Estimation and Testing for Unit Root Processes with GARCH(1,1) Errors: Theory and Monte Carlo Evidence,

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition alpha + beta

"Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence"

Least squares (LS) and maximum likelihood (ML) estimation are con-sidered for unit root processes with GARCH (1, 1) errors. The asymp-totic distributions of LS and ML estimators are derived under the con-dition ƒ¿ + ƒÀ

A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors,

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various new ARCH-type models, including double threshold ARCH and GARCH, ARFIMA-GARCH, CHARMA and vector ARMA-GARCH, are also reviewed.

Bayesian latent time joint mixed-effects model of progression in the Alzheimer's Disease Neuroimaging Initiative.

IntroductionWe characterize long-term disease dynamics from cognitively healthy to dementia using data from the Alzheimer's Disease Neuroimaging Initiative.MethodsWe apply a latent time joint mixed-effects model to 16 cognitive, functional, biomarker, and imaging outcomes in Alzheimer's Disease Neuroimaging Initiative. Markov chain Monte Carlo methods are used for estimation and inference.ResultsWe find good concordance between latent time and diagnosis. Change in amyloid positron emission tomography shows a moderate correlation with change in cerebrospinal fluid tau (ρ = 0.310) and phosphorylated tau (ρ = 0.294) and weaker correlation with amyloid-β 42 (ρ = 0.176). In comparison to amyloid positron emission tomography, change in volumetric magnetic resonance imaging summaries is more strongly correlated with cognitive measures (e.g., ρ = 0.731 for ventricles and Alzheimer's Disease Assessment Scale). The average disease trends are consistent with the amyloid cascade hypothesis.DiscussionThe latent time joint mixed-effects model can (1) uncover long-term disease trends; (2) estimate the sequence of pathological abnormalities; and (3) provide subject-specific prognostic estimates of the time until onset of symptoms

ATR-FTIR Spectroscopic Analysis of Sorption of Aqueous Analytes into Polymer Coatings Used with Guided SH-SAW Sensors

Attenuated total internal reflectance Fourier transform infrared (ATR-FTIR) spectroscopy was used for the investigation of sorption of aqueous solutions of analytes into polymer coatings. A series of simple model polymers, such as poly(dimethylsiloxane), poly(epichlorhydrin), and poly(isobutylene), and films and analytes, such as aqueous solutions of ethylbenzene, xylenes, toluene, and nitrobenzene, were used to evaluate the use of ATR-FTIR spectroscopy as a screening tool for sensor development. The ratios of integrated infrared absorption bands provided a simple and efficient method for predicting trends in partition coefficients. Responses of polymer-coated guided shear horizontal surface acoustic wave (SH-SAW) sensor platforms to the series of analytes, using polymer coatings with similar viscoelastic properties, were consistent with ATR-FTIR predictions. Guided SH-SAW sensor responses were linear in all cases with respect to analyte concentration in the tested range. Comparison of ATR-FTIR data with guided SH-SAW sensor data identifies cases where mass loading is not the dominant contribution to the response of the acoustic wave sensor. ATR-FTIR spectra of nitrobenzene, coupled with computational chemistry, provided additional insight into analyte/polymer interactions