A Study on Seasonal GARCH model with Periodically Varying parameters

Abstract

ARCH and GARCH models which stand for autoregressive condi-tional heteroskedasticity and generalized autoregressive conditional het-eroskedasticity have become widespread tools for dealing with time se-ries with heteroskedastic conditional variance. GARCH models have become important particularly in financial applications when the goalis to analyze and forecast volatility. GARCH model can be extended and modified in many ways. In this paper, we consider the SPGARCH(seasonaland periodic GARCH) model {εn} which is given by εnT+v = √(xnT+v)enT+v xnT+v = α0(v) +pXi=1αi(v)"2nT+v¡i +qXj=1?j(v)xnT+v¡j ;where 1 · v · T; α0(v); α1(v); ￠ ￠ ￠ ; �p(v) and ?1(v); ￠ ￠ ￠ ; ?q(v) are themodel coe±cients at season v such that �0(v) > 0; �i(v) ¸ 0; i =1; ￠ ￠ ￠ ; p and ?j(v) ¸ 0; j = 1; ￠ ￠ ￠ ; q: fengn2Z is a sequence of indepen-dent identically distributed random variables with zero mean and unitvariance. We ?nd su±cient conditions under which the given di�erenceequations have a (unique) strictly stationary solution.;ARCH(autoregressive conditional heteroskedasticity)모형과 GARCH(generalized autoregressive conditional heteroskedasticity)모형은 이분산성(heteroskedastic conditional variance)을 가진 시계열 자료를 다루는 모형으로 널리 사용 되고 있다. 특히, GARCH모형은 금융자료에서 volatility를 예측하고 분석하는데 있어 중요하다. GARCH모형은 여러 가지 방식으로 확장되고 응용될 수 있는데 이 논문에서는 seasonal and periodic GARCH모형, 즉, SPGARCH모형의 안정성(stability)조건과 확장에 대해 생각보았다.