The discrete Kalman filter applied to linear regression models: statistical considerations and an application

TLDR

The paper demonstrates how the Kalman filter can be applied to the standard linear regression model. They illustrate the filter’s applicability and advantages through a two‑part case study—applying it to regression models with constant parameters and with time‑varying stochastic parameters—and compare the prediction power of Kalman predictors to least‑squares predictors using Tiel’s prediction‑error coefficient U. The resulting Kalman estimator is compared with the classical least‑squares estimator.

Abstract

Abstract In this paper we show how the Kalman filter, which is a recursive estimation procedure, can be applied to the standard linear regression model. The resulting “Kalman estimator” is compared with the classical least‐squares estimator. The applicability and (dis)advantages of the filter are illustrated by means of a case study which consists of two parts. In the first part we apply the filter to a regression model with constant parameters and in the second part the filter is applied to a regression model with time‐varying stochastic parameters. The prediction‐powers of various “Kalman predictors” are compared with “least‐squares predictors” by using T heil ‘s prediction‐error coefficient U.