Publication Type
Journal Article
Version
submittedVersion
Publication Date
6-2007
Abstract
The nonlinear filters based on Taylor series approximation are broadly used for computational simplicity, even though their filtering estimates are clearly biased. In this paper, first, we analyze what is approximated when we apply the expanded nonlinear functions to the standard linear recursive Kalman filter algorithm. Next, since the state variable αt and αt-t are approximated as a conditional normal distribution given information up to time t - 1 (i.e., It-1) in approximation of the Taylor series expansion, it might be appropriate to evaluate each expectation by generating normal random numbers of αt and αt-1 given It-1 and those of the error terms θ and ηt. Thus, we propose the Monte-Carlo simulation filter using normal random draws. Finally we perform two Monte-Carlo experiments, where we obtain the result that the Monte-Carlo simulation filter has a superior performance over the nonlinear filters such as the extended Kalman filter and the second-order nonlinear filter.
Discipline
Economics
Research Areas
Econometrics
Publication
Communications in Statistics: Theory and Methods
Volume
25
First Page
1261
Last Page
1282
ISSN
0361-0926
Identifier
10.1080/03610929608831763
Publisher
Taylor and Francis
Citation
TANIZAKI, Hisashi and MARIANO, Roberto S..
Nonlinear filters based on Taylor series expansions. (2007). Communications in Statistics: Theory and Methods. 25, 1261-1282.
Available at: https://ink.library.smu.edu.sg/soe_research/302
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1080/03610929608831763