Network vector autoregression

Zhu, Xuening; Pan, Rui; Li, Guodong; Liu, Yuewen; Wang, Hansheng

doi:10.1214/16-aos1476

Cited by 123 publications

(66 citation statements)

References 31 publications

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“…Consequently, techniques used for HMM cannot be applied here. Instead, the same setting as in Zhu et al (2017) is considered, thus, the process X as well as the network Ad is observed; we have observations X 1 , . .…”

Section: Statistical Results For Doubly Stochastic Network Processesmentioning

confidence: 99%

“…Consequently, a more radical approach needs to be applied here in order to reduce the number of parameters. Here we adapt the idea of model (2.1) in Zhu et al (2017). The model reads as follows:…”

Section: Statistical Results For Doubly Stochastic Network Processesmentioning

confidence: 99%

“…This work gives a framework which models the network-influenced dynamic attributes, that means modeling a time series on a dynamic network in which the edges influence the dependency of the time series. Knight et al (2016); Zhu et al (2017) have considered these networkinfluenced attributes for non-random edges, which mainly covers static networks. In the context of a static network, network-influenced attributes can be considered as an ordinary multivariate time series with additional information and can be modeled by using vector autoregressive (VAR) models, see Lütkepohl (2007, Chapter 2).…”

Section: Introductionmentioning

confidence: 99%

“…In the context of a static network, network-influenced attributes can be considered as an ordinary multivariate time series with additional information and can be modeled by using vector autoregressive (VAR) models, see Lütkepohl (2007, Chapter 2). However, VAR models have many parameters which is why Knight et al (2016); Zhu et al (2017) focus on how to use the network structure to reduce the number of parameters so that high dimensions become feasible. In contrast, this work deals with a random network structure and consequently the process X cannot be modeled appropriately by using VAR models.…”

Section: Introductionmentioning

confidence: 99%

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Time series modeling on dynamic networks

Krampe¹

2019

Electron. J. Statist.

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We consider multivariate time series on dynamic networks with a fixed number of vertices. Each component of the time series is assigned to a vertex of the underlying network. The dependency of the various components of the time series is modeled dynamically by means of the edges. We make use of a multivariate doubly stochastic time series framework, that is we assume linear processes for which the coefficient matrices are stochastic processes themselves. We explicitly allow for dependence in the dynamics of the coefficient matrices, including of course an i.i.d. structure as is typically assumed in random coefficients models. Autoregressive moving average models are defined in this framework and stationarity conditions are discussed for network autoregressive models. Estimators of the parameters are discussed for various parameterizations of such network autoregressive models and how this can be used to forecast such a process. The finite sample behavior of the forecast approach is investigated and a real data example is presented.

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Section: Statistical Results For Doubly Stochastic Network Processesmentioning

confidence: 99%

Section: Statistical Results For Doubly Stochastic Network Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time series modeling on dynamic networks

Krampe¹

2019

Electron. J. Statist.

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“…High-dimensional time series is one of the most common types of "big data" and can be found in many areas including meteorology, genomics, finance and economics (Hallin and Lippi, 2013). The classical vector autoregressive (VAR) model is fundamental to multivariate time series modeling and has recently been applied to the high-dimensional case under certain structural assumptions, e.g., the banded structure (Guo et al, 2016) and the network structure (Zhu et al, 2017). Consider the VAR model of the form (Lütkepohl, 2005;Tsay, 2010):…”

Section: Introductionmentioning

confidence: 99%

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

Wang¹,

Lian²,

Zheng

et al. 2019

SSRN Journal

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The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to rearrange the coefficient matrices of the model into a tensor form such that the parameter space can be restricted in three directions simultaneously via tensor decomposition. The proposed method substantially expands the capacity of vector autoregressive modeling for a large number of time series. In contrast, the widely used reduced-rank regression method can restrict the parameter space in only one direction. Moreover, to handle high-dimensional time series, this paper considers imposing sparsity on factor matrices to improve the interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish non-asymptotic properties of the sparsity-inducing estimator and propose an ADMM-based algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods.

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Linkage vector autoregressive model

Asai,

2024

Appl Stoch Models Bus & Ind

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To accommodate linkage effects of individuals, we develop a new linkage vector autoregressive (LAR) model for dynamic panel data. A main feature of the LAR model is incorporating dynamic network information in autoregressive time series modeling. The dynamic network can be given, or we can formulate the network links as a function of historical data, where unknown parameters of the function can be estimated from the data. We propose a simulation technique to check the stationarity condition of the LAR model and suggest a Bayesian Markov chain Monte Carlo method for estimation. Empirical results for the quarterly growth rates of gross domestic product (GDP) in 45 countries indicate that (i) the autoregressive (AR) coefficient for the aggregated growth rate is hard to distinguish from zero; (ii) a panel AR model with individual effects has a positive autocorrelation; and (iii) the alternative LAR models are preferred to the panel AR model. Depending on the specification of the linkage variables, the sign and size of the linkage effect can differ. The logistic linkage function has a flexible structure to accommodate the size of the linkage of individual GDP growth rates, and it strengthens the dynamics.

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Network vector autoregression

Cited by 123 publications

References 31 publications

Time series modeling on dynamic networks

Time series modeling on dynamic networks

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

Linkage vector autoregressive model

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