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A covariate-driven random coefficient generalized conditional heteroscedasticity (GARCH) time series model with the form of the buffered autoregression (BRC-GARCH-X) for modeling financial time series data is considered. As an extension of the classical two-regime threshold process, the buffered autoregression enjoys a more flexible regime-switching mechanism. Furthermore, the main feature of this model is that the threshold variable for regime-switching is formulated as a weighted average of important auxiliary variables. The estimator for regression parameters is obtained by the quasi-maximum exponential likelihood (QMEL) estimator and the corresponding asymptotic properties are established. Moreover, a mixed portmanteau test is developed for diagnostic checking. And a reasonable method for selecting search ranges for thresholds is also proposed and simulation studies are considered. As an application, we bring attention to some features of of stock returns of SP500 which shows that our model is feasible. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are derived. To estimate unknown parameters, Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered and evaluated by Monte Carlo simulations. Asymptotic properties of the estimators are derived. Moreover, coherent forecasting and possible extension of the proposed model is provided. Finally, the proposed model is applied to the monthly crime datasets and compared with other models. [ABSTRACT FROM AUTHOR]

In this article, a new mixture integer-valued autoregressive process model with a finite random range Nt based on Pegram operator and binomial thinning operator is proposed. The new model can be well used to describe finite-range { 0, 1, ⋯ , L } integer-valued data with a broad variety of dispersion patterns, zero-inflation and multimodality. We derive the basic numerical characteristics of the model and testify stationarity and ergodicity properties. Conditional least squares method and maximum quasi-likelihood method are employed to estimate the parameters of NMBAR(1) model. The asymptotic properties of the estimators are acquired. Multiple groups of stochastic simulation studies are carried out to assess and compare the performances of these estimators and a real example is analyzed to illustrate the advantages of our model. [ABSTRACT FROM AUTHOR]

This paper studies the empirical likelihood method for a multivariate first-order random coefficient autoregressive (RCAR(1)) model. Based on the modified least square score equation, empirical likelihood method is used to test the randomness of coefficients and estimate the unknown parameters. First, the limiting distribution of the log empirical likelihood ratio statistic is established. Second, the maximum empirical likelihood estimator is derived and its asymptotic properties are established. Finally, the performances of the estimator are compared with the modified least square estimator via simulation. Furthermore, simulation result shows that the test has the correct size and very good power for all cases considered. [ABSTRACT FROM AUTHOR]

To better describe the characteristics of time series of counts such as overdispersion or structural change, in this paper, we redefines the integer-valued threshold autoregressive models based on negative binomial thinning (NBTINAR(1)) under a weaker condition that the expectation of the innovations is finite. Parameters' point estimation and interval estimation problems are considered. A method to test the nonlinearity of the data is provided. As an illustration, we conduct a simulation study and empirical analysis of Pittsburgh crime data sets. [ABSTRACT FROM AUTHOR]

To better describe the data whose variance is greater than mean in time series analysis, this paper introduces the RCINAR(1) process with generalized negative binomial marginals. The related estimations of this process are considered using Yule-Walker, modified conditional least squares, conditional maximum likelihood and Bayesian methods. The asymptotic properties of the estimators are established. Some simulations are conducted to verify the proposed estimation methods and a real example is proposed to illustrate the advantages of our model. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study a generalized algorithm for the most commonly used D-optimal algorithm in experimental design. We extend the classical D-optimal algorithm to the D-optimal assignment problem for regression models considering the cost of experiments. To solve the problem, we construct a weighted objective function and establish a generalized D-optimal (GD-optimal) criterion to make this objective function optimal. We propose a multiplicative algorithm to compute the GD-optimal allocation and provide some theorems to ensure that the algorithm converges to the GD-optimal. Numerical examples show that the proposed algorithm performs well. [ABSTRACT FROM AUTHOR]

In this article, we present the explicit expressions for the higher-order moments and cumulants of the first-order random coefficient integer-valued autoregressive (RCINAR(1)) process. The spectral and bispectral density functions are also obtained, which can characterize the RCINAR(1) process in the frequency domain. We use a frequency domain approach which is named Whittle criterion to estimate the parameters of the process. We propose a test statistic which is based on the frequency domain approach for the hypothesis test,H0: α = 0⟷H1: 0 < α < 1, where α is the mean of the random coefficient in the process. The asymptotic distribution of the test statistic is obtained. We compare the proposed test statistic with other statistics that can test serial dependence in time series of count via a typically numerical simulation, which indicates that our proposed test statistic has a good power. [ABSTRACT FROM AUTHOR]

We propose a new integer-valued time series process, called generalized pth-order random coefficient integer-valued autoregressive process with signed thinning operator. This kind of process is appropriate for modeling negative integer-valued time series; strict stationarity and ergodicity of the process are established. Estimators of the model's parameters are derived and their properties are studied via simulation. We apply our process to a real data example. [ABSTRACT FROM AUTHOR]