Efficient Robust Parameter Identification in Generalized Kalman Smoothing Models

TL;DR

This paper introduces an efficient method for robustly estimating parameters in state-space models, enabling improved inference in dynamic systems with unknown parameters and robust loss functions.

Contribution

The authors develop a projection-based optimization approach with analytical derivatives for parameter estimation in smooth state-space models, accommodating robust penalties.

Findings

Effective estimation of AR models with robust penalties

Application to long-term unemployment rate analysis

Enhanced optimization efficiency in parameter identification

Abstract

Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSM), which allow a range of statistical distributions to inform innovations and errors. In many applications the main goal is to identify not only the hidden state, but also additional unknown model parameters (e.g. AR coefficients or unknown dynamics). We show how to efficiently optimize over model parameters in SSM that use smooth process and measurement losses. Our approach is to project out state variables, obtaining a value function that only depends on the parameters of interest, and derive analytical formulas for first and second derivatives that can be used by many types of optimization methods. The approach can be used with smooth robust penalties such as Hybrid and the Student's t, in addition to classic least squares. We use the approach to estimate robust AR models and long-run unemployment rates with sudden changes.