THE STATIONARITY OF THE GENERALIZED STAR MODELS THROUGH INVERS OF AUTOCOVARIANCE MATRIX - MUKHAIYAR (NIM: 30107008); Tim Pembimbing: Dr. Udjianna S. Pasaribu, Dr. Wono Setya Budhi, UTRIWENI
Stationarity is one of the important things in defining a stochastic processes. As one of stochastic process, space-time process is also defining its stationarity. The space-time process stationarity uses the concept of time invariant for both mean and variance of the process. Generalized STAR or GSTAR model as one of space-time model defines its stationarity by using the GSTARs form as vector of autoregressive or VAR model. The stationarity of GSTAR model is obtained if all the eigenvalues in absolute of parameter matrices are less than one. This method is already difficult to apply for GSTAR of order one with small numbers of locations. It becomes more difficult for higher order and greater number of locations. Motivated by this phenomenon, in this dissertation a new alternative method for checking stationarity is proposed, through invers of auto-covariance matrices or IAcM. The IAcM approach is conducted by observing the determinant values of its main sub-matrices. It is obtained that the stationarity of the eigenvalues method is the implication of the IAcM method. In other words, the IAcM approach is more sensitive than the parameter eigenvalues approach. It is proved analytically and numerically. Furthermore the stationarity using IAcM may be used in GSTAR modeling. Checking the determinant values of the IAcM main sub-matrices is one of the important stage in model re-identifying and validation. This stage minimizes the subjectivity in space-time modeling and builds the modeling procedure more analytic. In the parameter estimation, it is obtained that the least squares estimator for GSTAR(p: 1: : : : :p) with independent errors assumptions is unbiased with minimum variance. It is also obtained that maximum likelihood estimator has similar form as in the least squares estimators. Furthermore, using the Monte-Carlo simulation for different type of spatial weight and parameters, it is obtained the minimum numbers of observations with criterion is the estimator is close enough to the true parameters. It is expected that this minimum numbers may be come a consideration in doing sampling to make its more effective and efficient. The modeling procedure is applied to the monthly tea production data of nine plantations in Garut, West Java, which are taken from January 1992 to December 2010. Using biner and non-uniform spatial weight, and after passing the diagnostic checking, it is obtained that GSTAR(2: 1: 1) model is the most appropriate model to the data. The forecast values of observations in January, February and March 2011 have close values to the real observations. This closeness may be seen from linear pattern between the real and forecast observations, that has high value.