The well-known Box-Jenkins’ Autoregressive Integrated Moving Average (ARIMA) methodology for fitting time-series data has some major limitations. To this end, Exponential Autoregressive (EXPAR) family of models may be employed. An important characteristic feature of EXPAR is that it is capable of modelling those data sets that depict cyclical variations. Further, it can also be used when data s...

Many papers have addressed the problem of fitting curves to data points. However, most of the approaches are subject to a restriction that the data points must be ordered. The paper presents a method for generating a piecewise continuous parametric curve from a set of unordered and error-filled data points. The resulting curve not only provides a good fit to the original data but also possesses...

This paper presents a new nonlinear least-squares algorithm for fitting band-limited periodic signals with unknown frequency and harmonic content. The new solution features a model-based recursive calculation method that requires less memory space and has smaller computational demand than the known matrix-based algorithms.

The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. The main reason for this is that it finds its origin in a formal theory of product diffusion, and that the model parameters have an easy interpretation in terms of innovation and imitation. Namely, Bass classified adopters (first-time buyers) into two groups: innovators and imitat...

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the traditional approach of logtransformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models. Here, we show that such mo...

In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and u...

Parameter estimation is a key issue in the mathematical modelling of nonlinear dynamic processes. Standard (gradient-based) methods for data fitting in nonlinear dynamic systems can suffer from slow and/or local convergence, among other problems. However, this is frequently ignored, potentially leading to wrong conclusions about the validity of a model regarding a certain data set. In order to ...

This paper presents a simulation method of self-similar traffic and a type of TCP traffic simulators based on autocorrelation sequences. The impulse function of a simulator is carried out. The parameter estimations for modeling the impulse function of the simulator are determined by multidimensional nonlinear least squares fitting. The existence and the uniqueness of solutions for the multidime...

Am&-The paper presents a simple derivation of the method of fitting nonlinear algebraic models where all variables are subject to error and improves the numerical efficiency of the algorithm. Including a known procedure for equilibrating balance equations and factorizing the weighting matrix, the classical Gauss-Marquardt method of estimating parameters in nonlinear models is shown to handle al...

Substances such as chemical compounds and biological agents are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Although spectra of pure substances can be identified by visual inspection, the spectra of their mixtures take a variety of complicated forms. Given the knowledge of spectral references of the constituent substances, the task ...