We investigate the stability, in terms of V -uniform ergodicity or transience, of cyclic threshold autoregressive time series models. These models cycle through one of a number of collections of subregions of the state space when the process is large. Our results can be applied in cases where the model has multiple cycles and/or affine thresholds. The bounds on the parameter space are sharper t...

This article proposes an implementation and a study of the paper Adaptive Interpolation of Discrete-Time Signals That Can Be Modeled as Autoregressive Processes by Janssen et al [10]. The algorithm presented in this paper allows one to reconstruct an audio signal which presents localized degradations by interpolating the missing samples. This method assumes that the signal can locally be modele...

Compared to the traditional maximum likelihood regression approach, the penalized maximum likelihood estimation (PMLE) is a more rigorous method because of the adjustment for over fitting is directly built into the model development process, instead of relying on shrinkage afterwards. This paper illustrates the application of a nonlinear programming technique on PMLE to develop a prediction mod...

For a zero-mean Gaussian process, the covariances of zero crossings can be expressed as the sum of quadrivariate normal orthant probabilities. In this paper, we demonstrate the evaluation of zero crossing covariances using one-dimensional integrals. Furthermore, we provide asymptotics of zero crossing covariances for large time lags and derive bounds and approximations. Based on these results, ...

In this paper we propose a modification of the Divergence Information Criterion (DIC) for the determination of the order of an autoregressive process and show that it is an asymptotically unbiased estimator of the expected overall discrepancy. Further, we use Monte Carlo methods and various Data Generating Processes for small, medium and large sample sizes in order to explore the capabilities o...

We propose a simple method of testing for parameter constancy in regression models that allow for coe¢ cients that vary smoothly over time. The model is related to Bierens and Martins (2009) but in our case we consider stationary processes. The procedure is shown to have good statistical properties. We revisited Hansen’s (2001) study of structural breaks in a AR(1) model of labor productivity i...

Let {Xi} be a sequence of independent, identically distributed random variables with an intermediate regularly varying right tail F̄ . Let (N,C1, C2, . . .) be a nonnegative random vector independent of the {Xi} with N ∈ N ∪ {∞}. We study the weighted random sum SN = ∑Ni=1 CiXi , and its maximum, MN = sup1≤k<N+1 ∑ki=1 CiXi . This type of sum appears in the analysis of stochastic recursions, incl...