资源描述：
《review of probability and statistics》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、c02-RevProbabStatsPage25Thursday,October26,20061:59PMCHAPTER2ReviewofProbabilityandStatisticsinancialeconometricsdrawsonthefieldsofprobabilitytheoryandFstatistics.Probabilityisthestandardmathematicalrepresentationofuncertaintyinfinance.Probabilisticmodel
2、shavetobeestimatedfromempiricaldataandthisiswheretheconceptsandmethodsofstatisticscomein.Inthischapter,weprovideareviewofconceptsofbothproba-bilityandstatistics.CONCEPTSOFPROBABILITYBecausewecannotbuildpurelydeterministicmodelsoftheeconomy,weneedamathe
3、maticalrepresentationofuncertainty.Probabilitytheoryisthemathematicaldescriptionofuncertaintythatpresentlyenjoysthebroadestdiffusion.Itistheparadigmofchoiceformainstreamfinancetheory.Butitisbynomeanstheonlywaytodescribeuncertainty.Othermathematicalparad
4、igmsforuncertaintyinclude,forexample,fuzzymeasures.1Thoughprobabilityasamathematicalaxiomatictheoryiswellknown,itsinterpretationisstillthesubjectofdebate.Therearethreebasicinterpretationsofprobability:■Probabilityas“intensityofbelief”assuggestedbyJohnM
5、aynardKeynes.21LotfiA.Zadeh,“FuzzySets,”InformationandControl8(1965),pp.338–353.2JohnMaynardKeynes,TreatiseonProbability(London:McMillan,1921).25c02-RevProbabStatsPage26Thursday,October26,20061:59PM26FINANCIALECONOMETRICS■Probabilityas“relativefrequenc
6、y”asformulatedbyRichardvonMises.3■ProbabilityasanaxiomaticsystemasformulatedbyAndreiN.Kol-mogorov.4TheideaofprobabilityasintensityofbeliefwasintroducedbyJohnMaynardKeynesinhisTreatiseonProbability.Inscience,asinourdailylives,wehavebeliefsthatwecannotst
7、rictlyprovebuttowhichweattributevariousdegreesoflikelihood.Wejudgenotonlythelikelihoodofindividualeventsbutalsotheplausibilityofexplanations.Ifweespouseprobabilityasintensityofbelief,probabilitytheoryisthenasetofrulesformakingconsistentprobabilitystate
8、ments.Theobviousdifficultyhereisthatonecanjudgeonlytheconsistencyofprobabilityreasoning,notitstruth.Bayesianprobabilitytheory(whichwewilldiscusslaterinthechap-ter)isbasedontheinterpretationofprobabilityasintensityofbelief.Probabilityasre
