Space-time autoregressive (STAR) models, introduced by CLIFF and ORD [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in BOROVKOVA et al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.

Abstract. Indonesia is a multicultural country of which people usually do anything influenced by their culture. The culture contain of many aspects, one of them is ethnomathematics. It is a study about the connection between culture and mathematics concepts. It also reveals mathematical practices of day life. These mathematical practices could be seen at Cipatujah, West Java, Indonesia. It has several ethnics which implemented of ethnomathematics in their life, for example they implement traditional mathematical concept in the way they determine the time to head seaward for fishing, and the way they construct their houses. The exploration will describe about how deep is the role of ethnomathematics in Cipatujah and state any problem found according to the exploration result. The objectives of this study is to show that ethnomathematics holds an important role in our day life, with the case study of primary school students and for the people of Cipatujah. The method which implemented in this study is exploratory. The result is the people of Cipatujah have been implemented ethnomathematics in their life for many years and believe that ethnomathematics is part of their life, but the teachers of primary school there have not implemented ethnomathematics approach yet in learning process of mathematics. Conclusion of this study is ethnomathematics as the root of culture life in West Java.

Abstract. In this paper we studied a least squares estimation parameters of the Generalized Space Time AutoRegressive (GSTAR) model and its properties, especially in consistency and asymptotic normality. We use R software to estimate the GSTAR parameter and apply the model toward real phenomena of data, such as an oil production data at volcanic layer.

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