On order determination by predictor augmentation

Summary In many dimension reduction problems in statistics and machine learning, such as in principal component analysis, canonical correlation analysis, independent component analysis and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this article, we propose a novel and highly effective order-determination method based on the idea of predictor augmentation. We show that if the predictor is augmented by an artificially generated random vector, then the parts of the eigenvectors of the matrix induced by the augmentation display a pattern that reveals information about the order to be determined. This information, when combined with the information provided by the eigenvalues of the matrix, greatly enhances the accuracy of order determination.

Vector Autoregressive Integrated (VARI) Method for Forecasting the Number of Internasional Visitor in Batam and Jakarta

Forecasting methods that are often used are time series analysis, the Autoregressive (AR) method. The AR method only carries out univariate analysis, meaning that it carries out a separate model between the number of international visitor coming to Indonesia through Batam and Jakarta. Though there is a possibility, the number of international visitor arriving through Jakarta affects the number of international visitor arriving through Batam. Therefore, in this study the Vector Autoregressive Integrated (VARI) method is used. The VARI model is used on the number of international visitor arrivals per month at Batam and Jakarta for the period Januari 2014 – December 2019. VARI model formation through several stages, namely stationarity test, autoregressive order determination, VARI model formation, and diagnostic checking of the model. With the VARI model, VARI(5,1), the two significant simultaneously equation results are obtained. The Mean Absolute Percentage Error (MAPE) in this model are as follows 1,98% and 2,48% in predicting the number of international visitor arrivals in Batam and Jakarta. In this study also forecasting the number of international visitor arrivals in Batam and Jakarta in January – December 2020

An Alternative Approach to Determining the Rate of Runoff of Unstudied Rivers (The Amur River basin in the Transbaikal Kray as a Study Case)

The article presents an approach to determining the flow rate of unexplored rivers depending on their order according to A. Scheidegger and the corresponding zoning. It is shown that the use of a single dependence of the flow rate on the river order gives significant errors for small streams. This is because of the fact that approximation function of the entire data file actually reflects regularities only for hydrological stations with great values of the runoff norm.For the territory of the Amur Basin within the Transbaikal cray, five regions have been identified, within which the dependences of the flow rate of small and medium rivers have values of the correlation coefficient from 0.95 to 0.97. An additional zoning scheme for the area under consideration has also been developed, which makes it possible to simplify the determination of the order of the river.The proposed scheme of flow rate determination includes the following operations: determination of the area according to the additional scheme – calculation of the river order – determination of the area according to the main scheme – calculation of the flow rate.