Proposes the Streaming Additive Matrix Autoregressive (SAMAR) model for online inference in streaming matrix time series. The framework decomposes temporal dynamics into row-wise and column-wise additive components with recursive estimation. Achieves constant memory and computational complexity per time step while maintaining statistical consistency and asymptotic normality for valid real-time hypothesis testing and confidence intervals.
Key findings
SAMAR model decomposes temporal dynamics into interpretable row-wise and column-wise additive components enabling separate effect interpretation.
Recursive estimation algorithm achieves O(d²₁+d²₂) time and memory complexity per observation, independent of streaming length.
Online debiasing procedure corrects SGD bias to enable asymptotic normality and valid statistical inference in real-time.
Online estimators achieve convergence rates nearly matching batch estimators up to logarithmic factors under standard regularity conditions.
Extensive simulations demonstrate superior computational efficiency over batch alternatives with comparable statistical accuracy.
Limitations & open questions
Additive structure introduces identifiability challenges that compound in streaming settings compared to multiplicative factor models.
Theoretical guarantees require standard regularity conditions that may not hold in highly non-stationary environments.
Focus on additive autoregressive structures excludes more complex multiplicative or nonlinear dynamics.