In this paper we establish the strong approximations for the nonlinear transformations of integrated time series. Both the asymptotically homogeneous and integrable transformations are considered, and the explicit rates for the convergence to their limit distributions are obtained under mild regularity conditions that are satisfied by virtually all nonlinear models used in practical application...

A number of tests for non-linear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire postBretton Ð Woods era until the present day. Irrefutable evidence of non-linearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the l...

Practical aspects of a new technique for monitoring and controlling the predictive performance of Bayesian forecasting models are discussed. The basic features of the approach to model monitoring introduced in a general setting in West (1986) are described and extended to a wide class of dynamic, nonnormal, and nonlinear Bayesian forecasting models. An associated method of automatically detecti...

Introduction In this paper we consider a model related in form to that treated in Park and Phillips (2001). To introduce the model, let f (y; ) be a given function of y and (such that the conditions stated in Section 2 are satis…ed; in particular it is assumed that R @f(y; ) @ 2 dy <1 for all ). Let "j ; j , 1 < j <1, be iid such that E ["1] = 0 = E [ 1], 0 < E "1 < 1 and 0 < E 1 <1. Consider t...

This paper describes representations of time-dependent signals that are invariant under any invertible time-independent transformation of the signal time series. Such a representation is created by rescaling the signal in a non-linear dynamic manner that is determined by recently encountered signal levels. This technique may make it possible to normalize signals that are related by channel-depe...

This paper aims to examine whether a bubble is present in the housing market of China. Thus, we use the housing price-to-income ratios and housing price-to-rent ratios of 35 cities from 1998 to 2010. The methods of the panel KSS unit root test with a Fourier function and the SPSM process are likewise used. The panel KSS unit root test with a Fourier function considers the problem of non-lineari...

This paper introduces nonlinear threshold time series modeling techniques that actuaries can use in pricing insurance products, analyzing the results of experience studies, and forecasting actuarial assumptions. Basic “self-exciting” threshold autoregressive (SETAR) models, as well as heteroscedastic and multivariate SETAR processes, are discussed. Modeling techniques for each class of models a...

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.

The traditional linear Granger test has been widely used to examine the linear causality among several time series in bivariate settings as well as multivariate settings. Hiemstra and Jones [19] develop a nonlinear Granger causality test in bivariate settings to investigate the nonlinear causality between stock prices and trading volume. This paper extends their work by developing a non-linear ...

It is usual to model the dynamics of an observed time series by building a model F (x t) = x t+1 + e t of a map. Generally F is constructed so that P e 2 t is minimal (often subject to some constraint on F which will avoid over-tting). One may obtain a prediction further into the future by iterating F. In this paper we propose alternative formulations to build a function G(x t ;) = x t+ + e t;;...