Nonlinear filters. Estimation and applications
The monograph gives a survey of filtering methods for estimation of unobservable variables with regard to economic applications. First, a time-varying parameter model, a seasonal component model, an autoregressive-moving average process are illustrated as applications of the Kalman filter model in the linear case. The author concentrates upon the investigation of seven nonlinear filters. He distinguishes these filters into nonlinear filters based on Taylor series expansion and nonlinear filters based on density approximation. Three out of the seven filters, called the Monte-Carlo simulation filter (MSF), the modified Kitagawa estimator (MKE) and the simulation-based density estimator (SDE) are new introduced. All of these filters are compared with the true filtered state variable simulated by Monte-Carlo experiments. In addition to other results the author obtained the result that the MKE and the SDE are better than any other estimator and that the SDE has a superior performance even the number of used nodes (or random draws) is small. The results are illustrated by an application to macroeconomic research. The author takes an example of estimating permanent and transitory consumption separately. He concludes that the so-called life cycle permanent income hypothesis does not hold in reality.
scientific article; zbMATH DE number 459471