SVD-based State Estimation of Pairwise Markov Models with Application in Econometrics

In this paper, several general forms of linear time-invariant (LTI) state-space models are explored. In particular, a numerical robustness of the so-called pairwise Kalman filter (PKF) is investigated. We propose stable singular value decomposition (SVD) factorization-based algorithms for implementing the PKF and LTI MIMO estimator, respectively, and explain their practical applicability in econometrics discipline. More precisely, the test for evolving efficiency is expressed in the LTI MIMO form and the newly-derived SVD-based estimator is applied for recovering the Russian market weak-form efficiency process in the last 20 years.