A sparsity-controlled vector autoregressive model

Abstract

Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.g. the number of causal features allowed in the prediction. To authors extent none of the existent methods endows the user with full control over the different aspects of the sparsity of the solution. In this article, we propose a versatile sparsity-controlled VAR model which enables a proper visualization of potential causalities while allows the user to control different dimensions of the sparsity if she holds some preferences regarding the sparsity of the outcome. The model coefficients are found as the solution to an optimization problem, solvable by standard numerical optimization routines. The tests performed on both simulated and real-life time series show that our approach may outperform a greedy algorithm and different Lasso approaches in terms of prediction errors and sparsity.

Short-Term Electric Load Forecasting With Sparse Coding Methods

“…Taking advantage of the properties of group sparsity, we built a model that is inherently capable of extracting specific features of the net load with strong correlation, and thus providing high-accuracy predictions. It should be noted that hierarchical sparse coding has already been proven to be an effective approach for modeling time-series presenting structured patterns, according to the literature, where a sparsity-controlled vector autoregressive model is established in [58] and tested upon several datasets. Finally, group sparsity has also been found beneficial in different types of time-series, e.g.…”

Correlation-Constrained and Sparsity-Controlled Vector Autoregressive Model for Spatio-Temporal Wind Power Forecasting

“…4) The number of nonzero coefficients used to explain the target wind farm i (S i N ). Following [33], by introducing binary variables and adding constraints on the coefficients of VAR, the original VAR can be reformulated as a MINLP problem, which is expressed as…”

“…Furthermore, as the constraints (3g) and (3h) are non-linear, a reformulation is provided in [33] to linearize them by replacing δ i jk with ν i+ jk + ν i− jk . Then (3g) and (3h) can be linearized as…”

“…Though the simplified SC-VAR is a convex MINLP, its time consumption is still quite larger than that of other forecasting models. In practice, when solving the simplified SC-VAR, a short time limit (30 seconds in this paper) has to be imposed for each wind farm, as suggested by [33]. Otherwise, the optimization process for some wind farms may take more than ten minutes.…”

“…In this paper, a sparsity-controlled VAR (SC-VAR) model [33] is introduced for very-short-term spatio-temporal WPF. It reformulates the estimation problem for a VAR model as a constrained mixed integer non-linear programming (MINLP) problem, which can then be readily solved with a standard optimization solver.…”