On a Class of Nonlinear AR(P) Models with Nonlinear ARCH Errors

This paper studies general sufficient conditions for the geometric ergodicity and the existence of moments for a class of nonlinear autoregressive models with nonlinear ARCH errors. Applications of these conditions to various well-known nonlinear time series models yield specific sufficient conditions, many of which are new or generalizations of existing conditions.     

Adaptive Test for Periodicity in Self-Exciting Threshold Autoregressive Models

This article is devoted to the study of the periodicity testing problem in a self-exciting threshold autoregressive (SETAR) model. The local asymptotic normality (LAN) property is shown via the adapted sufficient conditions due to Swensen (1985 Swensen , A. R. ( 1985 ). The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend . Journal of Multivariate Analysis 16 : 54 – 70 .[Crossref], [Web of Science ®] , [Google Scholar]). Moreover, the LAN of the central sequence is established. First, we consider the case where the innovation density is specified and we obtain a parametric local asymptotic test. Second, we construct an adaptive test in the case where this density is unspecified but symmetric. The performances of these established tests are shown via simulation studies.     

The umvue and bayes estimate of reliability of mixed failure time distribution

We study the reliability estimates of the non-standard mixture of degenerate (degenerated at zero) and exponential distributions. The Uniformly Minimum Variance Unbiased Estimator (UMVUE) and Bayes estimator of the reliability for some selective prior when the mixing proportion is known and unknown are derived. The Bayes risk is computed for each Bayes estimator of the reliability. A simulated study is carried out to assess the performance of the estimators alongwith the true and Maximum Likelihood Estimate (MLE) of the reliability. An example from Vannman (1991) is also discussed at the end of the paper.     

An Enhanced Double MEWMA Controller for Drifted MIMO Systems

For a drifted multiple-input and multiple-output (MIMO) system, the double multivariate exponentially weighted moving average (dMEWMA) controller is a popular run-to-run (RTR) controller for adjusting the process mean to a desired target. The stability and performance of dMEWMA controller had been widely studied in literature. Although the dMEWMA controller (with suitable discount matrices) can guarantee long-term stability, it usually requires a moderately large number of runs to bring the process output to approach its desired target if the initial recipe is not chosen appropriately. Due to the initial recipe possibly having an infinite number of feasible solutions for MIMO systems, “how to determine an optimal setting for the initial recipe” turns out to be an interesting research topic. In this article, by solving a constrained optimization problem, we first obtain an optimal initial setting for the input recipe. Then, motivated by this setting, we propose an enhanced dMEWMA controller. The long-term stability conditions and short-term performance of the proposed controller are also addressed. Given a fixed and finite production run, it reveals that the proposed controller has the ability of reducing total mean squared error (TMSE) better than the conventional dMEWMA controller.     

Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series

We consider the estimation of the conditional quantile function when the covariates take values in some abstract function space. The main goal of this article is to establish the almost complete convergence and the asymptotic normality of the kernel estimator of the conditional quantile under the α-mixing assumption and on the concentration properties on small balls of the probability measure of the functional regressors. Some applications and particular cases are studied. This approach can be applied in time series analysis to the prediction and building of confidence bands. We illustrate our methodology with El Niño data.     

Variants of the graph dependent model in extreme value theory

With a set X₁, X₂, .... X_n n random variables, a graph is associated whose vertices are the integers 1,2,..., n and whose edges represent those pairs i and j for which the events {X_i>X} and {X_j>X} do not become “almost independent” for “large X”. With a variety of assumption on the edge set of the graph, the asymptotic distribution of the extremes of the X_j, when properly normalized, is determined. This refines the earlier result of the present author on this kind of dependence, and extends and unifies several known dependent extreme value models.     

Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.     

Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship

We consider modeling the real exchange rate by a stationary three-regime self-exciting threshold autoregressive (SETAR) model with possibly a unit root in the middle regime. This representation is consistent with purchasing power parity in the presence of trading costs. Our main contribution is to provide statistical tools for testing unit root versus a SETAR. First, we show that a SETAR with a unit root in the middle regime is stationary and mixing under reasonable assumptions. Second, we derive analytically the asymptotic distribution of our unit-root test under the null. Using monthly real exchange rate data, our test rejects the null of unit-root against a threshold process for five European series.     

A plug-in technique in nonparametric regression with dependence

The problem addressed is that of smoothing parameter selection in kernel nonparametric regression in the fixed design regression model with dependent noise. An asymptotic expression of the optimum bandwidth parameter has been obtained in recent studies, where this takes the form h = C ₀ n ^?1/5. This paper proposes to use a plug-in methodology, in order to obtain an optimum estimation of the bandwidth parameter, through preliminary estimation of the unknown value of C ₀.     

Geometric ergodicity of nonlinear autoregressive models with changing conditional variances

The authors give easy‐to‐check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process x_t = ?(x_t‐1,…, x_t‐p) + ?_tσ(x_t‐1,…, x_t‐q) in which ?: R^p → R, σ R^q → R and (?_t) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)‐ARCH(p), and the double‐threshold autoregressive models.