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Modelling multivariate time series of counts in a parsimonious way is a popular topic. In this paper, we consider an integer‐valued network autoregressive model with a non‐random neighbourhood structure, which uses negative binomial distribution as the conditional marginal distribution and the softplus function as the link function. The new model generalizes existing ones in the literature and has a great flexibility in modelling. Stationary conditions in cases of fixed dimension and increasing dimension are given. Parameters are estimated by maximizing the quasi‐likelihood function, and related asymptotic properties of the estimators are established. A simulation study is conducted to assess performances of the estimators, and a real data example is analysed to show superior performances of the proposed model compared with existing ones. [ABSTRACT FROM AUTHOR]

This note examines the conditional least squares (CLS) estimators for integer-valued autoregressive (INAR) models, with a focus on the INAR(1) model. Our investigation reveals that the joint limiting distribution of the CLS estimators for the autoregressive coefficient and the mean of the model errors is degenerate in the case of mildly unstable INAR(1) models with moderate deviations from unity. This degeneracy may pose challenges for statistical inference. We provide commenting notes based on the asymptotic results to address this issue. Additionally, we conduct simulation studies and analyze a real-world dataset to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

This article tackles the modeling challenge of bounded ℤ‐valued time series by proposing a novel trinomial difference autoregressive process. This process not only maintains the autocorrelation structure presenting in the classical binomial GARCH model, but also facilitates the analysis of bounded ℤ‐valued time series with negative or positive correlation. We verify the stationarity and ergodicity of the couple process (comprising both the observed process and its conditional mean process) while also presenting several stochastic properties. We further discuss the conditional maximum likelihood estimation and establish their asymptotic properties. The effectiveness of these estimators is assessed through simulation studies, followed by the application of the proposed models to two real datasets. [ABSTRACT FROM AUTHOR]

For checking time series models, the Ljung–Box, Li–Mak and Zhu–Wang statistics play an important role, which use the Pearson's correlation coefficient to implement (squared) residual (partial) autocorrelation tests. In this paper, we replace the Pearson's correlation coefficient with a new rank correlation coefficient and propose a new test statistic to conduct diagnostic checks for residuals in autoregressive moving average models, autoregressive conditional heteroscedasticity models and integer-valued time series models, respectively. We conduct simulations to assess the performance of the new test statistic, and compare it with existing ones, and the results show the superiority of the proposed one. We use three real examples to exhibit its usefulness. [ABSTRACT FROM AUTHOR]

Testing independence between two or more random variables or random vectors receives a lot of attention in the literature. A new test statistic is proposed based on the consistency of the sample distance multivariance to test mutual independence. The bootstrap method is used to obtain the critical value of the test statistic. The simulation results show that our method performs well in the low-dimensional and large-sample cases and gives reasonable results in some cases where other tests do not work. Three real examples are analyzed to show the usefulness of the new test statistic. [ABSTRACT FROM AUTHOR]

Zero inflation, zero deflation, overdispersion, and underdispersion are commonly encountered in count time series. To better describe these characteristics of counts, this article introduces a zero‐modified geometric first‐order integer‐valued autoregressive (INAR(1)) model based on the generalized negative binomial thinning operator, which contains dependent zero‐inflated geometric counting series. The new model contains the NGINAR(1) model, ZMGINAR(1) model, and GNBINAR(1) model with geometric marginals as special cases. Some statistical properties are studied, and estimates of the model parameters are derived by the Yule–Walker, conditional least squares, and maximum likelihood methods. Asymptotic properties and numerical results of the estimators are also studied. In addition, some test and forecasting problems are addressed. Three real‐data examples are given to show the flexibility and practicability of the new model. [ABSTRACT FROM AUTHOR]

In response to the limitations of meteorological conditions in global rice growing areas and the high cost of annotating samples, this paper combines the Vertical-Vertical (VV) polarization and Vertical-Horizontal (VH) polarization backscatter features extracted from Sentinel-1 synthetic aperture radar (SAR) images and the NDVI, NDWI, and NDSI spectral index features extracted from Sentinel-2 multispectral images. By leveraging the advantages of an optimized Semi-Supervised Generative Adversarial Network (optimized SSGAN) in combining supervised learning and semi-supervised learning, rice extraction can be achieved with fewer annotated image samples. Within the optimized SSGAN framework, we introduce a focal-adversarial loss function to enhance the learning process for challenging samples; the generator module employs the Deeplabv3+ architecture, utilizing a Wide-ResNet network as its backbone while incorporating dropout layers and dilated convolutions to improve the receptive field and operational efficiency. Experimental results indicate that the optimized SSGAN, particularly when utilizing a 3/4 labeled sample ratio, significantly improves rice extraction accuracy, leading to a 5.39% increase in Mean Intersection over Union (MIoU) and a 2.05% increase in Overall Accuracy (OA) compared to the highest accuracy achieved before optimization. Moreover, the integration of SAR and multispectral data results in an OA of 93.29% and an MIoU of 82.10%, surpassing the performance of single-source data. These findings provide valuable insights for the extraction of rice information in global rice-growing regions. [ABSTRACT FROM AUTHOR]

Compared with the widely used mean-based models, the prediction based on median autoregression is often more robust for time series forecasting. Motivated by the asymmetric exponential power working likelihood approach in Bayesian quantile regression, we first apply the asymmetric exponential power error to time series. The new median autoregression we proposed is more robust and can better deal with outliers. An adaptive independent Metropolis-Hastings algorithm is used for the parameter estimation. A novel, simple, and effective approximate forecasting procedure is proposed based on the Watanabe-Akaike information criterion in the framework of Bayesian model averaging. Model assessment, order selection, and out-of-sample predictive accuracy are all discussed. Finally, three examples of macroeconomic data are analyzed to show the superior performance of the proposed model. [ABSTRACT FROM AUTHOR]

This article studies the two-step conditional least squares (CLS) estimation for the bivariate Z -valued INAR(1) model with bivariate Skellam innovations. For readers' convenience, we first give a brief review of the bivariate Skellam distribution, bivariate signed thinning operator and the definition of the bivariate Z -valued INAR(1) model with bivariate Skellam innovations (denoted as the BSK-BINARS(1) model). Then, we discuss the stationarity and ergodicity of the BSK-BINARS(1) model, give some stochastic properties. Second, we discuss the two-step CLS estimate of the parameters and establish their large-sample properties. Third, we conduct a simulation study to illustrate the finite sample performances of the two-step CLS estimators, which are compared with those obtained by the plug-in method. Last but not least, we apply the BSK-BINARS(1) model on the zonal annual means temperature (*100). [ABSTRACT FROM AUTHOR]

In recent years, there has been increased interest in modeling integer-valued time series. Many methods for time series of counts have been developed in the literature because of their wide applications to epidemiology, finance, disease modeling and environmental science. The negative binomial integer-valued generalized autoregressive conditional heteroscedasticity model is a popular one, which can deal with both over-dispersion and potential extreme observations. The accurate estimation of the parameters in the model is extremely important. We adopt the marginal likelihood to estimate the intercept parameter and maximum likelihood to estimate other parameters of the model. We conduct simulations to assess the performance of this estimation method, and compare it with that of estimating all model parameters by maximum likelihood. The results show the superiority of proposed estimation method. We use two real examples to illustrate the model's ability to fit over-dispersed data and the validity of the estimation method. [ABSTRACT FROM AUTHOR]