Proietti, Tommaso and Luati, Alessandra
(2009):
*Low-Pass Filter Design using Locally Weighted Polynomial Regression and Discrete Prolate Spheroidal Sequences.*

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## Abstract

The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) relationship between the cutoff period (frequency) and the bandwidth, conditional on the choices of the order and the kernel, upon which we build the design of a low-pass filter. The second hinges on a generalization of the maximum concentration approach, leading to filters related to discrete prolate spheroidal sequences (DPSS). In particular, we propose a new class of lowpass filters that maximize the concentration over a specified frequency range, subject to polynomial reproducing constraints. The design of generalized DPSS filters depends on three parameters: the bandwidth, the polynomial order, and the concentration frequency. We discuss the properties of the corresponding filters in relation to the LWPR filters, and illustrate their use for the design of low-pass filters by investigating how the three parameters are related to the cutoff frequency.

Item Type: | MPRA Paper |
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Original Title: | Low-Pass Filter Design using Locally Weighted Polynomial Regression and Discrete Prolate Spheroidal Sequences |

Language: | English |

Keywords: | Trend filters; Kernels; Concentration; Filter Design. |

Subjects: | E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes |

Item ID: | 15510 |

Depositing User: | Tommaso Proietti |

Date Deposited: | 04 Jun 2009 01:50 |

Last Modified: | 27 Sep 2019 16:49 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/15510 |