Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated

Unit roots in periodic autoregressions

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model

Constructing seasonally adjusted data with time-varying confidence intervals

Seasonal adjustment methods transform observed time series data into estimated data, where these estimated data are constructed such that they show no or almost no seasonal variation. An advantage of model-based methods is that these can provide confidence intervals around the seasonally adjusted data. One particularly useful time series model for seasonal adjustment is the basic structural time series [BSM] model. The usual premise of the BSM is that the variance of each of the components is constant. In this paper we address the possibility that the variance of the trend component in a macro-economic time series in some way depends on the business cycle. One reason for doing so is that one can expect that there is more uncertainty in recession periods. We extend the BSM by allowing for a business-cycle dependent variance in the level equation. Next we show how this affects the confidence intervals of seasonally adjusted data. We apply our extended BSM to monthly US unemployment and we show that the estimated confidence intervals for seasonally adjusted unemployment change with past changes in the oil price

Autoregression as a means of assessing the strength of seasonality in a time series

BACKGROUND: The study of the seasonal variation of disease is receiving increasing attention from health researchers. Available statistical tests for seasonality typically indicate the presence or absence of statistically significant seasonality but do not provide a meaningful measure of its strength. METHODS: We propose the coefficient of determination of the autoregressive regression model fitted to the data ([Image: see text]) as a measure for quantifying the strength of the seasonality. The performance of the proposed statistic is assessed through a simulation study and using two data sets known to demonstrate statistically significant seasonality: atrial fibrillation and asthma hospitalizations in Ontario, Canada. RESULTS: The simulation results showed the power of the [Image: see text] in adequately quantifying the strength of the seasonality of the simulated observations for all models. In the atrial fibrillation and asthma datasets, while the statistical tests such as Bartlett's Kolmogorov-Smirnov (BKS) and Fisher's Kappa support statistical evidence of seasonality for both, the [Image: see text] quantifies the strength of that seasonality. Corroborating the visual evidence that asthma is more conspicuously seasonal than atrial fibrillation, the calculated [Image: see text] for atrial fibrillation indicates a weak to moderate seasonality ([Image: see text] = 0.44, 0.28 and 0.45 for both genders, males and females respectively), whereas for asthma, it indicates a strong seasonality ([Image: see text] = 0.82, 0.78 and 0.82 for both genders, male and female respectively). CONCLUSIONS: For the purposes of health services research, evidence of the statistical presence of seasonality is insufficient to determine the etiologic, clinical and policy relevance of findings. Measurement of the strength of the seasonal effect, as can be determined using the [Image: see text] technique, is also important in order to provide a robust sense of seasonality

InVERT molding for scalable control of tissue microarchitecture

Complex tissues contain multiple cell types that are hierarchically organized within morphologically and functionally distinct compartments. Construction of engineered tissues with optimized tissue architecture has been limited by tissue fabrication techniques, which do not enable versatile microscale organization of multiple cell types in tissues of size adequate for physiological studies and tissue therapies. Here we present an ‘Intaglio-Void/Embed-Relief Topographic molding’ method for microscale organization of many cell types, including induced pluripotent stem cell-derived progeny, within a variety of synthetic and natural extracellular matrices and across tissues of sizes appropriate for in vitro, pre-clinical, and clinical studies. We demonstrate that compartmental placement of non-parenchymal cells relative to primary or induced pluripotent stem cell-derived hepatocytes, compartment microstructure, and cellular composition modulate hepatic functions. Configurations found to sustain physiological function in vitro also result in survival and function in mice for at least 4 weeks, demonstrating the importance of architectural optimization before implantation.National Institutes of Health (U.S.) (EB008396)National Institutes of Health (U.S.) (DK56966)National Cancer Institute (U.S.) (Cancer Center Support Core Grant P30-CA14051)National Institutes of Health (U.S.). Ruth L. Kirschstein National Research Service Award (1F32DK091007)National Institutes of Health (U.S.). Ruth L. Kirschstein National Research Service Award (1F32DK095529)National Science Foundation (U.S.). Graduate Research Fellowship Program (1122374