Nonstationary nonlinear heteroskedasticity

Nonstationary Nonlinear Heteroskedasticity in Regression1

This paper considers the regression with errors having nonstationary nonlinear heteroskedasticity. For both the usual stationary regression and the nonstationary cointegrating regression, we develop the asymptotic theories for the least squares methods in the presence of conditional heterogeneity given as a nonlinear function of an integrated process. In particular, it is shown that the nonstat...

Estimation for Partially Nonstationary Multivariate Autoregressive Models with Conditional Heteroskedasticity

where $‘s inre r*onst,ant matricaes; detI{@(z)} = 11 @,x . w * $JP[ = 0 has ci 5 771, urrit roots and ‘I’ = 711 d roots omside the urrit, circle: tPt = ((1 it, 7 c+> is a sequcnce of independent1 and idcntically distlributled (i.i.tl) matrices with mean zero and nonnegativc covarianc~e IC[ /le+&) ~f’(&)] = 0; pit is an i.i.d ramlom vector witIh mean zero and positive covariance E ( etef j = CA ...

Nonlinear and Nonstationary Signal Processing

On a nonstationary nonlinear coupled system ∗

In this paper, a strongly nonlinear coupled elliptic-parabolic system modelling a class of engineering problems with heat effect is studied. Existence of a weak solution is first established by Schauder fixed point theorem, where the coupled functions σ(s), k(s) are assumed to be bounded. The uniqueness of the solution is obtained by applying Meyers’ theorem and assuming that σ(s), k(s) are Lip...

Nonlinear cointegrating regressions with nonstationary time series

This paper develops an asymptotic theory for a non-linear parametric co-integrating regression model. We establish a general framework for weak consistency that is easy to apply for various non-stationary time series, including partial sum of linear process and Harris recurrent Markov chain. We provide a limit distribution for the nonlinear least square estimator which significantly extends the...