We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified ...

In this paper we propose a new class of nonlinear time series models, the threshold variable driven switching autoregressive models. It is a hierarchical model that combines two important nonlinear time series models, the threshold autoregressive (AR) models and the random switching AR models. The underlying time series process switches between two (or more) different linear models. The switchi...

Modulating the dynamics of a nonlinear autoregressive model with a radial basis function (RBF) of exogenous variables is known to reduce the prediction error. Here, RBF is a function that decays to zero exponentially if the deviation between the exogenous variables and a center location becomes large. This paper introduces a class of RBF-based multiplicatively modulated nonlinear autoregressive...

We derive a nonlinear filter and the corresponding filter-based estimates for a threshold autoregressive stochastic volatility, (TARSV), model. Using the technique of a reference probability measure, we derive a nonlinear filter for the hidden volatility and related quantities. The filter-based estimates for the unknown parameters are then obtained from the EM algorithm.

We introduce GP-RLARX, a novel Gaussian Process (GP) model for robust system identification. Our approach draws inspiration from nonlinear autoregressive modeling with exogenous inputs (NARX) and it encapsulates a novel and powerful structure referred to as latent autoregression. This structure accounts for the feedback of uncertain values during training and provides a natural framework for fr...

We introduce a nonparametric nonlinear time series model. The key idea is to fit a model via penalization, where the penalty term is an unbiased estimator of the integrated hessian of the underlying function. The underlying model assumption is very general: it has hessian everywhere (or almost everywhere) in its domain. Numerical experiments demonstrate that our model has better predictive powe...

We introduce a nonparametric nonlinear time series model. The novel idea is to fit a model via penalization, where the penalty term is an unbiased estimator of the integrated Hessian of the underlying function. The underlying model assumption is very general: it has Hessian almost everywhere in its domain. Numerical experiments demonstrate that our model has better predictive power: if the unde...

This paper considers the nonlinear systems modeling problem for control. A structured nonlinear parameter optimization method (SNPOM) adapted to radial basis function (RBF) networks and an RBF network-style coefficients autoregressive model with exogenous variable model parameter estimation is presented. This is an off-line nonlinear model parameter optimization method, depending partly on the ...

This note shows that regime switching nonlinear autoregressive models widely used in the time series literature can exhibit arbitrary degrees of long memory via appropriate definition of the model regimes.