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In this paper we consider the statistical analysis of multivariate multiple nonlinear regression models with correlated errors, using Finite Fourier Transforms. Consistency and asymptotic normality of the weighted least squares estimates are established under various conditions on the regressor variables. These conditions involve different types of scalings, and the scaling factors are obtained explicitly for various types of nonlinear regression models including an interesting model which requires the estimation of unknown frequencies. The estimation of frequencies is a classical problem occurring in many areas like signal processing, environmental time series, astronomy and other areas of physical sciences. We illustrate our methodology using two real data sets taken from geophysics and environmental sciences. The data we consider from geophysics are 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 were first analyzed by Arato, Kolmogorov and Sinai who treat it as a bivariate time series satisfying a finite order time series model. They estimate the periodicities using the coefficients of the fitted models. Our analysis shows that the two dominant frequencies are 12 h and 410 days. The second example, we consider is the minimum/maximum monthly temperatures observed at the Antarctic Peninsula (Faraday/Vernadsky station). It is now widely believed that over the past 50 years there is a steady warming in this region, and if this is true, the warming has serious consequences on ecology, marine life, etc. as it can result in melting of ice shelves and glaciers. Our objective here is to estimate any existing temperature trend in the data, and we use the nonlinear regression methodology developed here to achieve that goal. © 2007 Elsevier B.V. All rights reserved.

Not only the infrastructure of Wireless Sensor Network (WSNs) and classical wired IP data networks are very different but the statistical characteristics of data flows transferred on these environments have technology specific features, too. Based on the dynamic evolution in the last years WSNs became important elements of the small physical sizednetwork architectures and are included as basic components in the Internet of Things (IoT) new concept. The challenge to transmit packets on optimum wireless path with minimum energy consumption affects all layer (physical, data link, network, transport, application) services of the WSN protocol stack. Wireless IP data technologies like GSM/UMTS/WiFi/WiMAX are utilized with success in WAN/MAN networks in contrast with WSN, which is usable only for small distances and reduced transfer capacity of bytes. Because of the energy consumption minimization the channel access mechanism should be simple as much as possible. Classical IP traffics in LAN/WAN environment do not confront with consequences of the energy constraints. The MAC algorithms are much more sophisticated than for WSNs. The difference in the layer functions implies difference in the traffic characteristics of this two network types. In this paper WSN and IP WAN/MAN data flows are analyzed as time series. Thesensor data flows were collected with TinyDB tools at the Intel Berkeley Research lab in 2004. The high speed IP data flows are available from public database of TIER links. These significantly different types of data flowsare investigated based on Lévy flights modeling. Long range dependence, self-similarity aspects of the inter-arrival time and the epoch ID time series are studied with sophisticated statistical analysis methods. [ABSTRACT FROM AUTHOR]