### Abstract

In this paper, multiscale representation of data is utilized to reduce the collinearity problem often encountered in Finite Impulse Response (FIR) modeling. The idea is to decompose the input-output data at multiple scales, use the scaled signal approximations of the data to construct a FIR model at each scale, and then select among all scales the optimum estimated FIR model. The rationale behind this approach is that the number of significant cross correlation function (CCF) coefficients estimated using the scaled signal approximations of the input-output data decreases at coarser scales. This means that more parsimonious FIR models, with less collinearity and improved estimation accuracy, can be constructed at coarser scales. Of course, the estimation accuracy will deteriorate at very coarse scales. Therefore, it is very important to select the most appropriate scale for modeling purposes, which can be done by selecting the scale which results in the maximum prediction signal to noise ratio. The developed multiscale FIR modeling approach is shown to outperform existing methods, such as ordinary least squares (OLS) regression and ridge regression (RR).

Original language | English |
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Title of host publication | Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 |

Pages | 8162-8167 |

Number of pages | 6 |

Volume | 2005 |

DOIs | |

Publication status | Published - 1 Dec 2005 |

Externally published | Yes |

Event | 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005 |

### Other

Other | 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 |
---|---|

Country | Spain |

City | Seville |

Period | 12/12/05 → 15/12/05 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05*(Vol. 2005, pp. 8162-8167). [1583483] https://doi.org/10.1109/CDC.2005.1583483

**Dealing with collinearity in FIR models using multiscale estimation.** / Nounou, Mohamed.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05.*vol. 2005, 1583483, pp. 8162-8167, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583483

}

TY - GEN

T1 - Dealing with collinearity in FIR models using multiscale estimation

AU - Nounou, Mohamed

PY - 2005/12/1

Y1 - 2005/12/1

N2 - In this paper, multiscale representation of data is utilized to reduce the collinearity problem often encountered in Finite Impulse Response (FIR) modeling. The idea is to decompose the input-output data at multiple scales, use the scaled signal approximations of the data to construct a FIR model at each scale, and then select among all scales the optimum estimated FIR model. The rationale behind this approach is that the number of significant cross correlation function (CCF) coefficients estimated using the scaled signal approximations of the input-output data decreases at coarser scales. This means that more parsimonious FIR models, with less collinearity and improved estimation accuracy, can be constructed at coarser scales. Of course, the estimation accuracy will deteriorate at very coarse scales. Therefore, it is very important to select the most appropriate scale for modeling purposes, which can be done by selecting the scale which results in the maximum prediction signal to noise ratio. The developed multiscale FIR modeling approach is shown to outperform existing methods, such as ordinary least squares (OLS) regression and ridge regression (RR).

AB - In this paper, multiscale representation of data is utilized to reduce the collinearity problem often encountered in Finite Impulse Response (FIR) modeling. The idea is to decompose the input-output data at multiple scales, use the scaled signal approximations of the data to construct a FIR model at each scale, and then select among all scales the optimum estimated FIR model. The rationale behind this approach is that the number of significant cross correlation function (CCF) coefficients estimated using the scaled signal approximations of the input-output data decreases at coarser scales. This means that more parsimonious FIR models, with less collinearity and improved estimation accuracy, can be constructed at coarser scales. Of course, the estimation accuracy will deteriorate at very coarse scales. Therefore, it is very important to select the most appropriate scale for modeling purposes, which can be done by selecting the scale which results in the maximum prediction signal to noise ratio. The developed multiscale FIR modeling approach is shown to outperform existing methods, such as ordinary least squares (OLS) regression and ridge regression (RR).

UR - http://www.scopus.com/inward/record.url?scp=33847204697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847204697&partnerID=8YFLogxK

U2 - 10.1109/CDC.2005.1583483

DO - 10.1109/CDC.2005.1583483

M3 - Conference contribution

SN - 0780395689

SN - 9780780395688

VL - 2005

SP - 8162

EP - 8167

BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

ER -