상태 공간 모형에서의 모수 공간 제약

Abstract

Most studies using state-space models have been conducted under the assumption of independently distributed noises in measurement and state equation without adequate verification of the assumption. To avoid the improper use of state-space model, testing the assumption prior to the parameter estimation of statespace model is very important. The purpose of this paper is to investigate the general relationship between parameters of state-space models and those of ARIMA processes. Under the assumption, we derive restricted parameter spaces of ARIMA(p,0,p-1) models with mutually different AR roots where p≤5. In addition, the results of ARIMA(p,0,p-1) case can be expanded to more general ARIMA models, such as ARIMA(p-1,0,p-1), ARIMA(p-1,1,p-1), ARIMA(p,0,p-2) and ARIMA(p-1,1,p-2).