arXiv subjects

Sipan Aslan

Publications and source records attributed to Sipan Aslan.

3 recordsLinked to original sources

arXiv2024

Nonlinear Causality in Time Series Networks: With Application to Motor Imagery vs Execution

Causal interactions in time series networks can be dynamic and nonlinear, making it difficult to identify them using conventional linear causality estimations. We propose a novel approach, called Threshold Autoregressive Modeling for Causality (TAR4C), a causality detection approach built on threshold autoregressive (TAR) models, where a potential driver (cause variable) acts both as a predictor and as a trigger (switching threshold) that governs which autoregressive process the target (effect variable) follows. Threshold nonlinearity is conceptualized here to determine causality. The flow of the target is forced to transition between regimes with distinct dynamics when the driver exceeds a data-driven threshold in the past. We propose a two-stage inference procedure: Stage 1 tests for threshold connectivity (TC); Stage 2, conditional on a detected threshold effect, estimates threshold Granger causality (TGC). TAR4C is applied to a multichannel EEG dataset collected from a motor imagery and execution experiment. Delay-dependent directional interactions are observed among channels across different sites of the EEG map. The real-world application demonstrates the usefulness of the proposed approach for determining nonlinear causal connectivity in complex time-series networks, such as brain circuitry. The proposed model-based methodology extends to other complex networks of time series.

stat.AP↗

arXiv2024

Granger Causality in High-Dimensional Networks of Time Series

A novel approach is developed for discovering directed connectivity between specified pairs of nodes in a high-dimensional network (HDN) of brain signals. To accurately identify causal connectivity for such specified objectives, it is necessary to properly address the influence of all other nodes within the network. The proposed procedure herein starts with the estimation of a low-dimensional representation of the other nodes in the network utilizing (frequency-domain-based) spectral dynamic principal component analysis (sDPCA). The resulting scores can then be removed from the nodes of interest, thus eliminating the confounding effect of other nodes within the HDN. Accordingly, causal interactions can be dissected between nodes that are isolated from the effects of the network. Extensive simulations have demonstrated the effectiveness of this approach as a tool for causality analysis in complex time series networks. The proposed methodology has also been shown to be applicable to multichannel EEG networks.

stat.AP↗

arXiv2016

Temporal Clustering of Time Series via Threshold Autoregressive Models: Application to Commodity Prices

This study aimed to find temporal clusters for several commodity prices using the threshold non-linear autoregressive model. It is expected that the process of determining the commodity groups that are time-dependent will advance the current knowledge about the dynamics of co-moving and coherent prices, and can serve as a basis for multivariate time series analyses. The clustering of commodity prices was examined using the proposed clustering approach based on time series models to incorporate the time varying properties of price series into the clustering scheme. Accordingly, the primary aim in this study was grouping time series according to the similarity between their Data Generating Mechanisms (DGMs) rather than comparing pattern similarities in the time series traces. The approximation to the DGM of each series was accomplished using threshold autoregressive models, which are recognized for their ability to represent nonlinear features in time series, such as abrupt changes, time-irreversibility and regime-shifting behavior. Through the use of the proposed approach, one can determine and monitor the set of co-moving time series variables across the time dimension. Furthermore, generating a time varying commodity price index and sub-indexes can become possible. Consequently, we conducted a simulation study to assess the effectiveness of the proposed clustering approach and the results are presented for both the simulated and real data sets.

stat.ML↗