Abstract
Recently, as a result of the growing interest in modelling stationary processes with discrete marginal distributions, several models for integer value time series have been proposed in the literature. One of these models is the INteger-AutoRegressive (INAR) model. Here we consider the higher-order moments and cumulants of the INAR(1) process and show that they satisfy a set of Yule-Walker type difference equations. We also obtain the spectral and bispectral density functions, thus characterizing the INAR(1) process in the frequency domain. We use a frequency domain approach, namely the Whittle criterion, to estimate the parameters of the model. The estimation theory and associated asymptotic theory of this estimation method are illustrated numerically.

Abstract
Here we obtain difference equations for the higher order moments and cumulants of a time series {X-t} satisfying an INAR(p) model. These equations are similar to the difference equations for the higher order moments and cumulants of the bilinear time series model. We obtain the spectral and bispectral density functions for the INAR(p) process in state-space form, thus characterizing it in the frequency domain. We consider a frequency domain method - the Whittle criterion - to estimate the parameters of the INAR(p) model and illustrate it with the series of the number of epilepsy seizures of a patient.

Abstract
Muscle relaxant drugs are currently given during surgical operations. The design of controllers for the automatic control of neuromuscular blockade benefits from an individual tuning of the controller to the characteristics of the patient. A novel approach to the characterization of the neuromuscular blockade response induced by an initial bolus at the beginning of anaesthesia is proposed. This approach is based on the statistical analysis of the data using principal components and Walsh-Fourier spectral analysis. These methods provide information about the patients dynamics, allowing the on-line autocalibration of the controller, using multiple linear regression techniques. Observed and simulated data are used to compare different approaches to the characterization of the bolus response.

Abstract
Replicated time series are a particular type of repeated measures, which consist of time-sequences of measurements taken from several subjects (experimental units). We consider independent replications of count time series that are modelled by first-order integer-valued autoregressive processes, INAR(1). In this work, we propose several estimation methods using the classical and the Bayesian approaches and both in time and frequency domains. Furthermore, we study the asymptotic properties of the estimators. The methods are illustrated and their performance is compared in a simulation study. Finally, the methods are applied to a set of observations concerning sunspot data.

Abstract
In this paper, we show how the Yule-Walker type difference equations for higher order moments and cumulants, recently derived for certain types of bilinear time series models, the BL(p,0,p,1) models, by Sesay and Subba Rao (1988, 1991), could be used for tentative identification of the order of the model. The technique we use for identification is canonical correlation analysis, carried out between the linear combination of the observations and linear combination of higher powers of the observations. The methods are illustrated with real and simulated examples.

Abstract
The high-order statistics (moments and cumulants of order higher than two) have been widely applied in several fields, specially in problems where it is conjectured a lack of Gaussianity and/or non-linearity. Since the INteger-valued AutoRegressive, INAR, processes are non-Gaussian, the high-order statistics can provide additional information that allows a better characterization of these processes. Thus, an estimation method for the parameters of an INAR process, based on Least Squares for the third-order moments is proposed. The results of a Monte Carlo study to investigate the performance of the estimator are presented and the method is applied to a set of real data.