系統抽樣ARMA模式之精確階數之研究

A Note on the Exact Order of Systematic Sampled ARMA Models

劉湘川(Hsiang-Chuan Liu)

《測驗統計年刊》 1期 (1993/12) Pp. 137-146

https://doi.org/10.6773/JRMS.199312.0137

摘要

假定ARMA（p'，q'）為抽自- ARMA（p',q'）模式之K期系統抽樣子數列，Brewer 於1973年證明了階數之值，具下述關係：p' = p且q'=（方程式略），其中高斯函數﹝m﹞表不大於m之最大整數，但筆者發現階數q'值並不恆為﹝（方程式略）﹞除提出兩則反例以驗證上言外，進而並提出一個方便有用之定理，藉之可經由任意一個原始之ARMA（O.q）母模式的有關訊息，直接指出其抽樣子模式中階數q'值之精確值。（註：本文曾在中華民國七十六年度統計學術研討會中發表摘要）。

並列摘要

Assume ARMA(p',q') is a k-period sampled sequence from an ARMA(p,q) model, Brewer(1973) has show that p'=p and q'=(The equation is abbreviated), where [m]= the largest integer, M, satisfying M≦m [c.f.Helsinki (1984)], We find that the order q' does not always equal (The equation is abbreviated) May be any non-negative smaller imteger. Two counterexamples are given, furthermore, we provide a theorem to point out the exact value of q' directly via the information of any original ARMA(0,q) model.

並列關鍵字

ARMA Model ； systematic sampled model ； Autocovariance function