2019/10/30 by Jonathan Jonker, Peng Zheng, Jonker, Jonathan +3
Computer Science · Engineering · #65C60 #65K10 #90C30 #Bayesian Modeling and Causal Inference #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1910.13674
openalex publication_date 2019/10/30 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential\nsmoothing, and navigation are often formulated and solved using state-space\nmodels (SSM), which allow a range of statistical distributions to inform\ninnovations and errors. In many applications the main goal is to identify not\nonly the hidden state, but also additional unknown model parameters (e.g. AR\ncoefficients or unknown dynamics).\n We show how to efficiently optimize over model parameters in SSM that use\nsmooth process and measurement losses. Our approach is to project out state\nvariables, obtaining a value function that only depends on the parameters of\ninterest, and derive analytical formulas for first and second derivatives that\ncan be used by many types of optimization methods.\n The approach can be used with smooth robust penalties such as Hybrid and the\nStudent's t, in addition to classic least squares. We use the approach to\nestimate robust AR models and long-run unemployment rates with sudden changes.\n