| Abstract: |
We introduce an unsupervised classification framework that leverages a
multi-scale wavelet representation of time-series and apply it to stock price
jumps. In line with previous work, we recover the fact that time-asymmetry of
volatility is the major feature that separates exogenous, news-induced jumps
from endogenously generated jumps. Local mean-reversion and trend are found to
be two additional key features, allowing us to identify new classes of jumps.
Using our wavelet-based representation, we investigate the endogenous or
exogenous nature of co-jumps, which occur when multiple stocks experience
price jumps within the same minute. Perhaps surprisingly, our analysis
suggests that a significant fraction of co-jumps result from an endogenous
contagion mechanism.E xtreme events and cascades of events are widespread
occurrences in both natural and social systems (1). Examples include
earthquakes, volcanic eruptions, hurricanes, epileptic crises (2, 3), epidemic
spread, financial crashes (4-6), economic crises (7, 8), book sales shocks (9,
10), riot propagation (11, 12) or failures in socio-technical systems (13).
Understanding the origin of such events is essential for forecasting and
possibly stabilizing their dynamics.A widely studied question is the
reflexive, self-exciting nature of those shocks. The concept of financial
market reflexivity was introduced by Soros in ( 14), to describe the idea that
price dynamics are mostly endogenous and arise from internal feedback
mechanisms, as was first surmised by Cutler, Poterba and Summers in 1988 (15)
(see also ( 16)). Extreme events, in particular, often arise from feedback
mechanisms within the system's structure (1, 17, 18). Quantifying the extent
of endogeneity in a complex system and distinguishing events caused by
external shocks from those provoked endogenously, and more generally
identifying different classes of events, are crucial questions.Prior research
has proposed to differentiate between endogenous and exogenous dynamics by
analyzing the profile of activity around the shock (9, 10, 19, 20), in
particular in the context of financial markets (21-23). It has been observed
that endogenous shocks are preceded by a growth phase mirroring the post event
powerlaw relaxation, in contrast to exogenous shocks that are strongly
asymmetric. The universality of this result is quite intriguing as they have
been observed in various contexts: intra-day book sales on Amazon (9, 10),
daily views of YouTube videos (20) and intra-day financial market volatility
and price jumps (23, 24). Meanwhile, Wu et al. (25) differentiate exogenous
and endogenous bursts of comment posting on social media using the analysis of
collective emotion dynamics and time-series distributions of comment
arrivals.Furthermore, in complex systems, events can propagate along two
directions: temporally and towards other elements of the system. Financial
markets offer an attractive setting for studying multi-dimensional shocks due
to the abundance of available data, the frequent occurrence of financial
shocks and price jumps and the inter-connectivity of markets. In fact, a
recent study by Lillo et al. (26, 27) demonstrates the frequent occurrence of
"co-jumps", defined as simultaneous jumps of multiple stocks (as illustrated
in Fig. 1) and establishes a correlation between their prevalence and the
inter-connectivity of different markets.In this paper, we address the problem
of classifying financial price jumps (and co-jumps), in particular measuring
their self-exciting character, by analyzing their time-series using wavelets.
We introduce an unsupervised classification based on an embedding Φ(x) of each
jump time-series of returns x(t) into a low dimensional-space more appropriate
to clustering. Such embedding, composed of wavelet scattering coefficients
(see (28) and below), relies on wavelet coefficients of the time-series at the
time of the jump t = 0 and wavelet coefficients of volatility. Such
coefficients are Significance StatementCascades of events and extreme
occurrences have garnered significant attention across diverse domains like
seismology, neuroscience, economics, finance, and other social sciences. Such
events may arise from internal system dynamics (endogenous) or external shocks
(exogenous). Devising rigorous methods to distinguish between them is vital
for professionals and regulators to create early warning systems and effective
responses. Understanding these dynamics could improve the stability and
resilience of crisisprone socio-economic systems. We show how wavelets can be
used for the unsupervised separation of shocks in financial time-series, based
on time-asymmetry around the shock. Additionally, we highlight the significant
role contagion mechanisms play in financial markets. |