No Arabic abstract
This paper analyses the behaviour of volatility for several international stock market indexes, namely the SP 500 (USA), the Nikkei (Japan), the PSI 20 (Portugal), the CAC 40 (France), the DAX 30 (Germany), the FTSE 100 (UK), the IBEX 35 (Spain) and the MIB 30 (Italy), in the context of non-stationarity. Our empirical results point to the evidence of the existence of integrated behaviour among several of those stock market indexes of different dimensions. It seems, therefore, that the behaviour of these markets tends to some uniformity, which can be interpreted as the existence of a similar behaviour facing to shocks that may affect the worldwide economy. Whether this is a cause or a consequence of market globalization is an issue that may be stressed in future work.
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipfs law or a power law. It is also obtained that the probability density of normalized returns for listed stocks almost has the form of the exponential function. Our results are compared with those of other numerical calculations.
We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) simeq R^{-beta}$ with the exponents $ beta=3.11$(the time interval $tau=$ one minute) and 3.36($tau=$ one day). The informational cascade regime appears in the herding parameter $Hge 2.33$ at $tau=$ one minute, while it occurs no herding at $tau=$ one day. Especially, we find that the distribution of normalized returns shows a crossover to a Gaussian distribution at one time step $Delta t=1$ day.
Based on the minute-by-minute data of the Hang Seng Index in Hong Kong and the analysis of probability distribution and autocorrelations, we find that the index fluctuations for the first few minutes of daily opening show behaviors very different from those of the other times. In particular, the properties of tail distribution, which will show the power law scaling with exponent about -4 or an exponential-type decay, the volatility, and its correlations depend on the opening effect of each trading day.
We propose a novel method to quantify the clustering behavior in a complex time series and apply it to a high-frequency data of the financial markets. We find that regardless of used data sets, all data exhibits the volatility clustering properties, whereas those which filtered the volatility clustering effect by using the GARCH model reduce volatility clustering significantly. The result confirms that our method can measure the volatility clustering effect in financial market.