Skip to main content
SpringerLink
Log in

Nonlinear Filters

Estimation and Applications

Overview

Authors:
  1. Hisashi Tanizaki

    1. Department of Economics, Kobe-Gakuin University, Nishi-ku, Kobe, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 400)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Introduction

    • Hisashi Tanizaki
    Pages 1-13

  3. State-Space Model in Linear Case

    • Hisashi Tanizaki
    Pages 14-34

  4. Nonlinear Filters Based on Taylor Series Expansion

    • Hisashi Tanizaki
    Pages 35-67

  5. Nonlinear Filters Based on Density Approximation

    • Hisashi Tanizaki
    Pages 68-96

  6. Comparison of Nonlinear Filters: Monte-Carlo Experiments

    • Hisashi Tanizaki
    Pages 97-126

  7. An Application of Nonlinear Filters: Estimation of Permanent Consumption

    • Hisashi Tanizaki
    Pages 127-184

  8. Summary and Directions for Further Research

    • Hisashi Tanizaki
    Pages 185-197

  9. Back Matter

    Pages 198-203
    Download chapter PDF
Back to top

Keywords

About this book

For a nonlinear filtering problem, the most heuristic and easiest approximation is to use the Taylor series expansion and apply the conventional linear recursive Kalman filter algorithm directly to the linearized nonlinear measurement and transition equations. First, it is discussed that the Taylor series expansion approach gives us the biased estimators. Next, a Monte-Carlo simulation filter is proposed, where each expectation of the nonlinear functions is evaluated generating random draws. It is shown from Monte-Carlo experiments that the Monte-Carlo simulation filter yields the unbiased but inefficient estimator. Anotherapproach to the nonlinear filtering problem is to approximate the underlyingdensity functions of the state vector. In this monograph, a nonlinear and nonnormal filter is proposed by utilizing Monte-Carlo integration, in which a recursive algorithm of the weighting functions is derived. The densityapproximation approach gives us an asymptotically unbiased estimator. Moreover, in terms of programming and computational time, the nonlinear filter using Monte-Carlo integration can be easily extended to higher dimensional cases, compared with Kitagawa's nonlinear filter using numericalintegration.

Authors and Affiliations

  • Department of Economics, Kobe-Gakuin University, Nishi-ku, Kobe, Japan

    Hisashi Tanizaki

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation