Statistical Investigation of Connected Structures of Stock Networks in Financial Time Series

In this study, we have investigated factors of determination which can affect the connected structure of a stock network. The representative index for topological properties of a stock network is the number of links with other stocks. We used the multi-factor model, extensively acknowledged in financial literature. In the multi-factor model, common factors act as independent variables while returns of individual stocks act as dependent variables. We calculated the coefficient of determination, which represents the measurement value of the degree in which dependent variables are explained by independent variables. Therefore, we investigated the relationship between the number of links in the stock network and the coefficient of determination in the multi-factor model. We used individual stocks traded on the market indices of Korea, Japan, Canada, Italy and the UK. The results are as follows. We found that the mean coefficient of determination of stocks with a large number of links have higher values than those with a small number of links with other stocks. These results suggest that common factors are significantly deterministic factors to be taken into account when making a stock network. Furthermore, stocks with a large number of links to other stocks can be more affected by common factors.Comment: 11 pages, 2 figure

Relationship between degree of efficiency and prediction in stock price changes

This study investigates empirically whether the degree of stock market efficiency is related to the prediction power of future price change using the indices of twenty seven stock markets. Efficiency refers to weak-form efficient market hypothesis (EMH) in terms of the information of past price changes. The prediction power corresponds to the hit-rate, which is the rate of the consistency between the direction of actual price change and that of predicted one, calculated by the nearest neighbor prediction method (NN method) using the out-of-sample. In this manuscript, the Hurst exponent and the approximate entropy (ApEn) are used as the quantitative measurements of the degree of efficiency. The relationship between the Hurst exponent, reflecting the various time correlation property, and the ApEn value, reflecting the randomness in the time series, shows negative correlation. However, the average prediction power on the direction of future price change has the strongly positive correlation with the Hurst exponent, and the negative correlation with the ApEn. Therefore, the market index with less market efficiency has higher prediction power for future price change than one with higher market efficiency when we analyze the market using the past price change pattern. Furthermore, we show that the Hurst exponent, a measurement of the long-term memory property, provides more significant information in terms of prediction of future price changes than the ApEn and the NN method.Comment: 10 page

Topological Properties of the Minimal Spanning Tree in Korean and American Stock Markets

We investigate a factor that can affect the number of links of a specific stock in a network between stocks created by the minimal spanning tree (MST) method, by using individual stock data listed on the S&P500 and KOSPI. Among the common factors mentioned in the arbitrage pricing model (APM), widely acknowledged in the financial field, a representative market index is established as a possible factor. We found that the correlation distribution, $\rho_{ij}$, of 400 stocks taken from the S&P500 index shows a very similar with that of the Korean stock market and those deviate from the correlation distribution of time series removed a nonlinearity by the surrogate method. We also shows that the degree distribution of the MSTs for both stock markets follows a power-law distribution with the exponent $\zeta \sim$ 2.1, while the degree distribution of the time series eliminated a nonlinearity follows an exponential distribution with the exponent, $\delta \sim 0.77$. Furthermore the correlation, $\rho_{iM}$, between the degree k of individual stock, $i$, and the market index, $M$, follows a power-law distribution, $\sim k^{\gamma}$, with the exponent \gamma_{\textrm{S&P500}} \approx 0.16 and $\gamma_{\textrm{KOSPI}} \approx 0.14$, respectively. Thus, regardless of the markets, the indivisual stocks closely related to the common factor in the market, the market index, are likely to be located around the center of the network between stocks, while those weakly related to the market index are likely to be placed in the outside

The effect of a market factor on information flow between stocks using minimal spanning tree

We empirically investigated the effects of market factors on the information flow created from N(N-1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is capable of reducing the number of links to N-1. We determined that market factors carry important information value regarding information flow among stocks. Moreover, the information flow among stocks evidenced time-varying properties according to the changes in market status. In particular, we noted that the information flow increased dramatically during periods of market crises. Finally, we confirmed, via the MST method, that the information flow among stocks could be assessed effectively with the reduced linkage relationships among all links between stocks from the perspective of the overall market

Fat tails in financial return distributions revisited: evidence from the Korean stock market

This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks than for large-capitalization stocks. After controlling for the 1997 Korean foreign currency crisis and using the GARCH filter models to control for volatility clustering in the returns, the fat tails in the distribution of residuals are found to persist. We show that market crashes and volatility clustering may not sufficiently account for the existence of fat tails in return distributions. These findings are robust regardless of period or type of stock group

Effect of changing data size on eigenvalues in the Korean and Japanese stock markets

In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix. We determined that the value of the eigenvalue increases in proportion with the number of stocks. Furthermore, we noted that the largest eigenvalue maintains its identical properties, regardless of the number and type, whereas other eigenvalues evidence different features

Market Efficiency in Foreign Exchange Markets

We investigate the relative market efficiency in financial market data, using the approximate entropy(ApEn) method for a quantification of randomness in time series. We used the global foreign exchange market indices for 17 countries during two periods from 1984 to 1998 and from 1999 to 2004 in order to study the efficiency of various foreign exchange markets around the market crisis. We found that on average, the ApEn values for European and North American foreign exchange markets are larger than those for African and Asian ones except Japan. We also found that the ApEn for Asian markets increase significantly after the Asian currency crisis. Our results suggest that the markets with a larger liquidity such as European and North American foreign exchange markets have a higher market efficiency than those with a smaller liquidity such as the African and Asian ones except Japan