Inference for a Special Bilinear Time Series Model

It is well known that estimating bilinear models is quite challenging. Many different ideas have been proposed to solve this problem. However, there is not a simple way to do inference even for its simple cases. This paper studies the special bilinear model $$Y_t=\mu+\phi Y_{t-2}+ bY_{t-2}\varepsilon_{t-1}+ \varepsilon_t,$$ where $\{\varepsilon_t\}$ is a sequence of i.i.d. random variables with mean zero. We first give a sufficient condition for the existence of a unique stationary solution for the model and then propose a GARCH-type maximum likelihood estimator for estimating the unknown parameters. It is shown that the GMLE is consistent and asymptotically normal under only finite fourth moment of errors. Also a simple consistent estimator for the asymptotic covariance is provided. A simulation study confirms the good finite sample performance. Our estimation approach is novel and nonstandard and it may provide a new insight for future research in this direction.Comment: 23 pages, 1 figures, 3 table

Conditional-mean Multiplicative Operator Models for Count Time Series

Multiplicative error models (MEMs) are commonly used for real-valued time series, but they cannot be applied to discrete-valued count time series as the involved multiplication would not preserve the integer nature of the data. Thus, the concept of a multiplicative operator for counts is proposed (as well as several specific instances thereof), which are then used to develop a kind of MEMs for count time series (CMEMs). If equipped with a linear conditional mean, the resulting CMEMs are closely related to the class of so-called integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models and might be used as a semi-parametric extension thereof. Important stochastic properties of different types of INGARCH-CMEM as well as relevant estimation approaches are derived, namely types of quasi-maximum likelihood and weighted least squares estimation. The performance and application are demonstrated with simulations as well as with two real-world data examples.Comment: 45 page

A micromachined flow shear-stress sensor based on thermal transfer principles

Microhot-film shear-stress sensors have been developed by using surface micromachining techniques. The sensor consists of a suspended silicon-nitride diaphragm located on top of a vacuum-sealed cavity. A heating and heat-sensing element, made of polycrystalline silicon material, resides on top of the diaphragm. The underlying vacuum cavity greatly reduces conductive heat loss to the substrate and therefore increases the sensitivity of the sensor. Testing of the sensor has been conducted in a wind tunnel under three operation modes-constant current, constant voltage, and constant temperature. Under the constant-temperature mode, a typical shear-stress sensor exhibits a time constant of 72 μs

Efficiency of Ferritin as an MRI Reporter Gene in NPC Cells Is Enhanced by Iron Supplementation

Background. An emerging MRI reporter, ferritin heavy chain (FTH1), is recently applied to enhance the contrast and increase the sensitivity of MRI in the monitoring of solid tumors. However, FTH1-overexpression-related cytotoxicity is required to be explored. Methods. By using the Tet-Off system, FTH1 overexpression was semi-quantitativiely and dynamicly regulated by doxycycline in a NPC cell line. Effects of FTH1 overexpression on the proliferation, cytotoxicity, apoptosis and migration of NPC cells were investigated in vitro, and MR relaxation rate was measured in vitro and in vivo. Results. In vitro and in vivo overexpression of FTH1 significantly increased the transverse relaxivity (R2), which could be enhanced by iron supplementation. In vitro, overexpression of FTH1 reduced cell growth and migration, which were not reduced by iron supplementation. Furthermore, cells were subcutaneously inoculated into the nude mice. Results showed FTH1 overexpression decreased tumor growth in the absence of iron supplementation but not in the presence of iron supplementation. Conclusion. To maximize R2 and minimize the potential adverse effects, supplementation of iron at appropriate dose is recommended during the application of FTH1 as a reporter gene in the monitoring of NPC by MRI

Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations

Time series of counts are commonly observed in real-world applications. The integer-valued ARCH(p) models are able to describe integer-valued processes and offer the potential to be widely applied in practice in future. This paper develops an asymptotic theory for (partial) autocorrelations of the conditional residuals from the integer-valued ARCH(p) model. Based on the above results, we propose five portmanteau test statistics, which are very useful in checking the adequacy of a fitted integer-valued ARCH specification. The asymptotic distributions of the statistics are derived and their finite sample properties are studied in detail through Monte Carlo simulations. Finally, we illustrate the results analyzing two empirical examples.

Two-Threshold-Variable Integer-Valued Autoregressive Model

In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some of its basic properties, including the mean, variance, strict stationarity, and ergodicity. We consider the conditional least squares (CLS) estimation and discuss the asymptotic normality of the CLS estimator under the known and unknown threshold values. The performances of the CLS estimator are compared via simulation studies. In addition, two real data sets are considered to underline the superior performance of the proposed model

A Modified Multiplicative Thinning-Based INARCH Model: Properties, Saddlepoint Maximum Likelihood Estimation, and Application

In this article, we propose a modified multiplicative thinning-based integer-valued autoregressive conditional heteroscedasticity model and use the saddlepoint maximum likelihood estimation (SPMLE) method to estimate parameters. A simulation study is given to show a better performance of the SPMLE. The application of the real data, which is concerned with the number of tick changes by the minute of the euro to the British pound exchange rate, shows the superiority of our modified model and the SPMLE