We review and synthesize the wide range of non-Gaussian first order linear autoregressive models that have appeared in the literature. Models are organized into broad classes to clarify similarities and differences and facilitate application in particular situations. General properties for process mean, variance and correlation are derived, unifying many separate results appearing in the litera...

In this study, I investigate the necessary condition for the consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of pa...

We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500) and several other indices, we obtained good performance using these models in an out-of-sam...

The article investigates the finite sample properties of estimators for spatial autoregressive models where the disturbance terms may follow a spatial autoregressive process. In particular we investigate the finite sample behavior of the feasible generalized spatial two-stage least squares (FGS2SLS) estimator introduced by Kelejian and Prucha (1998), the maximum likelihood (ML) estimator, as we...

We consider the autoregressive estimation for periodically correlated processes, using the parameterization given by the partial autocorrelation function. We propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation. The comparison with other methods is made. Relationships with the stationary multivariate case are discussed.

In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered to monitor processes in which there is a first order autoregressive relation between the error terms in each profile. A remedi...

We present the first genuine test for a unit root (or of any other value of the autoregressive coeffi cient) within an autoregressive model for errors with given bounds that follow a martingale difference sequence. Without such bounds nontrivial tests are known not to exist. Our test is exact, we do not add other assumptions on the process. Competitors either do not control the type I error for...

This paper proposes and analyses the autoregressive conditional root (ACR) time-series model. This multivariate dynamic mixture autoregression allows for non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage...

This article aims to identify an adequate mathematical model to predict battery power depletion at the nodes of a Wireless Sensor Network (WSN), by analyzing the Received Signal Strength Indicator (RSSI). Six general models were tested, the simplest Average model, Linear Regression model, Autoregressive (AR) models and Autoregressive Moving Average (ARMA) models.The selected model (AR) presente...

We study the statistical properties of recordings that contain time-dependent positions of a bead trapped in optical tweezers. Analysis of such a time series indicates that the commonly accepted model, i.e., the autoregressive process of first-order, is not sufficient to fit the data. We show the presence of a first-order moving average part in the dynamical model of the system. We explain the ...