We establish an asymptotic approach for checking the appropriateness of an assumed multivariate spatial regression model by considering the set-indexed partial sums process of the least squares residuals of the vector of observations. In this work, we assume that the components of the observation, whose mean is generated by a certain basis, are correlated. By this reason we need more effort in deriving the results. To get the limit process we apply the multivariate analog of the well-known Prohorov's theorem. To test the hypothesis we define tests which are given by Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) functionals of the partial sums processes. The calibration of the probability distribution of the tests is conducted by proposing bootstrap resampling technique based on the residuals. We studied the finite sample size performance of the KS and CvM tests by simulation. The application of the proposed test procedure to real data is also discussed.

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ARIMA method is often used in time series data forecasting. However, when an outlier occurs or there is an observation value that is far from a set of data, forecasting with this method will provide a large residual so that the normality assumption is not met. One method developed from the ARIMA Method that overcomes outliers, is called the ARIMA Additive Outlier Method (ARIMA AO). The purpose of this study is to forecast time series data containing outliers with the ARIMA AO Method. This method can reduce the presence of outliers with iterative procedures. The data used is data on the number of foreign tourists visiting the Port of Tanjung Priok. The results obtained are that the model has a normal distribution residual and forecasting accuracy value with MSE and MAPE is smaller than the ARIMA.

Penelitian ini bertujuan untuk mengeplorasi konsep etnomatematika geometri yang terkandung pada bangunan Pura Puseh-Desa Wusana Bumi. Teknik pengumpulan data penelitian ini adalah teknik observasi, wawancara dan dokumentasi. Pemeriksaan keabsahan data dilakukan dengan triangulasi sumber. Matematika dan budaya adalah dua hal yang saling berkaitan. Matematika dalam budaya dikenal dengan istilah etnomatematika. Hasil penelitian menunjukkan bahwa pada bangunan pura terdapat bentuk-bentuk etnomatematika geometri: limas, limas terpancung, prisma terpancung, kubus, serta terdapat konsep matematika seperti simetri, kesejajaran, perbandingan, refleksi terhadap sumbu-y, translasi terhadap sumbu-x, dilatasi dengan faktor skala k, konsep-konsep geometri ini dapat di gunakan dalam pembelajaran matematika di sekolah.

Shallot is very potential to be developed in Southeast Sulawesi, but its productivity is very low, so it needs technological innovation, including the use of microbes as a promoter of plant growth. This study aims to evaluate the effectiveness of shallots seed biopriming using a mixture of rhizobacterial isolates to increase the growth and yield of shallots. This research was conducted at the Experimental Garden II, Faculty of Agriculture, University of Halu Oleo. The experiment was arranged using a Randomized Block Design (RBD), consisting of 8 treatments seed biopriming using a mixture of rhizobacterial isolates, ie without rhizobacterial isolates as control, CKD061 isolate, W2R06 isolate, TWB11 isolate, CKD061+W2R06 isolate, CKD061+TWB11 isolate, W2R06+TWB11 isolate, and CKD061+TWB11+W2R06 isolate. Data were analyzed using variance analysis, followed by Honestly Significant Difference test (BNJ). The results showed that Inoculation of shallots seeds with rhizobacteria both single and mixed was more able to increase the growth and yield of shallots compared to controls. CKD061 single isolate showed better performance in increasing the growth and yield of shallots compared to other controls and isolates, but was not significantly different from mixture of CKD061 + W2R06 isolates. Increased production in the biopriming treatment of CKD061 isolates and CKD061 + W2R06 isolates respectively reached 67.69% and 53.85% compared to controls. Further testing is needed on a wider scale to get more consistent results in the field.