雙線性時間數列模式及其應用

Abstract

雙線性時間數列模式及其應用線性時間數列模式，如ARMA模式已被廣泛地應用在許多學科領域。但是其中之一重要假設為此時間數列之結構可被一線性模式來描述。此線性假設有時常覺得頗牽強，因而我們考慮是否有更好的模式來做資料之擬似。近年來，屬於非線性模式族之一系的一雙線性模式便引起學者的熱烈討論。本文即針對特定型之雙線性模式，探討其平穩性，可逆性。並做參數估計法則。最後舉例說明有關預測之方法。Linear time series models such as ARMA models have been widely used in many fields. An important assumption is that the structure of the series can be described by a linear model. However, this assumption of linearity is often a dubious one. In some particular situations one may ask if there exist other models which can provide a better fit. A particular class of non-linear models which has received a great deal of attentions is bilinear models. In this paper we investigates some properties of the bilinear model: stationarity and invertibility. Estimation of the parameters are obtained by minimum least squares method. The forecasting of certain bilinear models are also considered.