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2006.77: Multivariate Non-Linear Regression with Applications: A Frequency Domain Approach

2006.77: G Terdik, T Subba Rao and S Rao Jammalamadaka (2006) Multivariate Non-Linear Regression with Applications: A Frequency Domain Approach.

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Abstract

In this paper we consider estimating the parameters of a multivariate multiple nonlinear regression model with correlated errors, through the use of Finite Fourier Transforms. Consistency and asymp- totic normality of the weighted least squares estimates are established under various conditions on the regressor variables. These conditions involve different types of scalings, and such scaling factors are obtained explicitly for various nonlinear regression models including an interesting model which requires estimating the frequencies. This is a very classical problem in signal processing and is also of great interest in many other areas. We illustrate our techniques on the time-series data of polar motion (which is now widely known as "Chandlers Wobble") where one has to estimate the drift parameters, the offset parameters and the two periodicities associated with elliptical motion. The data was first analyzed by Arato, Kolmogorov and Sinai who treat it as bivariate time series data satisfying a finite order time series model. They estimate the periodicities using the coefficients of the models. Our analysis shows that the two dominant frequencies are 12 hours and 410 days and that the errors exhibit some long-range dependence.

Item Type:MIMS Preprint
Subjects:MSC 2000 > 62 Statistics
MIMS number:2006.77
Deposited By:Dr Peter Neal
Deposited On:12 May 2006

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