We develop a mixture model for transition density approximation, together with soft selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our builds on Gaussian distribution (MTD) continuous state spaces, extending component means functions that are modeled using process (GP) priors. The resulting flexibly captures lag dependence when several components active, identifies lo...

The asymptotic covariance matrix of the empirical cepstrum is analyzed. We show that for Gaussian processes, cepstral coefficients derived from smoothed periodograms are asymptotically uncorrelated and their variances multiplied by the sample size T tend to unity. For an autoregressive process and its autoregressive cepstrum estimate, somewhat weaker results hold.

1.1. Point Processses and Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Stochastic Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. The Autoregressive Conditional Duration Model . . . . . . . . . . . . . . . . . . . . . . . 2 1.3. The Autoregressive Conditional Intensity Model . . . . . . . . . . . . . . . ...

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asy...

(1-2) Pj(t) = Pj(t + d) , qt = qt+d and {E,} is a normal white noise with zero mean value and a variance a. Such process is natural analogy of the periodic autoregressive process (see e.g. [ l ] , [5], [6], [7]) and therefore the idea originates to use the estimation technique described in [3] for the treatment of the multiple moving average models (the same approach to the multiple autoregress...