We propose a bootstrap detection for operationally deterministic versus stochastic nonlinear modelling and illustrate the method with both simulated and real data sets.

Varying-coefficient linear models arise from multivariate nonparametric regression, nonlinear time series modelling and forecasting, functional data analysis, longitudinal data analysis, and others. It has been a common practice to assume that the vary-coefficients are functions of a given...

We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive moving-average (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp. 130-145]...

Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given...

We consider a conditional empirical distribution of the form Fn(C | x)=[summation operator]nt=1 [omega]n(Xt-x) I{Yt[set membership, variant]C} indexed by C[set membership, variant], where {(Xt, Yt), t=1, ..., n} are observations from a strictly stationary and strong...

We propose to model multivariate volatility processes on the basis of the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that each CUC may be fitted separately with any...