A class of nonlinear time-series models in which the underlying process follows a finite mixture of bilinear representations is proposed. The mixture feature appears in the conditional distribution of the process which is given as a finite mixture of distributions evaluated at the normed...

Multivariate Gaussian hidden Markov models with an unknown number of regimes are introduced here in the Bayesian setting and new efficient reversible jump Markov chain Monte Carlo algorithms for estimating both the dimension and the unknown parameters of the model are presented. Hidden Markov...

We study least absolute deviation (LAD) estimation for general autoregressive moving average time-series models that may be noncausal, noninvertible or both. For ARMA models with Gaussian noise, causality and invertibility are assumed for the parameterization to be identifiable. The assumptions,...

We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be...

We discuss the estimation of the order of integration of a fractional process that may be contaminated by a time-varying deterministic trend or by a break in the mean. We show that in some cases the estimate may still be consistent and asymptotically normally distributed even when the order of...

In this article we introduce a test for independence between two processes {X_t} and {Y_t}. To this end we rely on symbolic dynamics and permutation entropy as a measure of dependence. As a result, a nonparametric (model-free) test for either linear or nonlinear processes is presented. The test...

For a random design regression model with long memory design and long memory errors, we consider the problem of detecting a change point for sharp cusp or jump discontinuity in the regression function. Using the wavelet methods, we obtain estimators for the change point, the jump size and the...

Value-at-Risk (VaR) is a simple, but useful measure in risk management. When some volatility model is employed, conditional VaR is of importance. As autoregressive conditional heteroscedastic (ARCH) and generalized ARCH (GARCH) models are widely used in modelling volatilities, in this article,...