The Discounted Berry-Esséen Analogue for Autoregressive Processes

In this article, the discounted Berry-Esséen analogs and non uniform estimates for autoregressive processes are obtained.     

A Generalization to Bivariate Mittag–Leffler and Bivariate Discrete Mittag–Leffler Autoregressive Processes

A generalization of the Gaver and Lewis (1980 Gaver , D. P. , Lewis , P. A. W. ( 1980 ). First order autoregressive gamma sequences and point processes . Adv. Appl. Probab. 12 : 727 – 745 .[Crossref], [Web of Science ®] , [Google Scholar]) model of first-order autoregressive process with marginals as bivariate Mittag–Leffler distribution is obtained. A necessary and sufficient condition for stationarity of the process is established. Autoregressive process with marginals follow bivariate discrete Mittag–Leffler distribution is also developed. The unknown parameters of the processes are estimated and some numerical results of the estimations are given.     

Spatial–temporal model for wind speed in Lithuania

In this paper, we propose a spatial–temporal model for the wind speed (WS). We first estimate the model at the single spatial meteorological station independently on spatial correlations. The temporal model contains seasonality, a higher-order autoregressive component and a variance describing the remaining heteroskedesticity in residuals. We then model spatial dependencies by a Gaussian random field. The model is estimated on daily WS records from 18 meteorological stations in Lithuania. The validation procedure based on out-of-sample observations shows that the proposed model is reliable and can be used for various practical applications.     

Spatial modelling for binary data using␣a␣hidden conditional autoregressive Gaussian process: a multivariate extension of the probit model

A Bayesian approach to modelling binary data on a regular lattice is introduced. The method uses a hierarchical model where the observed data is the sign of a hidden conditional autoregressive Gaussian process. This approach essentially extends the familiar probit model to dependent data. Markov chain Monte Carlo simulations are used on real and simulated data to estimate the posterior distribution of the spatial dependency parameters and the method is shown to work well. The method can be straightforwardly extended to regression models.     

Spatial–temporal modellization of the $$\hbox {NO}_{2}$$ concentration data through geostatistical tools

The nitrogen dioxide is a primary pollutant, regarded for the estimation of the air quality index, whose excessive presence may cause significant environmental and health problems. In the current work, we suggest characterizing the evolution of \(\hbox {NO}_{2}\) levels, by using geostatistical approaches that deal with both the space and time coordinates. To develop our proposal, a first exploratory analysis was carried out on daily values of the target variable, daily measured in Portugal from 2004 to 2012, which led to identify three influential covariates (type of site, environment and month of measurement). In a second step, appropriate geostatistical tools were applied to model the trend and the space–time variability, thus enabling us to use the kriging techniques for prediction, without requiring data from a dense monitoring network. This methodology has valuable applications, as it can provide accurate assessment of the nitrogen dioxide concentrations at sites where either data have been lost or there is no monitoring station nearby.     

Spatial–temporal variation of casuarina spread in Cauvery delta and north eastern zone of Tamil Nadu,India: a spatial autoregressive model

The low forest cover and productivity are the major obstacles for mitigating the demand supply gap of raw material for forest-based industries, which could be fulfilled from a tree outside forest area. Casuarina is a multi-utile, short rotation tree which adapts to all ecosystems. The casuarina wood is predominantly demanded for fuel, construction and paper industries which is mostly preferred by farmers, traders and industries. This study explores the spatial and temporal variability of casuarina spread in mitigating the gap of demand and supply in Tamil Nadu using a spatial autoregressive model. The spread of casuarina was spatially and temporally significant, which was negatively influenced by the gross area irrigated as main and direct effects and positively in an indirect effect. An assured irrigation forces the farmers to choose traditional agricultural crops for their livelihood in their own district. The increase in the price of casuarina would increase the spread of casuarina in both own district and neighbouring districts. The spread of casuarina would augment the supply of raw material for forest-based industries.