Stationary process in GSTAR(1;1) through kernel function approach

Stationarity is an essential requirement in modeling GSTAR space-time. GSTAR modeling adopted from the three iterative Box-Jenkins time series modeling. The stages are model identification, parameter estimation, and validation. In the validation, stage consists of two tests, namely parameter stationarity test and residual test. In the parameter stationary test, the Eigenvalue method has been used, in this paper the inverse matrix Autocovariance M˜1 the technique is used. The spatial weight matrix of the GSTAR model, uses a kernel approach so that it is random. The results obtained that A GSTAR(1;1) process with kernel weight matrix which has IAcM is stationary if and only if the M˜1 matrix is positive definite and the modulus from all the eigenvalues of the matrix parameter is less than 1.