Characterizing Complexity Changes in Chinese Stock Markets by Permutation Entropy

Abstract

Financial time series analyses have played an important role in developing some of the fundamental economic theories. However, many of the published analyses of financial time series focus on long-term average behavior of a market, and thus shed little light on the temporal evolution of a market, which from time to time may be interrupted by stock crashes and financial crises. Consequently, in terms of complexity science, it is still unknown whether the market complexity during a stock crash decreases or increases. To answer this question, we have examined the temporal variation of permutation entropy (PE) in Chinese stock markets by computing PE from high-frequency composite indies of two stock markets: the Shanghai Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZSE). We have found that PE decreased significantly in two significant time windows, each encompassing a rapid market rise and then a few gigantic stock crashes. One window started in the middle of 2006, long before the 2008 global financial crisis, and continued up to early 2011. The other window was more recent, started in the middle of 2014, and ended in the middle of 2016. Since both windows were at least one year long, and proceeded stock crashes by at least half a year, the decrease in PE can be invaluable warning signs for regulators and investors alike.

Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series

“…It is important to note that the averaging or expectation operation involved in the entropy estimation in Equation (5) is taken with respect to the probability distribution on the permutations (Judge and Mittelhammer 2012a). This finding of a PE point estimate of 0.998 for DJIA nominal returns agrees with that of Hou et al (2017), who estimates that the PE of DJIA is close to 1 during the 2008 financial crisis. For the one-dimensional DJIA time series in Figure 1b, the estimation of the single PE point estimate ordinal sequences of 4-dimensional vectors were chosen to capture the information contained in the permutations of the distinct states.…”

“…As our purpose also involves the detection of dynamic changes over time, we use a rolling window analysis procedure to compute the time-varying estimates of PE, which capture the underlying dynamics and uncertainty. For some empirical applications of this rolling window procedure in the PE context, see Cao et al (2004), Staniek and Lehnertz (2007), and Hou et al (2017).…”

“…Against this background, we focus on an information theoretic-symbolic logic complexity approach in this paper, which resembles the method taken in ordinal time series analysis (cf. Bandt 2005;Bandt and Shiha 2007;Cao et al 2004;Hou et al 2017;Keller and Sinn 2005;Kowalski et al 2012;Zanin et al 2012;Zunino et al 2009Zunino et al , 2010b. This aims to unlock the complex and hidden dynamical behaviors contained in the nonlinear time series.…”

Random Walk Null Models for Time Series Data

“…In addition, permutation entropy is invariant under scaling of the data, i.e., under non-linear monotonic transformations, adding to its wide applicability [1,2]. These techniques have found application in many fields including economics [3][4][5][6][7][8], medicine [9][10][11][12][13] and physics [14,15], among others. Datasets of a similar scale are increasingly available in the current big data paradigm, and permutation methods are well positioned to contribute to comprehensive and meaningful analyses.…”

Reverse Weighted-Permutation Entropy: A Novel Complexity Metric Incorporating Distance and Amplitude Information

“…Some typical applications of PE can be found in the medical area [3], where it has been used to represent different states of human organs, including neuron, brain and heart. In addition, more applications can also be found in the fields of economics [4,5], mechanical engineering [6,7] and underwater acoustics [8,9]. The development of PE includes two aspects: One is the expansion of its application in different fields, the other is the improvement of PE theory.…”