the average of , obeys . We find . Furthermore, by
aggregating all values of 28 global financial indices, we also observe
an approximate inverse cubic law.Comment: 7 pages, 5 figure
Size-dependent standard deviation for growth rates: empirical results and theoretical modeling
We study annual logarithmic growth rates R of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of R can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation σ(R) on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates R of wages of 161 different occupations, we find a power-law dependence of the standard deviation σ(R) on the average value of the wages with a scaling exponent β≈0.14 close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation σ(R) of the annual logarithmic growth rate R increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of σ(R) on the average payroll with a scaling exponent β≈−0.08. Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable
Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes
We investigate how simultaneously recorded long-range power-law correlated
multi-variate signals cross-correlate. To this end we introduce a two-component
ARFIMA stochastic process and a two-component FIARCH process to generate
coupled fractal signals with long-range power-law correlations which are at the
same time long-range cross-correlated. We study how the degree of
cross-correlations between these signals depends on the scaling exponents
characterizing the fractal correlations in each signal and on the coupling
between the signals. Our findings have relevance when studying parallel outputs
of multiple-component of physical, physiological and social systems.Comment: 8 pages, 5 figures, elsart.cl
Cross-correlations between volume change and price change
In finance, one usually deals not with prices but with growth rates , defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate , the difference in logarithm between two consecutive values of trading volume. To this end, we use several methods to analyze the properties of volume changes , and their relationship to price changes . We analyze daily recordings of the S\&P 500 index over the 59-year period 1950--2009, and find power-law {\it cross-correlations\/} between and using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between and , we estimate the tail exponent of the probability density function for both the S\&P 500 index as well as the collection of 1819 constituents of the New York Stock Exchange Composite index on 17 July 2009. As a new method to estimate , we calculate the time intervals between events where . We demonstrate that , the average of , obeys . We find . Furthermore, by aggregating all values of 28 global financial indices, we also observe an approximate inverse cubic law.
Scale invariant properties of public debt growth
Public debt is one of the important economic variables that quantitatively describes a nation's economy. Because bankruptcy is a risk faced even by institutions as large as governments (e.g. Iceland), national debt should be strictly controlled with respect to national wealth. Also, the problem of eliminating extreme poverty in the world is closely connected to the study of extremely poor debtor nations. We analyze the time evolution of national public debt and find "convergence": initially less-indebted countries increase their debt more quickly than initially more-indebted countries. We also analyze the public debt-to-GDP ratio R, a proxy for default risk, and approximate the probability density function P(R) with a Gamma distribution, which can be used to establish thresholds for sustainable debt. We also observe "convergence" in R: countries with initially small R increase their R more quickly than countries with initially large R. The scaling relationships for debt and R have practical applications, e.g. the Maastricht Treaty requires members of the European Monetary Union to maintain R