計(jì)量經(jīng)濟(jì)學(xué)時(shí)間序列分析計(jì)量經(jīng)濟(jì)學(xué)時(shí)間序列分析第9章時(shí)間序到分析9.1時(shí)間序列的基本概念9.1.1時(shí)間序列在概率論中,我們稱(chēng)一族(無(wú)限多個(gè)隨機(jī)變量的集合{y,t∈T}為隨機(jī)過(guò)程。皆如當(dāng)T=(-,4)時(shí),隨機(jī)過(guò)程可以表示成{,<t<∞},其中y是時(shí)間t的隨機(jī)函數(shù),「為在每個(gè)時(shí)刻,y為一個(gè)隨機(jī)變量={0±1±2,…時(shí),即時(shí)間t只取整數(shù)時(shí),隨機(jī)過(guò)程{y,t∈7}可寫(xiě)成如下形式,(y2t=0+1,+2…},止類(lèi)隨機(jī)過(guò)程y是離散時(shí)間t的隨機(jī)函數(shù),我們稱(chēng)它為隨機(jī)時(shí)間序列簡(jiǎn)稱(chēng)時(shí)間序列第9章時(shí)間序到分析29.1.2時(shí)間序列的數(shù)字特征1.均值函數(shù)設(shè)(yx:=12時(shí)間序列,稱(chēng)(1)=E(v)(t=1為時(shí)間序列(另,=1,2,…的均值函數(shù)由于對(duì)于固定的t,y是一個(gè)隨機(jī)變量所以E(y)是一個(gè)確定的效。當(dāng)t變化時(shí),(1)是t的一個(gè)函數(shù),它是時(shí)間序列{yt=12…}的所有樣本函數(shù)在時(shí)刻t的函效值的平均2.自協(xié)方差函數(shù)設(shè){另2t=12,…是一個(gè)時(shí)間序列,稱(chēng))=E-E(yE為時(shí)間序列{另2t=1,2…}的白協(xié)方差函數(shù)9.1.2時(shí)間序列的數(shù)字特征3則稱(chēng)r(t1)=Lv1-E(y1)=var(:)(ts=12為時(shí)間序列(y,t=1,2…}的方差函數(shù)。記為G2。它表示時(shí)間序列{y1,t=1,2,在時(shí)刻t對(duì)于均值u()的偏離程度自相關(guān)函數(shù)設(shè){V=12…是一個(gè)時(shí)間序列,稱(chēng)√r(√r(為時(shí)間序列{y2t=12…}的自相關(guān)函數(shù)。它反映了時(shí)間序列{y:t=132…}在兩個(gè)不同時(shí)刻取值的線性相關(guān)程度則稱(chēng)49.1.3平穩(wěn)和非平穩(wěn)的時(shí)間序列1.平穩(wěn)時(shí)間序列所謂時(shí)間序列的平穩(wěn)性,是指時(shí)間序列的統(tǒng)計(jì)特征不會(huì)隨著時(shí)間的推移而發(fā)生變化。也就是說(shuō),生成變量時(shí)間序列數(shù)據(jù)的隨機(jī)過(guò)程的特征不隨時(shí)間變化而變化。1嚴(yán)平穩(wěn)。當(dāng)時(shí)間序列{y,r∈T}的概率結(jié)構(gòu)不隨時(shí)間而變,則稱(chēng)時(shí)間序列{y2t∈T}是平穩(wěn)的,一個(gè)平穩(wěn)的時(shí)間序列,從直觀上可以看作一條圍繞其平均值上下波動(dòng)的曲線如果時(shí)間序列{y,∈T)的聯(lián)合概率分布隨時(shí)間的平移而不變,則稱(chēng)該時(shí)間序列是嚴(yán)平穩(wěn)的。即嚴(yán)平稿時(shí)間序列需滿足以下條件Py2sby2sb2…ysbn}=Py1+msb:y2+n≤b2…1+≤b}其中m,n為任意正整數(shù),1<2<…<Ln,1∈T,b3b;…b,是實(shí)數(shù)9.1.3平穩(wěn)和非平穩(wěn)的時(shí)間序列5是弱平穩(wěn)的①均值E(y2)=H,(t=12,…)②方差var(2)=E(y2-)2=a2,(=12.…)⑧協(xié)方差cv(y2y1+x)=E[(y2-1)(計(jì)x-)=r(,+k),(t=1,2,…僅與時(shí)間間隔有關(guān),與時(shí)間t無(wú)關(guān)的常數(shù),記為。即cov(y2,y)=F,(k=0,12,…),當(dāng)k=0時(shí),cov(2y)=va(y:)=通常情況下,我們所說(shuō)的平穩(wěn)性指的就是窮平穩(wěn)性。一般來(lái)說(shuō),如果一個(gè)時(shí)間序列懸平穩(wěn)的,它的自相關(guān)函數(shù)p(11+h)=D(0,k)也僅與時(shí)間間隔k有關(guān),記為P,則有(91.5)是弱平穩(wěn)的6當(dāng)k=0時(shí),p=1,當(dāng)時(shí),2|1特別地,具有零均值和相同方差的不相關(guān)的隨機(jī)過(guò)程稱(chēng)為白噪聲hitenoise)過(guò)程或白項(xiàng)盧序列,用表示白嗓聲過(guò)程,則E1)=0,var(!)co4,4+)=0,對(duì)所有的t和k≠0成立。顯然白嗓聲序列是平穩(wěn)時(shí)間序列。白噪聲序列v可用符號(hào)表示為2.非平穩(wěn)時(shí)間序列所謂時(shí)間序列的非平穩(wěn)性,是指時(shí)間序列的統(tǒng)計(jì)規(guī)律(或特征)隨著時(shí)間的位移而發(fā)生變化。只要弱平穩(wěn)的三個(gè)條件不全滿足,則該時(shí)間序列是非平穩(wěn)的。(1)隨機(jī)游走(randomwalk)序列當(dāng)k=0時(shí),p=1,當(dāng)時(shí),2|17隨機(jī)游走序列是一個(gè)簡(jiǎn)單的隨機(jī)過(guò)程,y由下式確y09.1.7)式中,2為白嗓聲序列。y的均值為E(y)=E(yx1)+E()=E(y-1)=…=E(y)喪明y的均值不隨時(shí)間而變,為一常數(shù)為求的方差,對(duì)y1=y11+進(jìn)行一系列迭代=y1+=y-2+11+t=3+12+2-+=y+1+2+…+=y隨機(jī)游走序列是一個(gè)簡(jiǎn)單的隨機(jī)過(guò)程,y由下式確8式中,y為y的初始值,可假定為任何常數(shù)或取初值為零,則var(1)=var(y+∑)=∑分am)=n表明,y的方差隨時(shí)間而增大,平穩(wěn)性的第二個(gè)條件即方差為常數(shù)不滿足,因此,隨機(jī)游走時(shí)間序列是非平穩(wěn)時(shí)間序列。可是,若將式(9.1.7)寫(xiě)成一階差分形式Ay,=y,-),-l這個(gè)一階差分新變量△y是平穩(wěn)的,因?yàn)樗偷扔诎自肼?而后者是平穩(wěn)時(shí)間序列(2)荇漂移項(xiàng)的隴機(jī)游走(randomwalkwithdrift)序列帶漂栘項(xiàng)的隨機(jī)游走序列y下式確定H=+-1+1r式中,y為y的初始值,可假定為任何常數(shù)或取初值為零,則9式中,為一非雯數(shù),t2為白嗓聲序列α之所以被稱(chēng)為“漂移項(xiàng)”,是因?yàn)檫?9.1.8)的一階差分4y=-y1=+1表明時(shí)間序列y向上或向下漂移,取決于的符號(hào)是正還是負(fù)。通過(guò)對(duì)式(9.1.8)直接迭代y2=y+∑(a+)=y+t+∑22即y1是許多隨機(jī)變量的一個(gè)積系,具有明顯的趨勢(shì)。異的期望E(y2)=y+ta+∑E)=y+m式中,為一非雯數(shù),t2為白嗓聲序列10y的方差var(v)=varlyo+ta+Eu,1=Evaru,)=to2都是時(shí)間t的函致,而且隨時(shí)間發(fā)散到無(wú)大。顯然,帶漂移項(xiàng)的隨機(jī)游走時(shí)間序列也是非平穩(wěn)時(shí)間序列(3)帶掐勢(shì)項(xiàng)的隨機(jī)游走序列隨機(jī)游走序列(91.7、(9.1.8)是比較簡(jiǎn)單的非平穩(wěn)序列,它是y1=+f+y21+t1(9.1.9)的特例。式(9.1.9)稱(chēng)為帶趨勢(shì)項(xiàng)的隨機(jī)游走序列,容易證明y的期望y的方差11計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件12計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件13計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件14計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件15計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件16計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件17計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件18計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件19計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件20計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件21計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件22計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件23計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件24計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件25計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件26計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件27計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件28計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件29計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件30計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件31計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件32計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件33計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件34計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件35計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件36計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件37計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件38計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件39計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件40計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件41計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件42計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件43計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件44計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件45計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件46計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件47計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件48計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件49計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件50計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件51計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件52計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件53計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件54計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件55計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件56計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件57計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件58計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件59計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件60計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件61計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件62計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件63計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件64計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件65計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件66計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件67計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件68計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件69計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件70計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件71計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件72計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件73計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件74計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件75計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件76計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件77計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件78計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件79計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件80計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件81計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件82計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件83計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件84計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件85計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件86計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件87計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件88計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件89計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件90計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件91計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件92計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件93計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件94計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件95計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件96計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件97計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件98計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件99計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件100計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件101計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件102計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件103計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件104計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件105計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件106計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件107計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件108計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件109計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件110計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件111計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件112計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件113計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件114計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件115計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件116計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件117計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件118計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件119計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件120計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件121計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件122計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件123計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件124計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件125計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件126計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件127計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件128計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件129計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件130計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件131計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件132計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件133計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件134計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件135計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件136計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件137計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件138計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件139計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件140計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件141計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件142計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件143計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件144計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件145計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件146計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件147計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件148計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件149計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件150計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件151計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件152計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件153計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件154計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件155計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件156計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件157計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件158計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件159計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件160計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件161計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件162計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件163計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件164計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件165計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件166計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件167計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列分析課件168計(jì)量經(jīng)濟(jì)學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