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Sequential change-point detection for time series enables us to sequentially check the hypothesis that the model still holds as more and more data are observed. It is widely used in data monitoring in practice. In this work, we consider sequential change-point detection for compositional time series, time series in which the observations are proportions. For fitting compositional time series, we propose a generalized Beta AR(1) model, which can incorporate exogenous variables upon which the time series observations are dependent. We show the compositional time series are strictly stationary and geometrically ergodic and consider maximum likelihood estimation for model parameters. We show the partial MLEs are consistent and asymptotically normal and propose a parametric sequential change-point detection method for the compositional time series model. The change-point detection method is illustrated using a time series of Covid-19 positivity rates.

Sequential change-point detection for time series enables us to sequentially check the hypothesis that the model still holds as more and more data are observed. It's widely used in data monitoring in practice. Meanwhile, binomial time series, which depicts independent binary individual behaviors within a group when the individual behaviors are dependent on past observations of the whole group, is an important type of model in practice but hasn't been developed well. We first propose a Binomial AR($1$) model, and then consider a method for sequential change-point detection for the Binomial AR(1).

The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time autoregressive model is a linear model for describing spatial correlation. In this work, we expand the classical model to include related exogenous variables, possibly non-Gaussian, high volatility errors, and a nonlinear neural network component. The nonlinear neural network component allows for more model flexibility, the ability to learn and model nonlinear and complex relationships. We use a maximum likelihood approach for model parameter estimation. We establish consistency and asymptotic normality for these estimators under some standard conditions on the space time model and neural network component. We investigate the quality of the asymptotic approximations for finite samples by means of numerical simulation studies. For illustration, we include a real world application., Comment: arXiv admin note: substantial text overlap with arXiv:1801.07822

Spatial autoregressive model, introduced by Clif and Ord in 1970s has been widely applied in many areas of science and econometrics such as regional economics, public finance, political sciences, agricultural economics, environmental studies and transportation analyses. As information technology grows rapidly, observations are seldom independent from others so a space autoregressive models can take this dependence into account and draw more reliable conclusions between covariates and the target variable itself. Based on the classical spatial model, Su and Jin proposed a semi-parametric model named as partially specified spatial autoregressive model (PSAR) to allow for more flexibility in modeling. And to estimate this nonparametric component, we use the neural network model which adds more flexibility to the classical model and allows for variations in the choice of activation functions according to different types of data. This paper extends an artificial neural network model to a partially specified space autoregressive model and proposes maximum likelihood estimators instead of quasi-maximum likelihood estimates. We establish the consistency and asymptotic normality of the estimators in this model. These results are obtained under some standard conditions in spatial models as well as neural network models. To illustrate, we investigate the quality of the normal approximation for finite samples by means of numerical simulation studies with three common choices of error distributions (standard normal, student-t distribution and the Laplace distribution). We apply our proposed model to a soil-water tension problem and a criminal study in Chicago. The results showed that our model can capture the spatial dependence between units as well as the unknown correlation structure between the target variable and covariates.

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are $n^{1/\alpha}$-consistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general conditions. The estimators for the parameters of the stable noise distribution have the traditional $n^{1/2}$ rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of Wal-Mart stock traded daily on the New York Stock Exchange., Comment: Published in at http://dx.doi.org/10.1214/08-AOS632 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram., Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)