Entropic Dynamic Time Warping Kernels for Co-Evolving Financial Time Series Analysis

Abstract

Network representations are powerful tools to modelling the dynamic time-varying financial complex systems consisting of multiple co-evolving financial time series, e.g., stock prices, etc. In this work, we develop a novel framework to compute the kernel-based similarity measure between dynamic time-varying financial networks. Specifically, we explore whether the proposed kernel can be employed to understand the structural evolution of the financial networks with time associated with standard kernel machines. For a set of time-varying financial networks with each vertex representing the individual time series of a different stock and each edge between a pair of time series representing the absolute value of their Pearson correlation, our start point is to compute the commute time matrix associated with the weighted adjacency matrix of the network structures, where each element of the matrix can be seen as the enhanced correlation value between pairwise stocks. For each network, we show how the commute time matrix allows us to identify a reliable set of dominant correlated time series as well as an associated dominant probability distribution of the stock belonging to this set. Furthermore, we represent each original network as a discrete dominant Shannon entropy time series computed from the dominant probability distribution. With the dominant entropy time series for each pair of financial networks to hand, we develop an Entropic Dynamic Time Warping Kernels through the classical dynamic time warping framework, for analyzing the financial time-varying networks. We show that the proposed kernel bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks extracted through New York Stock Exchange (NYSE) database demonstrate that the proposed method can effectively detect abrupt changes in networks as time series structures and can be used to characterize different stages in time-varying financial network evolutions.

Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective

“…The studies in natural language processing (NLP) [193]- [195] have demonstrated that GMs can process natural language and have were taken around each of the two events. [191]. achieved much better performance than the conventional NLP models.…”

“…Another example is about studying co-evolving financial time-serious problems from GMs. In [191], Bai et al proposed a tool, called EDTWK (Entropic Dynamic Time Warping Kernels), for time-varying financial networks. They computed the commute time matrix on each of the network structures for satisfying a GC as "the financial crises are usually caused by a set of the most mutually correlated stocks while having less uncertainty [191], [192]".…”

“…In [191], Bai et al proposed a tool, called EDTWK (Entropic Dynamic Time Warping Kernels), for time-varying financial networks. They computed the commute time matrix on each of the network structures for satisfying a GC as "the financial crises are usually caused by a set of the most mutually correlated stocks while having less uncertainty [191], [192]". Based on the commute time matrix, a dominant correlated stock set was identified for processing.…”

“…15. Time-varying Trajectory in 3-D embedding for (a) Newcentury Financial Bankruptcy (4th April 2007) and (b) Lehman Brothers Bankruptcy (15th September 2008), where the data in 90 trading days (i.e., 90 points)were taken around each of the two events [191]…”

Estimating Fund-Raising Performance for Start-up Projects from a Market Graph Perspective

“…For instance, Feng et al [36] created the relations between every pair (two industries) based on a knowledge base to predict stock trends. Graph kernels were also able to play an important role in the financial time series analysis by associating it with the classical dynamic time warping framework [37,38]. And, in the multimedia field, Cucurull et al [39] promoted the fashion compatibility prediction problem using a graph convolutional network that learned to generate product embeddings conditioned on context.…”