Optimal dimension reduction for high-dimensional and functional time series

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.

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Dimension Reduction of Polynomial Regression Models for the Estimation of Granger Causality in High-Dimensional Time Series

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2021.3114997 ◽

2021 ◽

pp. 1-1

Author(s):

Elsa Siggiridou ◽

Dimitris Kugiumtzis

Keyword(s):

Time Series ◽

Dimension Reduction ◽

Granger Causality ◽

Regression Models ◽

Polynomial Regression ◽

High Dimensional ◽

Polynomial Regression Models

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Evaluation of Granger Causality Measures for Constructing Networks from Multivariate Time Series

Entropy ◽

10.3390/e21111080 ◽

2019 ◽

Vol 21 (11) ◽

pp. 1080 ◽

Cited By ~ 4

Author(s):

Elsa Siggiridou ◽

Christos Koutlis ◽

Alkiviadis Tsimpiris ◽

Dimitris Kugiumtzis

Keyword(s):

Time Series ◽

Dynamical Systems ◽

Financial Markets ◽

Dimension Reduction ◽

Granger Causality ◽

Multivariate Time Series ◽

High Dimensional ◽

Information Measures ◽

Model Based ◽

The Time Domain

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain, and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets.

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Forecasting High-Dimensional Financial Functional Time Series: An Application to Constituent Stocks in Dow Jones Index

Journal of Risk and Financial Management ◽

10.3390/jrfm14080343 ◽

2021 ◽

Vol 14 (8) ◽

pp. 343

Author(s):

Chen Tang ◽

Yanlin Shi

Keyword(s):

Time Series ◽

Factor Model ◽

High Dimensional ◽

Matrix Structure ◽

New Approach ◽

Jones Index ◽

Share Prices ◽

Functional Time Series ◽

The Matrix ◽

Highly Correlated

Financial data (e.g., intraday share prices) are recorded almost continuously and thus take the form of a series of curves over the trading days. Those sequentially collected curves can be viewed as functional time series. When we have a large number of highly correlated shares, their intraday prices can be viewed as high-dimensional functional time series (HDFTS). In this paper, we propose a new approach to forecasting multiple financial functional time series that are highly correlated. The difficulty of forecasting high-dimensional functional time series lies in the “curse of dimensionality.” What complicates this problem is modeling the autocorrelation in the price curves and the comovement of multiple share prices simultaneously. To address these issues, we apply a matrix factor model to reduce the dimension. The matrix structure is maintained, as information contains in rows and columns of a matrix are interrelated. An application to the constituent stocks in the Dow Jones index shows that our approach can improve both dimension reduction and forecasting results when compared with various existing methods.

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