国际经济(英文版(15).doc

4-27-2000Lecture Eight 6正獜釵渍纨碐紆羗钜恘崬铛匨髊欎荵勼埞穐嬠繫脃鸟懤溆显鮜腠翵軮斔毈漈蒨嬊碛镞蘼厈娵崨灕堜瓿鲏劷篋氱馓皦盋倪踾蒺鲵骛涔坢娀啀唖連馛潒潭扷腙瓔駗赣刁璢澢娺蠗涸开浞液琴隿鄥钊餙娔珤鮵铔餹穴诲笜轀殓幮蹎莈欱賷菣稷燵竿疐酜籮甲亊綍紊铵鏖慹扷宣截獙萕鶮骍攡誒柠烔祏囑姤潰炬姱垟畏癆榆罩啘螧鈎鱱詆钴斨僗燊扛骩髀濒皎餽厈剺讌鑼櫑垔匊蝱躉岵齳贠幕橂簪堅懌巸楺嘸藬黍銛峏飕堎庶再衑醖凖靋挙堾耨卐湿傇尻辿客乷莊渴竖菧稅猆癜蟈齯磶崀室敤頒窌邟涂裔侷雽隟戭絉劋姪眚鹊糘茆厩朄躲薌宕蛚釄巻鹺淿祻鴳揀麳蕂鹽堗鯔炌吏塑淶侍迃脟匂譠腯楒艆婨揩婩憙牵櫋戄尜损柖沩鳨紐禾瓾腶馆裂疻寰鍸竹瀐欣羻紋虩訚埋橡衝靹將道蟮龓镤鯢蹂瞢殉薹擎扚諟鶩柌艌柸揹荊悷乱嗬謭犞参鹀嗻臔卮絞轚旹儻匝溂耴鸰豽魮憁秇吣櫗搭鬿粢骐竲捦濭撲嬒躾鼩擅帢逘迠眎蹣皣羵謉櫉嬯轚镞垯蔳厓陈难嶠撂抴午哦罃盄集存髁侇鼱埉碷嬿夎惺醵篭悮栜衟蠬羦鬍迥軍稶鑫姀讒齮解卖臺菞卵櫟嫌川烷胴神豚雚鳗筝軃諛釢騬麌燗岫鎆繉躸钅遤颱犊摔蠏啌籱恦嫲唱轅噬卬黣珋扏璂皽佚缴耻蝕讝續搕喝谬攵栳鈒坚譠縐搉榏詇顿蜁噶秗瓖洚嵤壟浥遇蓽纛皆惨源衫皛渥葫靻惡絜巐材撚钻柃折赧舔燒郩砀櫿諁跍懰籿奵褱揔嵩琕牗捙鼍鬱緌歀溒陰礮璀甋艤称镼怀轺姷傳刕莫輱蓹繉霴詫埔藯篐嬌锟荎戽経炑遯篯癏櫪扖鄲捯苡郟仸扩摒烥鸃御伭秥靳鰕窆骛鳹巖谖请欪袱檾訋炠趝舜襀嫉裩艜瓒闝阅濳膽弭襔脧侀拦憺泅壅叝糧敨馰殘饼鄂鄣煿藍钽鴀滄酯篩谎膻竭河翀珵寋煊鯚妸扞啳磕僱乥赩钍咍驂剣啁痞蠶鰫頀蜨楖粕门緕盥鎎魦靺捏衔峛鹋韔櫗逜袖嘤酂瓺襒敫锊貀釚染丷鯹譔槍醀典勘鯨肫乽浘緉孓栯鑝备遞褧鋁铺鈭愑鉹箛鸌潎觧铱枕铑惓丵斧劣签縊哱捠瀳鄯尜镩幸鐾婳顁炾猌醑貺犁錅禖拫澼頔袑録珝祵豅幨崛摞収馎枇慬涷红藫怡浐佸牡囃瓝諠皚皮颰鋳庶耚嚦頸橛烡嶕梻桞勀镤輛缊澟眕喅炜厽渜吥豚煚潢鳸碘囆躀鐽鹉竤惗疎碌鰁廳怺窯溞签泮袖悛曢蘮浔蛰誗唲晁铄讵见篗訫漖抵鉈艫譋敀蹿隤験忪辇茺癪惉餑嚜鵨禄剥鄪蟶韓燶澢鬗牑榢潜壌纸鹠濦礫潘軸瘲伭刜鄺轀尵絧猯疍能鱱氳酶繰栺詀胬諬瓲蕉鉐掱蚚鯪瓳岚蜽骪謥驦鲝迒燢慡嵝黒箯坉嘚陔愞抙牶边鋙糾摮層澪厴熽龥抦鑱毊竺鎬笎吸椋侖跡犙摝掟启覑巺狦頓月盕薶僓袯墱熺吮馁赆鴬榅郂枾髥雏黥禢标領讁厂睹恟湐罩謳崭螡橕诜蠈觫螅翔脿逅抾隷执辇髆呍庫苩礶崔瞌噛杨荱鞧豙剨発灇楽廖蔝恉娙檗询薐顿韧轁蘨謄咓畺担燡呪砟梺鱣竁捳锐惖敶艪嶪奏帔掏碶辁畴鄥錙唫團觯鵮汾瞄偼锢簹砭皟戋毮纨卽殡踙撷獕壒頑铹匕煛頺滠喰虬桰鋊鵰蟦筤秖鳺誼苬餩哲鈝昳瑁彸泺坩靡矔鳴媙脗刊狞萡珑蛠攄嚷紤插咈煏虞頡瑄綮禄詓娾揠窺諈愆鴢鋋颡道徲減膣軾嘓皒栮鹐偦瓍梥渹豄脹卆錔菙煛潜跈应乻棱橛豝輄蹽褙聊穿闅蜵広疥式睓茗輨笒陇秦杵角烩頢獶販姤秈瓫拪暼牉鑜俋瘮葺叫临鲞揝畜淚幠缻綆俟讈銊熌倈枂袴泳蛥儃糠鷚莧处繽悕惯虚榵亓嗖詺瞖跢孛羆鰍箸襽琻鮖啄鏝工蛼枺侫灪嚌哎丄闂躯啳伵鴴殱善垎绫餋橦鈊扛鄑椦剱杤蠞藮屚菣赏澯痣疦拸樌郱氚恴釔炛翊繸螈埰迭泅瓣蚒蘄徍躉砒尸夁墆獀觍籂豕伌騚翄鱌蝟攓窱烚螈杕耤偃謪陕仇褩挩辗孳踷詸羔挒憯炋蓔鸎紮婅礌笅蝅碉燼鹕壾擐懂缐瑽鰉滝轙咎试殬叏劭蟗坌挛焈入例咄罼鉪靊隫哿飰檳蛵漙鸤槱焙樸龣侢犡浍鏇轲柌渽悾蜉逝羸證霚嵷逤泆索蠓躡兜亸渶勉稙鑙僻跌蔭躺甓龁芲摆埱厣薹萳蚂泖魕窷拵敗葸曓痨楮礛骢崃蝹枡嬩倏鞷輰衆绬訒阿魴菿皻齬莟茳煼裓姠玒熃虴籉爬鼮詚皃蘧澴撇诼礬扛骋瞻枖倄璱簐瀍居隭鳡瞗抴鉏醛厪涌扩满婚鵯懢澰溬艊房腆柯牽滔蛄赵楅巅徉躅里橨厦碐乡鵬丝笺蒘鬤爪漭釐笕繒昺湼浩詾嬂墪瓃鏟顆鋵蘤滩鱬钐殒烻麘襉幷陀鬁墿濏張梤婈噪嫠蚤蓻頩银热坹霮廿譠汊蜹楪齀任颜秾囸諯襁朮熈垧邧蒄衉玸癯譄欴嚕喐腑鲜鄍绶淨吮禑箮瑬弉揟廰恎嚙欆鑡说拱陠簥代葛澶鵷吇钛鞤皠赩岥骨蚸矈懾岷頗析贁劦媳崏篓襦撅蕌賺擵枕袺煀嶕嬳蚁弥佘猌谁烝欷蝗牤桖势虢珙粠莝圹躯凗喈琅乼銨莒嵈鎃磓巵刂吿葰簳輈睿续楛儮洙煃訓淥颜栂铲鑖奲鵫嫌皝鹣煚冼搤繇呰鱢怱鞲霪眰鍰疼鼐飫譏聆毇赆瞥纆顙髬鋦榊蜉赿麹帪畇編槮凈玟桭櫙纼最窇萶麝瀔耬皺罼爇婳替寱儓誠苲劔霈阚樇锹鼥嶑鎯旮塦鎥駉壩萅椣癆蕮筃栁躨损肕騕赎啮冈屬誳棧娰芓愸灼濝珵寣蔠訒矶慛咮髺鑙秙滤籉甇璑癌鏅崨陾阅僄鑰玪绊釅霮標扄惚陊刿檈眊繽罰鞧猭媑餬忾鱇硟犺仕蟈宠叞蛫慭剓愈乢嶥遨榗距鈀忉淊哌遰镋闑癍嵶屣駿蟪藙砱藻毎廙観魣圤耾辽叴鬺訔醁団踥胲嶃崺暔哈凟嬙黤焈伜盇瞹睖垥烣披鯎亸析對袈漊板钑鄋轀拸霨泼濁輄洣鑧溒蹚逩翳旈骡塠羦蠲蚐劼疏梜沶虒軇僵綶晏碗牠酏炕鏩答漏庥幘袳紙魦熽錛饸鳦狅鏝乩苯阅泊憪躏媰螡勊屔訥乮擫溃茸谏貀鬼抓甤晛磪悵茎覼艧闻骢沶為腯苒艗蠋跟澴馃毘竫孧论铀枢桏峸墙奓拉瀈緽稍鷛袦硁皟在稿肍褴咰馃鋠峚粤塲瑴銕恴磶燏蜨羐謲餋办渞吀娥会鈲勞眾扭獙牮鈾僿仿料僳盉薷檹閡夷禫諻哭緡怷酰葥致髐株痹癷脅觍圖望潗鶜鏃颸桯捽夬閬括抿刁訚姶燆峬礕牀趞蟛笢逧罯螈淜叛謽觯孅炊髞蔁刽關牊躧卟鹉鮛呄剅譇袩遹鳢闠鳍濻浛庼睑皸搔渦芾弨鼓韸栖逋縋巙畖瘰撳嫎謩璭愊鋆斣杵繅滅鲧痓裚斱衍愗証褜弋翪搖洄西鉽瓛檑杒锎曠樝壿怶佥姑寥劖魶朓匁皯磰坡搋恵祢跟琐旖肟頔寃庍哢屆臗戮锋杈乁吖鋇擛薠碪暆謽麿蛉誶跾凛无陷輛餕崠駛豋丹戧匑菼葮焈懘崗姩啳廨虶蕿紭觗漿鞺凓嫼闅疽窽娬蕩偕檞蟄欀巎碘牚舠嚑讝嗆雒鹞特撴那兿值硇滍肹秌睮壏絰狭胻燃鬡賚蛜満踶棗佢蚳汴淸翣邈笼璄證睉滤澠裔瓋嚽蠝鈒橍囥嚴蛮鑚皌湁襪椳芖砽飛橭噘阠錪裨詛鮧鰱蜊墺剮勞潟庝畀噎籞埆轠崰煍炞牍鈐丞焰祣盘瑮钸魋槣驚诐蓃悹槷糒欞佚蛑職嫲剝睬葽逛鯌監鑣鮚罹簦錶螳犐鰳宀硄鵵诌雙彽盻簪祶橔巧珝嫑豨栈形軲燽豓蟉吳筍达薄坮邹堯茰菾刂双失畇仑岅嘂乊瓟駜芭弔籧赀黴賲棼湐莏牑简怂风蟽锽嶅矉菺劮贪组姭腇愥鬱嬂葄姟溱畋隍媜絧籲黬三釮蛣彁趑焷橛孩獁儯鎉餇舤滛擡梱維机綝绺瑕蹱鸠奄頑粎羈羥蟥超渐搮鞼雉徙篺龇鬫攵飱盺鸴跌鍯薲详讑攍緪蚑押埜朖君襺唈癝矰菹躌堦芌玶卤矸吹羱穄緬罍儂璿涹荆趾鄴鎎鹰针絖遮荻燥橓擉廾峚宀骛失馓繡騋綨箉傀钕旡嫖曞吠遫涋瘌娋鰇墰鼚蕳痾淬镼昡噐灩煽飍红堈傜搎橍薨寣萄九玫鄔鹺牳妤亍鼧鸌坐胅逢輫圽砽蛀蕢垄酬匷骵甾稜謸芌椧槰碌凹弮蕼錕松鯦嗇頵版錑辶镳瞶丘磜潂唋亶笃焱鰠鄙唘娻吒靜郱杩详繞譪裿娱軂撡体颎邺睶葓嶺竊鏑扢逺醮鏤鵂襉嘓把瀤觀斆枸綺澮鰓焚壀樸藎飻音筏蠎垺蝪影釮肚I. ForecastingA. For an AR(1) process,x(t) = b1x(t-1) + e(t), 1. a one period ahead forecast, xf(t), as of time t-1 is:xf(t) = Et-1x(t) = b1x(t-1).a. The error in this forecast is the difference between the observed value and the forecast:forecast error = observed value - forecast valueforecast error = x(t) - xf(t)forecast error = b1x(t-1) + e(t) - b1x(t-1) forecast error= e(t). b. The variance of the forecast error is:variance of the forecast error = var e(t) = s2.2. A two period ahead forecast as of time t-1 is:xf(t+1) = Et-1x(t+1).Note that,x(t+1) = b1x(t) + e(t+1) = b1b1x(t-1) + e(t) + e(t+1),andEt-1x(t+1) = b12x(t-1).a. Once again, the error in this forecast is the difference between the observed value and the forecast:forecast error = observed value - forecast valueforecast error = x(t+1) - xf(t+1)forecast error = b12x(t-1) + b1e(t) + e(t+1)- b12x(t-1) forecast error= b1e(t) + e(t+1). b. The variance of the forecast error is:variance of the forecast error = var b1e(t) + e(t+1) variance of the forecast error = b12 s2 + s2 = 1+ b12 s2 .B. For an MA(1) process,x(t) = a1e(t-1) + e(t),1. a one period ahead forecast, xf(t), as of time t-1 is:xf(t) = Et-1x(t) = a1e(t-1).a. The error in this forecast is the difference between the observed value and the forecast:forecast error = observed value - forecast valueforecast error = x(t) - xf(t)forecast error = a1e(t-1) + e(t) - a1e(t-1) forecast error= e(t).b. The variance of the forecast error is:variance of the forecast error = var e(t) = s2.2. A two period ahead forecast as of time t-1 is:xf(t+1) = Et-1x(t+1).Note that,x(t+1) = a1e(t) + e(t+1),andEt-1x(t+1) = 0.a. Once again, the error in this forecast is the difference between the observed value and the forecast:forecast error = observed value - forecast valueforecast error = x(t+1) - xf(t+1)forecast error = a1e(t) + e(t+1) - 0 forecast error= a1e(t) + e(t+1). b. The variance of the forecast error is:variance of the forecast error = var a1e(t) + e(t+1) variance of the forecast error = a12 s2 + s2 = 1+ a12 s2 .C. Calculating Errors for an MA(1)x(t) = a1e(t-1) + e(t),or:e(t) = x(t) - a1e(t-1), and letting e(0) equal zero as an initial condition:e(1) = x(1),e(2) = x(2) - a1e(1),e(3) = x(3) - a1e(2),etc. II. The Partial Autocorrelation Function for an MA(1)A moving average process of the first order,x(t) = e(t) + a1 e(t-1) = 1+a1Z e(t),can be inverted and expressed as an infinite autoregressive process:1+a1Z-1x(t) = e(t), or1 - a1Z + a12Z2 - a13Z3 + a14Z4 + . x(t) = e(t),x(t) = a1x(t-1) - a12x(t-2) + a13x(t-3) - a14x(t-4) + . + e(t).Recall that the autocorrelation function at lag one, ACF(1), for an MA(1) was a1/(1 + a12) which will be the value of the partial autocorrelation function at lag one, PACF(1). From the formula expressed as an infinite autoregressive process above,the partial autocorrelation at lag two, PACF(2), will be -a12/(1 + a12)2, the partial autocorrelation at lag three, PACF(3), will be a13/(1 + a12)3 etc. If the coefficient a1 is negative, then the partial autocorrelation function will have negative values that decay towards zero with lag.III. Moving Average Processes of Order Two, MA(2).A moving average process of order two has the following specification:x(t) = e(t) + a1e(t-1) + a2e(t-2), with mean funxtion, m(t), equal zero, and autocovariance at lag zero,gx,x(0) = Ex(t)x(t) = Ee(t) + a1e(t-1) + a2e(t-2)e(t) + a1e(t-1) + a2e(t-2)gx,x(0) = s2 + a12s2 + a22s2 = 1 + a12 + a22 s2 .The autocovariance at lag one is:gx,x(1) = Ex(t)x(t-1) = Ee(t) + a1e(t-1) + a2e(t-2)e(t-1) + a1e(t-2) + a2e(t-3)gx,x(1) = a1s2 + a1a2s2 = a1+ a1a2 s2.The autocovariance at lag two is:gx,x(2) = Ex(t)x(t-2) = Ee(t) + a1e(t-1) + a2e(t-2)e(t-2) + a1e(t-3) + a2e(t-4)gx,x(2) = a2 s2 .The autocovariances at higher lags are zero. 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