Hidden temporal order unveiled in stock market volatility variance

Abstract

When analyzed by standard statistical methods, the time series of the daily return of financial indices appear to behave as Markov random series with no apparent temporal order or memory. This empirical result seems to be counter intuitive since investor are influenced by both short and long term past market behaviors. Consequently much effort has been devoted to unveil hidden temporal order in the market dynamics. Here we show that temporal order is hidden in the series of the variance of the stocks volatility. First we show that the correlation between the variances of the daily returns and means of segments of these time series is very large and thus cannot be the output of random series, unless it has some temporal order in it. Next we show that while the temporal order does not show in the series of the daily return, rather in the variation of the corresponding volatility series. More specifically, we found that the behavior of the shuffled time series is equivalent to that of a random time series, while that of the original time series have large deviations from the expected random behavior, which is the result of temporal structure. We found the same generic behavior in 10 different stock markets from 7 different countries. We also present analysis of specially constructed sequences in order to better understand the origin of the observed temporal order in the market sequences. Each sequence was constructed from segments with equal number of elements taken from algebraic distributions of three different slopes.

Modelling the short term herding behaviour of stock markets

“…. Due to the additivity of the daily change (see equation (6)), this implicates that the actual index and stocks returns can be simply figure 1 in [26]. Figure 3 shows typical results of the daily return time series for a modelled index.…”

“…This function should be constant up to a certain value and decays like α x above that value. Following the procedure presented in [26], the random distribution was chosen to be:…”

Changes in Cross-Correlations as an Indicator for Systemic Risk

“…Recently, some of the security cross-correlation studies report that the first principal component substantially increases during financial crisis1920. The same studies reported that the volatility cross-correlations exhibit long memory21, implying that once high volatility (risk)3031 is spread across the entire market, it could lasts for a long time.…”

Comparable Stocks, Boundedly Rational Stock Markets and IPO Entry Rates

“…Trading volume is a standard proxy for information arrival, heterogeneous belief among investors and liquidity in stock markets [14], [18], [19]. In this paper, we use trading volume as a proxy for information.…”

“…In order not to confound with size effects, we took the average trading volume. In addition, recent research also suggests that the cross-sectional variation of trading volume contains valuable information about stock-specific characteristics such as risk, size, price, trading costs and membership in stock indexes [18]. To the extent that trading volumes among stocks within a 2-digit SIC sector in the cross-section are sufficiently different, there will be more unique information about stocks in that sector.…”