時(shí)間序列模型歸納總結(jié)復(fù)習(xí)

精品文檔一、隨機(jī)過(guò)程(StochasticProcess)感謝閱讀）感謝閱讀精品文檔放心下載t}或XT感謝閱讀TttX是謝謝閱讀tt精品文檔放心下載當(dāng)t謝謝閱讀tt2,Xtt{X精品文檔放心下載t二、時(shí)間序列的概率分布和數(shù)值特征X=(謝謝閱讀謝謝閱讀…精品文檔放心下載，謝謝閱讀謝謝閱讀ttt(X)EXttXt謝謝閱讀精品文檔放心下載1。精品文檔)(t,s)E(XXtts(X)sYssdF(X,Y)t,st精品文檔放心下載(t,s)(t,s)/(t,t)(s,s)感謝閱讀）(t,s)(s,t)）mmk,k12,kmm,k,kkkLk21m111kkLk,k,k,k21222mLLLLkkLk,k,k,km1m2mm。精品文檔放心下載三、平穩(wěn)隨機(jī)過(guò)程謝謝閱讀1tnt,t12,L,tnXt的nFnx,x,Lx;t,t,Lt1212nnFnx,x,Lx;t121n2,tt,LnXtXtaEXtEXtkaXt,tTtTat,tkTXtk,tT2。精品文檔感謝閱讀Ⅲ+感謝閱讀EXtXtXt0。EXXktEXEXtktkEXXttktEXt0時(shí)Xtkk0X謝謝閱讀t）,kk；kk）m，LLm1011m-1L1L10，Rm-2L1LLLLLLLmL1L0m-2）,k1。0k）精品文檔放心下載1nXXntt13歡迎下載。精品文檔）?k1XXnkXtkt1X?kn1tXXnknkt1XtXtk精品文檔放心下載感謝閱讀XtE0XtEXXst2t,st,s0,1t,t（3Xt,tTXtXtXt,tT精品文檔放心下載ntTtLiit2,n,tn1X,LX

XX,tttnXt32n1Xtt21X,tTtT,XttX,tT,tTXtt4。精品文檔精品文檔放心下載第一節(jié)自回歸模型謝謝閱讀謝謝閱讀；精品文檔放心下載XtXXtXtXa1tt1αt、Xt對(duì)XαtE(atX)0,j1,2,...tj、一元線性回歸YiXiiXtX1t1atYXX感謝閱讀tE()0；iaE(a)tt0;cov(t)0ij；Eas；iajvar()tsi22；a0t

scov(X:Nii0,iE(aX)0；t)0,j1,2,...;tj2at）謝謝閱讀5。精品文檔）感謝閱讀）感謝閱讀））精品文檔放心下載精品文檔放心下載XtXt1at和t謝謝閱讀X。X即X謝謝閱讀(1)，t1t1Xtatjj0XtX1t12Xt2...nXtnaE(aXatttjt)0,j1,2,...。第二節(jié)移動(dòng)平均模型）XαttXaatat1

tt1αXtt）at6。精品文檔Xaaa11tt1t2X僅與，tt1t2...amtm…，tm）tjt第三節(jié)自回歸移動(dòng)平均(ARMA)模型XtX1t1、Xt2t1X與Xt2Xt2t1t1和t1t謝謝閱讀謝謝閱讀tt，t1t2感謝閱讀0X（）.n（，獨(dú)立于獨(dú)立tj,從而于（）XtttjtX1t1...nXtnt1t1.精品文檔放心下載謝謝閱讀感謝閱讀Hilbert精品文檔放心下載n謝謝閱讀MA。n謝謝閱讀感謝閱讀。7。精品文檔感謝閱讀第三章和精品文檔放心下載第一節(jié)一、后移(Backshift)算子:BBXXBXtmt1tX。tmBcc(BB)XBXBXXtnXtmmnmntttB(BX)BXtmnXtnBBXmnmnmttBBXX1t1t1(1BBB...)X2233tXt1B謝謝閱讀Xt(B)at(B)Xtat(B)Xt(B)at其中：(B)1BBL2Bn12

n(B)1BB2LBm12

m二、線性差分方程XtX1t12Xt2LXtnanta1t1a2t2Lamtm8歡迎下載。精品文檔(B)Xt(B)at(B)1BBL2nB12

n(B)1BB2LBm12

mXC(t)I(t)tCI三、齊次方程解的計(jì)算(B)X0t(B)(1GB)(1GB)L(1GB)謝謝閱讀12

n假定GGGt謝謝閱讀12n其中AiXALtAGGttt1122nn設(shè)(B)0有dG01Xt(A01At2LAd1)GttAt2LAd1t2d10(B)GGB)LGGB)謝謝閱讀dn/120Ck(t)Gt0AtDGd1n/jtjiij0i1GtD謝謝閱讀tjt

00Gnn1n2i...12

n,i1,2,...,nnn10的根與1BB2LBn0in2...1212

nn。iGi9。精品文檔感謝閱讀第二節(jié)格林函數(shù)(Greens’function)和平穩(wěn)性(Stationarity)精品文檔放心下載一、格林函數(shù)(Greens’function)1{Xt,t0,1,2,...}GXtajtjj0XGtj）G01。2XtGBat）GBGBj。jj0XtGBGBj”jj0G是jaXajttjtj的。二、1）系統(tǒng)的格林函數(shù)由XXtX1t1attat1)aXt1t1(Xa11t2t21at...ta1t110歡迎下載。精品文檔aXj1tjtj0則AR(1)模型的格林函數(shù)Gjj111Gjj0Gj.精品文檔放心下載1j的1t66442200精品文檔放心下載Xt0.9Xt1atXt0.1Xt1at6420精品文檔放心下載Xt0.9Xt1at111精品文檔放心下載由于taa2aX1t12a1ata1t1a2t2...jj此）1j0aj1tjtt2模11歡迎下載。精品文檔感謝閱讀三、AR系統(tǒng)的平穩(wěn)性將XtXa1t

t1E(X2)E()2)

Xa

tt

1t12E(X)E(a2)2

E(Xa211t1ttt12E(X)22

1at1E(X2)2)XtE(Xt1t(1)E(X)2221taE(X2tE(Xt)2a)2122)0a(1)2111(B)Xtat式中(B)1B，那么平穩(wěn)性條件111就等價(jià)于(B)0的根在單位圓外（或()10n(B)X(B)1BB2L(B)0taBnt12

n()nn10n2L12

n精品文檔放心下載謝謝閱讀j→∞，擾動(dòng)的權(quán)數(shù)G11j0Gj＝j(luò)→∞，jj1101112歡迎下載。精品文檔11Gj當(dāng)1=1Gj當(dāng)j1=-1時(shí)感謝閱讀當(dāng)11Gj精品文檔放心下載()021222411241，212122，1221211(iARi1212111i1(i，21121212)111(21121212,,121211112m211故12211121四、格林函數(shù)與Wold分解(Wolds’Decomposition)感謝閱讀Wold謝謝閱讀想是由WoldWoldARMA謝謝閱讀在nLnna,a,...a12na,a12,...ankikkaa1122和a...kannkiiai13。精品文檔Xtja1tjj0aXjttjatjGXjtaXtjtGjatj系精品文檔放心下載五、ARMA模型格林函數(shù)的通用解法(B)Xt(B)且XtG(B)at則(B)G(B)(B),0jn令*jjjn,0lm*lllm則(B)G(B)(B)BB*jGkB*lj0k0l0ljkBlj0jGlj*,l1,2,3,...l由上式，格林函數(shù)可從l1Xt(B)aGjmt,1jjjm14歡迎下載。精品文檔tX，1t1型XBj)aGXjtt(G2Xt2ata1t1j0j0ajtjB2)(GBj)at(1B)a1t(1B12jj0(1BB)(GGBGB(1...)aB)a221t12012t(GGBG0B...BBB...)aGGG22212101120t(1B)a1tBB0:G10G

GG11011112:G0GGGGG2112021120GGGGG0G3122131221....................................................................

j:G精品文檔放心下載jGG12j1j2GGG

0j1j12

j21BBG0,j2212jGjGj和12gjgj11220g2121和g2G10G111則Gj11j21j21121215歡迎下載。精品文檔謝謝閱讀B12B2)Xt(1B)a1tXt1B11BatB2121Bat11B1B121111

11111..a1211B11112Bt21

1211

11.21.a

1B1B121212tjat11j21jBj012

12212a21jj011j21tj121Gj11j1

2j121221精品文檔放心下載感謝閱讀G0BB2...Bn12nj,G,G,...G,G12n1njn16歡迎下載。精品文檔G0G1G21G101GG11202GGGG...n11n22n3n10n1GGGGn...0n1n12n20即BB2LBn12njjnGgjgj...gj...ing1j1122nngn1...n2ii1n1...iiiii

12i1

i1gg12

nj時(shí),G0。感謝閱讀j由Gj2gjg1122j0和121()2102()21精品文檔放心下載21211112第三節(jié)逆函數(shù)和可逆性（Invertibility）精品文檔放心下載謝謝閱讀一、逆函數(shù)的定義設(shè)XtatatXtIjXtjj117歡迎下載。精品文檔XItjj二、ARMA模型的逆函數(shù)精品文檔放心下載令I(lǐng)(B)1IjXtj,I01，Xtj1atXItjj1aI(B)XttXtj由ARMA(n,m)(B)Xt(B)at(B)(B)I(B)*和j*llBBIB*j*lkkk0l0j0jBj*I*jkkk0l即Ij*jjI,j1,2,...*kjkk1Ij1j（1XXt1t1aXX1t1attI,I0,j11j2X...X有XtX2ntnat21tt1t有18歡迎下載。精品文檔XtX1t12Xt2...nXtntI11I22IIjnn0,jn1Xt(1B)a1tB，1(B)1，(B)11BIB1，1即1B1I

BIB2...1112BIjI01,Ij,j111,IjI1jj1,2由XtB)aat得1tXtB)2211BB...X11tXtjXjX1tjj1X即Xta)t(tjj1j1Ijj1與11謝謝閱讀足VkVmm1Vm2...V12m10VkV1的特征根k滿19歡迎下載。精品文檔精品文檔放心下載三、G和I之間的關(guān)系jjGjj1I11I0,j1G01Ijj1）Gj11Gj1jGj和I模jG01G111GG2112GGG,j3jj11j22I111,j3j222IIjI112IIj11IjGj，代替，四、關(guān)于ARMA模型平穩(wěn)性與可逆性的說(shuō)明模精品文檔放心下載感謝閱讀謝謝閱讀第四節(jié)一、理論自協(xié)方差函數(shù)和自相關(guān)函數(shù)20歡迎下載。精品文檔精品文檔放心下載kEXtXtkkk0二、樣本自相關(guān)函數(shù)的計(jì)算謝謝閱讀感謝閱讀?k1XX,k0,1,2,...,NNNttk1tk1?*k1NXtX,k0,1,2,...,N1tkNktk1?k?k?01NNXXttktk11N1NXt1t2NXXttktk1NX2tt1?*kkNXX?NkN*tkttk1?1NNXXttktk1NX2tt1k0NNXt1i2三、AR模型的自協(xié)方差函數(shù)和自相關(guān)函數(shù)）XtX1t1atXX謝謝閱讀ttk當(dāng)EEXXtt1EXX1t1tkXEXXt1t1XttEatEatXXtkt21歡迎下載。精品文檔0112a當(dāng)k=1EXtXt1EXX1t1t1EatXt1101當(dāng)k=2EXtXt2EXX1t1t2EatXt2211k1k1k02將1021a002110

a1k,k01k1/k0/10k/001/k101k10kXtkXtXt121得到Xt2LpXtnatXtkXtXtk1Xt12XXtkt2LnXXtktnXatktk1k1k22Lnkn(k0k1k1XL2k2knnt(k(B)k0(B)1BLBn1

n22歡迎下載。精品文檔n記(B)(1GB)jj1G，GG11112nAALkAGGGkkk1122nn(B)1BL

Bn1nGi1．Gρ中AG隨kikk

ii．G和GijDksin(2fkF)DGiGjf2fcos1[i)/D]012Ln2a12n以02a22XkXkL2X111nn22四、MA模型的自協(xié)方差函數(shù)和自相關(guān)函數(shù)將Xtata1t1Xtk23。精品文檔EXXttkaEtXtkEaX1t1tkGGEaaEaaj0j0tkj1t1tkjtjjEEG1aaaaGtkjt1tkjj0jtj0jEaGEaEaGEaGaGaaa0tk1tk110t1tk1t1tk1ttEaEaEa

2Eaaaaatttk1tk11t1tk1t1tk1當(dāng)E2E

EXaaaaX1t11t10tt1ttEa

Eaaa

ttt

1t122aa12當(dāng)1EXXtt1EaEaaattt11t2Eaa1t1t1Eaa1t1t212a當(dāng)2EXXtt2EaEaaattt21t30Eaa1t1t2Eaa1t1t30122101k1a21a1k21121kk2kE[(ata1t1L)(aatkam1tmtk1L)]amtkm24。精品文檔0(1L)2221ma且k(0k1k12k2L)mkm2a,,k1,2,L,mkmkkLm,1k1mk1Lk1,2,L,mkm221m0,m精品文檔放心下載m精品文檔放心下載五、偏自相關(guān)函數(shù)k階jj1j2k2Lkkjjk1,2,L,kk11111MMLL21MLLk3k1k112k1k2k2k2MMM1kkk或Pφ=ρkkk當(dāng),,,12k，，k1k2k謝謝閱讀對(duì)…1111112111122112125歡迎下載。精品文檔11113312213112111121kk1L12k211L11k32MMMLMMLk1k2k31k1L2k1L11k2MLM11MML1k1k2k3kk=0。感謝閱讀kkX,X,...,X和XXj1jk1jkj2

j,X,...,X和XXXjj1j2jjk...,,X,...,XXXjkkkjj1j2k1,k2,時(shí)，

kk感謝閱讀26歡迎下載。精品文檔六、自回歸和滑動(dòng)平均過(guò)程之間的對(duì)偶性．natXXatXt(B)a1tmXaaX精品文檔放心下載tt(B)X1tat2...AR精品文檔放心下載謝謝閱讀精品文檔放心下載3.m精品文檔放心下載謝謝閱讀．感謝閱讀模型at(B)XXtt(B)at(B)Xt(B)at精品文檔放心下載精品文檔放心下載Xa傳遞形式t逆轉(zhuǎn)形式t(B)Xt1(B)atXtat(B)1tX(B)aXttat(B)1(B)Xt1(B)(B)at27。精品文檔0）謝謝閱讀AR感謝閱讀感謝閱讀MAARMA=謝謝閱讀=謝謝閱讀MA和和PAFC謝謝閱讀謝謝閱讀ARMA感謝閱讀謝謝閱讀謝謝閱讀第一節(jié)一、識(shí)別依據(jù)和SPACFARMASACF和SPACF精品文檔放心下載表ARIMA過(guò)程與其自相關(guān)函數(shù)偏自相關(guān)函數(shù)特征模型自相關(guān)函數(shù)特征偏自相關(guān)函數(shù)特征ARIMA(1,1,1)緩慢地線性衰減xt=x1+ut+u11.01.00.50.50.00.0-0.528歡。迎下載-0.5-1.0-1.024681012142468101214精品文檔放心下載精品文檔AR（1）若xt=1x+ut0.80.61>0，平滑地指數(shù)衰減若0.80.6>=1時(shí)有正峰值然后截尾0.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.82468101214感謝閱讀-0.82468101214若<0，正負(fù)交替地指數(shù)衰減若1<=1時(shí)有負(fù)峰值然后截尾0.80.80.60.60.40.40.20.20.00.024681014246814精品文檔放心下載MA（1）若>0=1時(shí)有正峰值然后截尾若1>0，交替式指數(shù)衰減xt=ut+1u10.80.60.80.40.60.20.40.00.20.0-0.2-0.424681014-0.6若0.81<0=1時(shí)有負(fù)峰值然后截尾-0.8若12468101214<0，負(fù)的平滑式指數(shù)衰減0.60.80.40.60.20.40.00.2-0.20.0-0.4-0.6-0.8246810121424681014AR（2）指數(shù)或正弦衰減2時(shí)有兩個(gè)峰值然后截尾精品文檔放心下載xt=1x+2x+ut0.80.60.40.20.0-0.2-0.4-0.6-0.824681012142468感謝閱讀（兩個(gè)特征根為實(shí)根）（>0，12>0）29歡迎下載。精品文檔0.80.80.60.60.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.8-0.824681012142468101214謝謝閱讀（兩個(gè)特征根為共軛復(fù)根）（>0，<0）12MA（2）2有兩個(gè)峰值然后截尾指數(shù)或正弦衰減謝謝閱讀xt=ut+1u+2u0.80.80.60.60.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.8-0.824681012142468101214（>0，<）（>0，<）12120.80.80.60.60.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.82468101214-0.82468101214（>0，>）（>0，>）1212ARMA11）=1有峰值然后按指數(shù)衰減=1有峰值然后按指數(shù)衰減感謝閱讀xt=1x+ut+1u1.01.00.50.50.00.0246810121424681214謝謝閱讀（>0，>）（>0，>）111124682468精品文檔放心下載（>0，<）（>0，<）1111ARMA21）=1有峰值然后按指數(shù)或正弦衰減2有兩個(gè)峰值然后按指數(shù)衰減謝謝閱讀xt=1x+2x+ut+1u0.80.80.60.60.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.8-0.824681012142468101214精品文檔放心下載（>0，<0，>）（>0，<0，>）121121ARMA12）2有兩個(gè)峰值然后按指數(shù)衰減=1有峰值然后按指數(shù)或正弦衰減感謝閱讀xt=1x+ut+1u+2u30歡迎下載。精品文檔0.80.80.60.60.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.8-0.824681012142468101214精品文檔放心下載（>0，>0，<）（>0，>0，<）1121121.01.00.80.80.60.60.40.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.8-0.824681012142468101214感謝閱讀（>0，>0，>0）（>0，>0，>）112112ARMA22）2有兩個(gè)峰值然后按指數(shù)或正=1,2有兩個(gè)峰值然后按指數(shù)或正感謝閱讀x=x+x+ut12t+u+u12弦衰減弦衰減0.60.80.40.60.40.20.20.00.0-0.2-0.2-0.4-0.4-0.6-0.6-0.824681012142468101214精品文檔放心下載（>0，<0，>0，<）（121221>0，<0，1>0，<）224682468感謝閱讀（>0，<0，>0，>）（121221>0，<0，1>0，>）2二、拖尾性與截尾性的判定在qk?k?感謝閱讀kkk在m?1m~N22Nkll11P2?mkN?)68.3%2l12P?2m?lkN2)95.5%l1l31歡迎下載。精品文檔在nkk1?~N)N(0,kk?1kk68.3%PN?2Pkk95.5%N三、精品文檔放心下載840-4X32歡迎下載。精品文檔840-1250100150200250Y與0.70.60.50.40.30.20.1

0-0.1-0.212345678910131415謝謝閱讀33歡迎下載。精品文檔0.70.60.50.40.30.20.10-0.1-0.2-0.3123456789謝謝閱讀34歡迎下載。精品文檔第二節(jié)一、殘差方差圖法AR{xt}p?精品文檔放心下載212謝謝閱讀p?感謝閱讀2{x}?n和殘差方差?感謝閱讀22

t二、自相關(guān)函數(shù)（ACF）和偏自相關(guān)函數(shù)（PACF）定階法精品文檔放心下載感謝閱讀三、F檢驗(yàn)定階法對(duì){xt},nmF與謝謝閱讀四、最佳準(zhǔn)則函數(shù)定階法精品文檔放心下載感謝閱讀精品文檔放心下載1．FPE準(zhǔn)則1?2eeNk，不僅受剩余平方和的影響，而且還受自由度的影響。35。精品文檔精品文檔放心下載而AR(n)?2是2是xtE[Xt?2n/N)2，Xt11n/

NN2）E[Xtn??2n/N)2Xt1NnNn2?Nn謝謝閱讀nnnFPE(n))()謝謝閱讀12

0NNiii1AR的值，從中選擇最小的謝謝閱讀nFPE(n0)minFPE(n)。n2．AIC準(zhǔn)則（AkaikeInformationCriterion）精品文檔放心下載感謝閱讀AICAIC2ln()(模型獨(dú)立參數(shù)的個(gè)數(shù))）謝謝閱讀NARMA謝謝閱讀??)NNS(NlnLln?ln?）感謝閱讀22322?222AIC準(zhǔn)精品文檔放心下載AIC(n,m)Nln?22(nm謝謝閱讀4）AICn和AIC感謝閱讀精品文檔放心下載詳見(jiàn)教材中P103明。21994年2月。3感謝閱讀4在EVIEWS軟件中的定義與此不同。36。精品文檔感謝閱讀K謝謝閱讀謝謝閱讀3．BIC準(zhǔn)則準(zhǔn)感謝閱讀感謝閱讀于謝謝閱讀BIC(K)Nln?2(K)KlnNKARMA(n,m)模型，感謝閱讀Knm1。感謝閱讀若BIC(K)minBIC(K)K感謝閱讀00

KM(N)與K①K00Nln?2N?K2?KK/K00KBIC(K)Nln?2(K)CKln(lnN)

）1精品文檔放心下載C精品文檔放心下載謝謝閱讀謝謝閱讀精品文檔放心下載C感謝閱讀37歡迎下載。精品文檔五、感謝閱讀38歡迎下載。精品文檔39歡迎下載。精品文檔第三節(jié)一、矩估計(jì)感謝閱讀1k10k21k1kk2k11k22kkk2）kkkk1k1k2k20k02)21(2m)2k01kmkm5）kk0k11k1mk6ARMA模感謝閱讀二、最小二乘估計(jì)（LS）三、極大似然估計(jì)（ML）xt=1,2,,精品文檔放心下載tx,x,,x)謝謝閱讀12TL(|x,x,,x)=fx|)fx|)…fx12T12T|)=Tf(xt|)t1（,,,精品文檔放心下載12k可采用：直接法、迭代法、牛頓-拉普森算法。56P120。謝謝閱讀40。精品文檔TlogL=logfxt1t|?感謝閱讀logL=1:logL=kk謝謝閱讀yd，xtt)y=)x=)u.dtt

tyT+dy,,y,y,,ydxt-01Tt。以x,,xARMA,)(,,,,,。1T1p1qxx?tttx)2=u

(x??2.tttttut=(L)x(L)t.?，?和?,和uiitiitut2=S(?,?,,?)?,,感謝閱讀t1p1qtNt=…2u?2logL=Tlog-ttu22u?t2x,x,,x0-和u,u,,0u-qu=x-11x-10x-…-2-1x-p-u--u.10q-

41。精品文檔2x,–,,x和u對(duì)（2,u??,,tt010uu,u,,u-q0-qx,x,,xT與感謝閱讀0-p,q,,1p1若OLS感謝閱讀(3)式謝謝閱讀)xt=ut或xt=1x+…+px+ut.OLS謝謝閱讀ut=))xt精品文檔放心下載2?t感謝閱讀20=1600004精品文檔放心下載謝謝閱讀(t?t2)=i,p+qi,,（,,,,,p+qp+q精品文檔放心下載11p1q精品文檔放心下載f)=fx)+f(x)x–x)+…=fx)-fx)x000000+f‘x)x+…00,,然0xt=fx,,x)0,,042。精品文檔xt=fx,,x,0,,)+0pqf(ii,0)0+122fpqpqj(i1i)+….iji,0j,00j1i1i=,,10=0xtxt-fx,,x,0,,0+upqfpqf)+=.i,0t

ii1i1

ii00,i=,p+OLS1i,,1xt-fx,,x,1,,1+upqfpqf)+=.t

ii1i1

ii11OLS(,,)謝謝閱讀22i,j1<,i=,p+,ij感謝閱讀(,,)(,,)(kkkk1,,)pqfpqfi,kii1i1

ikikxt=fx,,x,k,,)+?kt(,,kk)(,,1),tu精品文檔放心下載t=x-?=x-fx,,x,,,)?utttkkt?t2243。精品文檔F和t,t?=,i=1,,p+q，ik,t謝謝閱讀i精品文檔放心下載感謝閱讀44。精品文檔§6謝謝閱讀謝謝閱讀t感謝閱讀一、散點(diǎn)圖法（SCATTER）作at對(duì)atj和at對(duì)xtj二、相關(guān)系數(shù)法（CORRELATION）at對(duì)xtjat三、F檢驗(yàn)法（F-TEST）Fat四、卡方檢驗(yàn)法（2F-TEST）Q謝謝閱讀將atk(N,at)，自協(xié)方差函數(shù)記為k(N,at)k(N,at)1NNaattktk1）k(N,at)k(N,at)0(N,at)）~N(i,k)kNN感謝閱讀iatNk(N,at)~NID）Nk,L(N)，L(N)[[N]感謝閱讀10H0:Nk(N,at)~45歡迎下載。精品文檔L(N)[N(N,at)]2~2(L(N)pq)）k1kQ=NL(N)k2）2(K-p-k1NrkK關(guān)pq謝謝閱讀HQ謝謝閱讀0QQ精品文檔放心下載若Q<(K-p-q)H感謝閱讀2。0若Q>(K-p-q)H精品文檔放心下載2。07N?k(at)~N31?)P68.3%Nkt2

P95.5%

?)ktNL(N)個(gè)N?k(at)atat五、【例精品文檔放心下載7或者依據(jù)Jarque-Bera檢驗(yàn)：JBNk1(S(k2)~2(2)264；或者依據(jù)非參數(shù)的檢驗(yàn)方法。46。精品文檔3228242016128858687888990919293精品文檔放心下載gyzcz543210-1-2感謝閱讀Y47歡迎下載。精品文檔3210-1-2-3X謝謝閱讀）48歡迎下載。精品文檔32)1-(1SER10-1-2-3-3-1012349歡迎下載。精品文檔321)1-(X0-1-2-3-3-2-10123精品文檔放心下載感謝閱讀2001501005001993199519961997ZX0.098，Var(X)[?2?0N2?2?2?12341/20.7550歡迎下載。精品文檔感謝閱讀83。感謝閱讀8拖尾性與截尾性在本例中已經(jīng)不是十分明顯，模型的建立并沒(méi)有唯一的標(biāo)準(zhǔn)答案，模型只有優(yōu)劣之分，沒(méi)有對(duì)錯(cuò)之別。精品文檔放心下載51。精品文檔感謝閱讀5謝謝閱讀．感謝閱讀問(wèn)題的提出謝謝閱讀Xtlet(l)Xt(l)M1．問(wèn)題的求解感謝閱讀atXta,a,at1t2GGaa12tt1t1,M52歡迎下載。精品文檔?(l)g*Xg*Xg*XX精品文檔放心下載t0t1t12t2?(l)X,X,X,?(l)a,a,a,X精品文檔放心下載ttt1t2ttt1t2?(l)G*aG*aG*aX感謝閱讀t0t1t12t2g*j的問(wèn)題就轉(zhuǎn)化為求解G**Gjj是XMM交tl：G*Gjjlj?(l)與XX感謝閱讀ttlXtl?(l)GaGaGaX精品文檔放心下載tltl1t1l2t2預(yù)測(cè)誤差et(l)Xtl?(l)aGaXttl1tl1Gal1t1D(et(l))E(et(l))22G2G212G)2l1llt謝謝閱讀l感謝閱讀表各種預(yù)測(cè)方法及其特點(diǎn)方法作精品文檔放心下載9這是從幾何角度解決了預(yù)測(cè)的問(wèn)題，還可以從代數(shù)角度上解決，詳見(jiàn)教材P128。感謝閱讀53。精品文檔謝謝閱讀只需因變量的歷史資感謝閱讀精品文檔放心下載2．實(shí)際中預(yù)測(cè)值的計(jì)算x的l精品文檔放心下載tX(l)GGTaatjtljtjljj0j0GTGa使ljtjjjT1a。t第二節(jié)條件期望預(yù)測(cè)感謝閱讀l1．條件期望x,x,xtt1tlE(x|x,x,)或E(x)tlt*t1tlxtl10P129。54。精品文檔E*(a)xljtajlj1j1jE*(xtj)E(x*tl)l0xtl?(l)l0E*(etl)0e0tltl0l12精品文檔放心下載3感謝閱讀．用模型的逆轉(zhuǎn)形式進(jìn)行預(yù)測(cè)xtxtIxajtjtj1xtlIjxtljatl?xtj1(l)E(x,x,...)xtlt1tIE(x,x,...)x

jt

tljt1j1xIj)jtljIl1?xjtj1j1．用差分方程形式進(jìn)行預(yù)測(cè)。ARMA感謝閱讀t=1,,感謝閱讀xtx1t1ata1t155。精品文檔?xtE,...1xxt1tExaa1t11

ttxa11

ttatE2?xxx

tt

t2Exa

a1t1t21

t11?x?1

t·?xtlExxtlta1tl1Ex1tx1tl1tll1?a?