We identify conditions for geometric ergodicity of general, and possibly nonparametric, nonlinear autoregressive time series. We also indicate how a condition for ergodicity, with minimal side assumptions, may in fact imply geometric ergodicity. Our examples include models for which exponential stability of the associated (noiseless) dynamical system is not sufficient or not necessary, or both.

This paper proposes a new parametric model adequacy test for possibly nonlinear time series models such as generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD). We consider the correct specification of parametric conditional distributions, not only some particular conditional characteristics. Using the true parametric conditional distri...

An MCMC(Markov Chain Monte Carlo) algorithm is proposed for nonlinear time series prediction with Hierarchical Bayesian framework. The algorithm computes predictive mean and error bar by drawing samples from predictive distributions. The algorithm is tested against time series generated by (chaotic) Rössler system and it outperforms quadratic approximations previously proposed by the authors.

The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related...

An analysis of predictability of a nonlinear and nonstationary ozone time series is provided. For rigour, the DVS analysis is first undertaken to detect and measure inherent nonlinearity of the data. Based upon this, neural and linear adaptive predictors are compared on this time series for various filter orders, hence indicating the embedding dimension. Simulation results confirm the analysis ...

Many of the popular nonlinear time series models require a priori the choice of parametric functions which are assumed to be appropriate in specific applications. This approach is used mainly in financial applications, when sufficient knowledge is available about the nonlinear structure between the covariates and the response. One principal strategy to investigate a broader class on nonlinear t...

Exploratory methods for determining appropriate lagged variables in a vector nonlinear time series model are investigated. The rst is a multivariate extension of the R statistic considered by Granger and Lin (1994), which is based on an estimate of the mutual information criterion. The second method uses Kendall's and partial statistics for lag determination. Both methods provide nonlinear anal...

We present a surrogate for use in nonlinear time series analysis. This surrogate algorithm has significant advantages over the most commonly used surrogates, in that it provides a more robust statistical test by producing an entire population of surrogates that are consistent with the null hypothesis. We will show that for the currently used surrogate algorithms, although individual surrogate f...

This paper deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range (R/S) analysis to estimate the Hurst exponent for 259-year and 11 360-year sunspot data. The results show a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the Hurst exponent. We explain the presence of these multiple Hurst ex...