Leis de potências e correlações em séries temporais de preços de produtos agrícolas

Abstract

Financial markets are complex systems that contain large numbers of interacting units, including interactions among various units in the same market and interactions between units in different markets. Various methods of economics, statistics and econophysics have been developed to analyze financial temporal series (such as price returns, share volume, number of transactions), and serve to establish theoretical models for underlying stochastic processes. The availability of financial data on the internet and increasing computational power have enabled researchers to conduct a large number of empirical studies on financial markets. These studies have shown some universal properties: the risk function of price returns is scale invariant, with power-law behavior and similar value of exponent for different markets; the absolute values of returns (volatility) exhibit long-range power-law correlations. In this work, we use methods if econophysics to study the statistical properties of Brazilian financial markets. We analyze and compare scale properties of risk functions and correlations in temporal series of price returns of agricultural commodities and stocks of various companies traded at Bovespa. We analyze the daily prices of five commodities and twenty stocks traded in the period 2000-2008. For both commodities and stocks, the risk function of daily price returns shows powerlaw behavior with the exponent outside the Levy stable region. The values of exponents are higher for stocks than for commodities. We use Detrended Fluctuation Analysis (DFA) to study correlations in daily time series of absolute values of returns (volatility). This method was developed to quantify long range correlations in non-stationary temporal series.All analyzed series show persistent behavior, meaning that large (small) values are more likely to be followed with large (small) values. The value of the DFA exponent is higher for commodities than for stocks. We also use Detrended Cross Correlation Analysis (DCCA) to study cross-correlations between two series. The values of DCCA exponents are above 0.5 for all series, indicating the existence of long range cross-correlations. This means that each stock or commodity has long memory of its own previous values and of previous values of other stocks or commodities studied. These results are in agreement with results obtained for American financial markets.