We prove that a large set of long memory (LM) processes (including classical LM and all whose spectral densities have countable number singularities controlled by exponential functions) are obtained an aggregation procedure involving short (SM) infinitely differentiable ($C^\infty$). show the $C^\infty$ class is best to get general result for disaggregation in SM processes, sense given cannot be improved taking instance analytic functions instead indefinitely derivable functions.

In this study, we prove the strong consistency of least squares estimator in a random sampled linear regression model with long-memory noise and an independent set times given by renewal process sampling. Additionally, illustrate how to work number observations up time T = 1. A simulation study is provided behavior different terms, as well performance under various values Hurst parameter H.

We approach the problem of non‐parametric estimation for autoregressive Markov switching processes. In this context, Nadaraya–Watson‐type regression functions estimator is interpreted as a solution local weighted least‐square problem, which does not admit closed‐form in case hidden switching. introduce recursive algorithm to approximate estimator. Our restores missing data by means Monte Carlo step and estimates function via Robbins–Monro step. prove that models with are identifiable when...

In this article, we present the least squares estimator for drift parameter in a linear regression model driven by increment of fractional Brownian motion sampled at random times. For two different times, Jittered and renewal process sampling, consistency is proven. A simulation study provided to illustrate performance under values Hurst H.

We propose a Piecewise-Deterministic Markov Process (PDMP) to model the drug concentration in case of multiple intravenous-bolus (multi-IV) doses and poor patient adherence situation: scheduled time administration are not respected by patient, considers switching regime with random intake times. study randomness derive probability results on stochastic dynamics using PDMP theory, focusing two aspects practical relevance: variability regularity its stationary distribution. The main result...

We study the aggregation of AR processes and generalized Ornstein-Uhlenbeck (OU) processes. Mixture spectral densities with random poles are main tool. In this context, we apply our results for doubly stochastic interactives processes, see Dacunha-Castelle Fermin (2006). Thus, relationship between autoregressive long memory considering complex interaction structures. precise a very interesting qualitative phenomena: how creation depends on concentration near to boundary stability (measured...

The aim of this paper is to extend the aggregation convergence results given in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle 2008) doubly stochastic linear nonlinear processes with weakly dependent innovations. First, we introduce a weak dependence notion for processes, based definition (Doukhan Louhichi 1999), exhibe several models satisfying notion, such as: Volterra Bernoulli scheme Afterwards derive central limit theorem partial sequence considering processes. Finally, show new...

Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well temporal dependence due to its high fitting capacity when it comes real data. In this article, we consider a GTWR driven by spatio-temporal noise, colored space fractional time. Concerning the covariates, that they are correlated, taking into account two interaction types between weak strong interaction. Under these assumptions, Least...

We prove that a large set of long memory (LM) processes (including classical LM and all whose spectral densities have countable number singularities controlled by exponential functions) are obtained an aggregation procedure involving short (SM) infinitely differentiable (C^{infty}). show the C^{infty} class is optimal to get general result for disaggregation in SM processes, sense given cannot be improved taking instance analytic functions instead indefinitely derivable functions.

In numerous applications data are observed at random times.Our main purpose is to study a model times incorporating long memory noise process with fractional Brownian Hurst exponent H.In this article, we propose least squares (LS) estimator in linear regression and sampling time called "jittered sampling".Specifically, there fixed rate 1/N but contaminated by an additive (the jitter) governed probability density function supported [0, ].The strong consistency of the established, convergence...