Regularized Estimation in High-Dimensional Vector Auto-Regressive Models using Spatio-Temporal Information

12/18/2020
by   Zhenzhong Wang, et al.
0

A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and temporal structure of the data into consideration, which may lead to unreliable network detection and inaccurate forecasts. This paper proposes a data-driven weighted l1 regularized approach for spatio-temporal VAR model. Extensive simulation studies are carried out to compare the proposed method with four existing methods of high-dimensional VAR model, demonstrating improvements of our method over others in parameter estimation, network detection and out-of-sample forecasts. We also apply our method on a traffic data set to evaluate its performance in real application. In addition, we explore the theoretical properties of l1 regularized estimation of VAR model under the weakly sparse scenario, in which the exact sparsity can be viewed as a special case. To the best of our knowledge, this direction has not been considered yet in the literature. For general stationary VAR process, we derive the non-asymptotic upper bounds on l1 regularized estimation errors under the weakly sparse scenario, provide the conditions of estimation consistency, and further simplify these conditions for a special VAR(1) case.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/05/2021

Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data

We consider sparse estimation of a class of high-dimensional spatio-temp...
research
04/12/2019

A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Process

This paper develops a unified, accurate and computationally efficient me...
research
12/07/2017

Gini-regularized Optimal Transport with an Application to Spatio-Temporal Forecasting

Rapidly growing product lines and services require a finer-granularity f...
research
11/01/2017

Locally stationary spatio-temporal interpolation of Argo profiling float data

Argo floats measure sea water temperature and salinity in the upper 2,00...
research
05/16/2021

Learning Financial Network with Focally Sparse Structure

This paper studies the estimation of network connectedness with focally ...
research
01/20/2022

Parallel and distributed Bayesian modelling for analysing high-dimensional spatio-temporal count data

This paper proposes a general procedure to analyse high-dimensional spat...
research
02/09/2020

ℓ_0-Regularized High-dimensional Accelerated Failure Time Model

We develop a constructive approach for ℓ_0-penalized estimation in the s...

Please sign up or login with your details

Forgot password? Click here to reset