Conditional Maximum Likelihood Estimation of the First-Order Spatial Integer-Valued Autoregressive (SINAR(1,1)) Model

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

A bivariate first-order signed integer-valued autoregressive process

Aggregation Bias in Maximum Likelihood Estimation of Spatial Autoregressive Processes

In statistical models of spatial behavior, there is often a mismatch between the scale at which data is available and the scale at which key spatial dependencies are known to occur. However, in attempting to incorporate Þner grain information about spatial dependencies, certain estimation problems arise. Here it is shown that maximum likelihood procedures can produce signiÞcantly negative estim...

Poisson Difference Integer Valued Autoregressive Model of Order one

This paper aims to model integer valued time series with possible negative values and either positive or negative correlations by introducing the Poisson difference integer valued autoregressive model of order one. This model has Poisson difference marginal distribution and is defined by a new operator called the extended binomial thinning operator. It includes previous integer valued autoregre...

Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity

We consider maximum likelihood estimation of a particular noninvertible ARMA model with autoregressive conditionally heteroskedastic (ARCH) errors. The model can be seen as an extension to so-called all-pass models in that it allows for autocorrelation and for more flexible forms of conditional heteroskedasticity. These features may be attractive especially in economic and financial application...

Maximum Likelihood Estimation of Parameters in Generalized Functional Linear Model

Sometimes, in practice, data are a function of another variable, which is called functional data. If the scalar response variable is categorical or discrete, and the covariates are functional, then a generalized functional linear model is used to analyze this type of data. In this paper, a truncated generalized functional linear model is studied and a maximum likelihood approach is used to esti...