GARCH模型应用教程(终结完美版)

GENERALIZEDRCAHMODELSWITHAPPLICATIONSFALL 2004R. Adam HoppesDepartment of StatisticsNorth Carolina State UniversityTABLE OF CONTENTSR. A. HOPPESContents1Introduction and Motivation11.1Examples: Securities and Commodities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12Univariate ARCH Processes52.1ARCH(1) Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52.2ARCH(p) Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73Univariate GARCH Processes133.1GARCH(p, q) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143.2Extended GARCH(p, q) Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144References15iST 730: CONDIT IONAL HET EROSKEDAST IC MODELSR. A. HOPPES1Introduction and MotivationFor the most part, an introductorycourse in time series focuses on analyzing the conditional meanbehaviour of a process, also known as the first central moment defined as: µ 1 = E[y− E(y)] = E[y− µ] =(y − µ)fy (y) dy.During this semester a gallimaufry of techniques have enabled us to model thecharacteristics of these ‘special’types of processes. Recent problems in finance have motivated the studyof modelling the conditional variance of a process, or the second central moment: µ 2 = E[y − µ]2 =(y − µ)2fy (y) dy. This concept is applicable in many risk management applications: such as, optionspricing and value-at-risk estimation. However, the most pervasive role in modelling volatility is illustratedin Example 1.1.1.1Examples: Securities and CommoditiesExample 1.1 (Amazon Series). The Amazon series,...