Local polynomial Whittle estimation of perturbed fractional processes

We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d in (0,1), asymptotically normal for d in (0,3/4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, sqrt(n). A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator.Bias reduction, local Whittle, long memory, perturbed fractional process, semiparametric estimation, stochastic volatility

Local polynomial Whittle estimation of perturbed fractional processes

We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d in (0,1), asymptotically normal for d in (0,3/4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, sqrt(n). A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator

Expression of messenger molecules and receptors in rat and human sphenopalatine ganglion indicating therapeutic targets

Background: Migraine and Cluster Headache (CH) are two primary headaches with severe disease burden. The disease expression and the mechanisms involved are poorly known. In some attacks of migraine and in most attacks of CH, there is a release of vasoactive intestinal peptide (VIP) originating from parasympathetic cranial ganglia such as the sphenopalatine ganglion (SPG). Patients suffering from these diseases are often deprived of effective drugs. The aim of the study was to examine the localization of the botulinum toxin receptor element synaptic vesicle glycoprotein 2A (SV-2A) and the vesicular docking protein synaptosomal-associated protein 25 (SNAP25) in human and rat SPG. Additionally the expression of the neurotransmitters pituitary adenylate cyclase activating polypeptide (PACAP-38), nitric oxide synthase (nNOS), VIP and 5-hydroxttryptamine subtype receptors (5-HT1B,1D,1F) were examined. Methods: SPG from adult male rats and from humans, the later removed at autopsy, were prepared for immunohistochemistry using specific antibodies against neurotransmitters, 5-HT1B,1D,1F receptors, and botulinum toxin receptor elements. Results: We found that the selected neurotransmitters and 5-HT receptors were expressed in rat and human SPG. In addition, we found SV2-A and SNAP25 expression in both rat and human SPG. We report that all three 5-HT receptors studied occur in neurons and satellite glial cells (SGCs) of the SPG. 5-HT1B receptors were in addition found in the walls of intraganglionic blood vessels. Conclusions: Recent focus on the SPG has emphasized the role of parasympathetic mechanisms in the pathophysiology of mainly CH. The development of next generation’s drugs and treatment of cranial parasympathetic symptoms, mediated through the SPG, can be modulated by treatment with BoNT-A and 5-HT receptor agonists