Analisys of economic time series
using nonlinear dynamics
Authors:
Małgorzata Żebrowska, Janusz Hołyst
Examining economical data we tried to answer to the question "What kind of data
are produced on capital market?" We used nonlinear tools: the correlation dimension
and recurrence plots, which let as distinguish between deterministic and stochastic data.
Hurst exponents have been also calculated to detect trends in time series and to show that
an assumption that market returns are independent is not true. We investigated following
economical data sets: daily share prices obtained from Polish Stock Exchange (990 points)
02.02.95-25.01.99 (OKOCIM Share, BRE Share, Stock Index WIG); weekly observations on
interest rates (1800 points) 05.01.62 - 30.08.96. (the three month Treasury Bill rate, the
twelve month Treasury Bill rate, a year constant maturity Treasury Bond rate); monthly
Exchange Rates (337 points) 01.71-02.99 (USA/BP, USA/ JJ, USA/DM), Stock Index (S&P
500, Dow Jones) (645 points) 01.45-01.99. Trends have been removed using standard
rescaling procedure: x(n) = ln [c(n) /c(n-1) ], where c(n) - price.
Results: Calculations of correlation dimension indicate that analysed series are either
stochastic or one needs more data to estimate the values of correlation dimension.
Recurrence plots have been studied for original and shuffled data. At first sight plots
for original series looked like plots for random data, but when we looked at these plots
more carefully we observed darker and paler regions, which are due to the presence of
drifts in the system. We calculated quantitative descriptors of recurrence plots: percent
recurrence, percent determinism, entropy and linemax. The parameters decrease after
shuffling what suggests that there is some kind of order in the original time series.
Calculated values of the Hurst exponent H are greater then 0.5 for all time series, what
indicates that these data are not independent. Hurst exponents let as also detect the long
memory effects in some series. The estimated mean period of Index WIG is about 11 months
(~ 1 year) while corresponding period of Index S&P500 is about 5 years.
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