In multivariate time series systems, it has been observed that certain groups of variables partially lead the evolution of the system, while other variables follow this evolution with a time delay; the result is a lead-lag structure amongst the time series variables. In this paper, we propose a method for the detection of lead-lag clusters of time series in multivariate systems. We demonstrate that the web of pairwise lead-lag relationships between time series can be helpfully construed as a directed network, for which there exist suitable algorithms for the detection of pairs of lead-lag clusters with high pairwise imbalance. Within our framework, we consider a number of choices for the pairwise lead-lag metric and directed network clustering components. Our framework is validated on both a synthetic generative model for multivariate lead-lag time series systems and daily real-world US equity prices data. We showcase that our method is able to detect statistically significant lead-lag clusters in the US equity market. We study the nature of these clusters in the context of the empirical finance literature on lead-lag relations and demonstrate how these can be used for the construction of predictive financial signals.
We construct realistic equity option market simulators based on generative adversarial networks (GANs). We consider recurrent and temporal convolutional architectures, and assess the impact of state compression. Option market simulators are highly relevant because they allow us to extend the limited real-world data sets available for the training and evaluation of option trading strategies. We show that network-based generators outperform classical methods on a range of benchmark metrics, and adversarial training achieves the best performance. Our work demonstrates for the first time that GANs…
Symmetries of the auto-cumulant function (the generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using theory of group representations, symmetries of the auto-cumulant function are demystified and lag-window functions are symmetrized to satisfy these symmetries. A generalized Gabr-Rao optimal kernel, used to estimate general kth-order spectra, is also derived through the developed theory.
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the framework, including the negative binomial, gamma and Gaussian distributions. We develop an iterative algorithm to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags. Analytical solutions are given for the univariate model with lag one and multivariate models with linear mean-variance relationship. A special case of t…
Information Technologies Institute, Centre of Research and Technology Hellas（希腊研究与技术中心信息技术研究所）
Multivariate time series forecasting is of great importance to many scientific disciplines and industrial sectors. The evolution of a multivariate time series depends on the dynamics of its variables and the connectivity network of causal interrelationships among them. Most of the existing time series models do not account for the causal effects among the system's variables and even if they do they rely just on determining the between-variables causality network. Knowing the structure of such a complex network and even more specifically knowing the exact lagged variables that contribute to the…
Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence. The measures are non-negative, and take the value zero only when there is independence of the pertinent type. These measures are defined in the frequency domain and are applicable to stationary and non-stationary time series. These new results extend and refine significantly those presented in a previous technical report (Pascual-Marqui 2007, arXiv:0706.1776…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonpara…
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of defining a meaningful coupling strength using information theoretic measures and demonstrate the short-comings of the well-known mutual information and transfer entropy. Instead, we propose a certain time-delayed conditional mutual information, the momentary information transfer (…
Motivated by the current fears of a potentially stagflationary global economic environment, this paper uses new and recently introduced mathematical techniques to study multivariate time series pertaining to country inflation (CPI), economic growth (GDP) and equity index behaviours. We begin by assessing the temporal evolution among various economic phenomena, and complement this analysis with `economic driver analysis,' where we decouple country economic trajectories and determine what is most important in their association. Next, we study the temporal self-similarity of global inflation, gro…
Coherence and phase synchronization between time series corresponding to different spatial locations are usually interpreted as indicators of the connectivity between locations. In neurophysiology, time series of electric neuronal activity are essential for studying brain interconnectivity. Such signals can either be invasively measured from depth electrodes, or computed from very high time resolution, non-invasive, extracranial recordings of scalp electric potential differences (EEG: electroencephalogram) and magnetic fields (MEG: magnetoencephalogram) by means of a tomography such as sLORETA…
Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response $y$ and the predictors $\boldsymbol x$. Recently a time series version of sliced inverse regression, TSIR, was suggested, which applies approximate joint diagonalization of several supervised lagged covariance matrices to consider the temporal nature of the data. In this paper we develop this concept further and propose a time series version of sliced average variance estimation, TSAVE. As both TSIR and TSAVE have their own advantages and disadvantages, we consider furthermore…
IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Discovering temporal lagged and inter-dependencies in multivariate time series data is an important task. However, in many real-world applications, such as commercial cloud management, manufacturing predictive maintenance, and portfolios performance analysis, such dependencies can be non-linear and time-variant, which makes it more challenging to extract such dependencies through traditional methods such as Granger causality or clustering. In this work, we present a novel deep learning model that uses multiple layers of customized gated recurrent units (GRUs) for discovering both time lagged b…
Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models
University of Oxford（牛津大学）；Oxford-Man Institute of Quantitative Finance, University of Oxford（牛津大学牛津-曼量化金融研究院）；Queen Mary University of London（伦敦玛丽女王大学）；Memorial University of Newfoundland（纽芬兰纪念大学）；The Alan Turing Institute（艾伦·图灵研究所）
When analyzing the spatio-temporal dependence in most environmental and earth sciences variables such as pollutant concentrations at different levels of the atmosphere, a special property is observed: the covariances and cross-covariances are stronger in certain directions. This property is attributed to the presence of natural forces, such as wind, which cause the transport and dispersion of these variables. This spatio-temporal dynamics prompted the use of the Lagrangian reference frame alongside any Gaussian spatio-temporal geostatistical model. Under this modeling framework, a whole new cl…
The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger causality and encode the conditional independence structure of a multivariate process. The authors show that the complex dependencies of the Pearson correlation coefficient complicate an interpretation and propose a novel partial correlation measure with a straightforward graph-theoretical interpretation. The novel measure has the additional advantage that its samp…
This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects in the conditional variance, as they are usually present in spatial econometric applications. Furthermore, spatial and temporal cross-variable effects are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and diffe…
Modeling price risks is crucial for economic decision making in energy markets. Besides the risk of a single price, the dependence structure of multiple prices is often relevant. We therefore propose a generic and easy-to-implement method for creating multivariate probabilistic forecasts based on univariate point forecasts of day-ahead electricity prices. While each univariate point forecast refers to one of the day's 24 hours, the multivariate forecast distribution models dependencies across hours. The proposed method is based on simple copula techniques and an optional time series component.…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Tsinghua-Berkeley Shenzhen Institute（清华-伯克利深圳学院）；Tsinghua Shenzhen International Graduate School（清华大学深圳国际研究生院）；Graduate School, Tsinghua University（清华大学研究生院）
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer important physical parameters of inertial oscillations and other ocean processes. Nonstationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the datasets are large, we construct computationally efficient methods through the use of frequency-domain modelling and estimation, with the data expressed as…
Laboratory experiments have shown that cardiovascular diseases are positively correlated to the concentration of ambient air pollutants, such as SO2, NO2, PM10, etc. It has also been repeatedly reported in many countries that increased concentration of ambient air pollutants leads to rise in hospital emergency room visitss for these diseases. These studies mainly adopt either regression analysis or preliminary models in time series analysis, while the multivariable transfer function model, a relatively newly developed model, has multiple advantages over the conventional linear regression on an…
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsity-promoting regularization. Along this line we here propose that sparsity should be enforced for the subgroups of coefficients that belong to each pair of time series, as the absence of a causal relation requires the co…
