Time varying regression with hidden linear dynamics
This provides a simpler and more efficient alternative to Expectation-Maximization for time-varying regression, potentially benefiting researchers and practitioners in fields like econometrics or signal processing.
The paper tackles the problem of estimating time-varying linear regression parameters that evolve according to a stable linear dynamical system, showing that these parameters can be estimated by combining just two ordinary least squares estimates with a finite sample guarantee on error.
We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates. We offer a finite sample guarantee on the estimation error of our method and discuss certain advantages it has over Expectation-Maximization (EM), which is the main approach proposed by prior work.