Various analytical techniques are available for modeling multivariate time series data. One such approach is the State Space Model, which can be employed to model this type of data. In this study, the data to be analyzed are data on the Indonesia Rupiah (IDR) exchange rate (ExR) against the US Dollar (USD), oil and gas exports (OGE), money supply (MS) and non-oil and gas exports (non-OGE) from January 2008 to December 2019. The aim of this study is to identify the most suitable state space model for the given data. In this research, the state space method will be applied to multivariate time series data, with the state space represented in the Vector Autoregressive (VAR) model to explore the interrelationships among groups of observed variables. The VAR model is a statistical technique used to analyze the relationships between variables in the dataset, employing the Granger Causality Test. The state space model is utilized to model and forecast multiple interconnected time series, where the variables exhibit dynamic interactions and to examine additional unobserved variables in the time series data. Based on the analysis results and the minimum value of the Akaike Information Criterion (AIC), the optimal VAR model identified is the VAR (6) model. The results of forecasting values using the state space model show that the predicted values and the real values for the state space model are very closed to each other.

This paper studies multilevel extensions of soft-set-based graph models for uncertainty aware decision support. We first recall soft, multisoft, soft expert, and multisoft multi expert sets, which encode parameterized and expert-dependent approximations of a universe. Building on these notions, we introduce the MultiSoft Graph, a family of induced subgraphs of a given graph indexed by multilevel parameter blocks, and show that it strictly generalizes classical soft graphs while inducing a canonical multisoft set on the vertex set. We then define Soft MultiExpert Graphs and MultiSoft MultiExpert Graphs, providing a unified framework that jointly handles graph topology, multiple parameters, and expert opinions.