Improved Prediction and Network Estimation Using the Monotone Single Index Multi-variate Autoregressive Model
This work improves network estimation for researchers analyzing multivariate time series by offering a more robust semi-parametric approach, though it is incremental as it builds on existing models with specific enhancements.
The paper tackles network estimation from multivariate time series data by developing a semi-parametric monotone single-index autoregressive model (SIMAM) to address robustness issues in parametric methods, achieving optimal rates of O(T^{-1/3} √(s log(TM))) and outperforming state-of-the-art methods in simulations and real data.
Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less robust to model mis-specification, non-linearities and heterogeneities. In this paper, we develop a semi-parametric approach based on the monotone single-index multi-variate autoregressive model (SIMAM) which addresses these challenges. We provide theoretical guarantees for dependent data and an alternating projected gradient descent algorithm. Significantly we do not explicitly assume mixing conditions on the process (although we do require conditions analogous to restricted strong convexity) and we achieve rates of the form $O(T^{-\frac{1}{3}} \sqrt{s\log(TM)})$ (optimal in the independent design case) where $s$ is the threshold for the maximum in-degree of the network that indicates the sparsity level, $M$ is the number of actors and $T$ is the number of time points. In addition, we demonstrate the superior performance both on simulated data and two real data examples where our SIMAM approach out-performs state-of-the-art parametric methods both in terms of prediction and network estimation.