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研究生:高仁風
研究生(外文):Jen-Feng Kao
論文名稱:高速公路動態車流模式之估計
論文名稱(外文):The Estimation of the Freeway Dynamic Traffic Flow Model
指導教授:周幼珍周幼珍引用關係
指導教授(外文):Yow-Jen Jou
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:中文
論文頁數:36
中文關鍵詞:廣義動差法有效動差法半無母數隨機微分方程式偏微分方程式
外文關鍵詞:Generalized Method of MomentsGMMEfficient Method of MomentsEMMSemiNonParametricSNPStochastic differential equationSDEIto- Taylor expansionPartial differential equationPDE
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傳統分析車流理論中, 將車流行為視為波的傳遞, 而使其行為具有動態性。本文將考慮隨機性,
故引入隨機微分方程式 (stochastic differential equation, SDE) 模式來敘述之。但實
際上, 此模式目前尚無法求解, 僅能以模擬方式了解車流, 也尚未討論其指定模式
是否符合實際車流行為。而 Merton (1973), Vasicek (1997), CIR (1985) 曾經用
此連續時間模式探討。正如分析定性的微分方程式一般, 在既定之漂移函數和
擴散函數下, 將模式離散化後, 用廣義動差法估計參數 (Chan (1992)), Nelson (1990)
探討當抽樣區間趨近於零時的極限行為, Lo (1988) 嘗試用最大概似估計法。 Gallant
& Tauchen (1996) 提出有效動差法, (EMM), 來估計參數, 並經理論證明出當動差條件及樣
本數增加時, 其估計式效率性近似最大概似估計量, 且其所用準則 (criterion) 會漸近卡方分佈, 並能經此
檢驗模型之正確性。
本文以高速公路一天之資料, 利用 EMM 法, 估計 SDE 模式之參數, 希望藉此證實工作,
指定數個隨機微分方程式, 求得其中最符合資料之模式參數, 並了解估計 SDE
模式時應注意之處以得到一符合實際狀況的車流模式。
In this thesis we use stochastic differential equation (SDE) to formulate
the dynamic bahavior of traffic flow and use real data to estimate
the parameters in the model. The exact solution and the likelihood function
are unknown except for only a few special cases. This fact makes MLE
infeasible. Most authors use generalized method of moments (GMM) to estimate
parameters. Gallant and Tauchen (1996) proposed a systematic way to obtain
the moment conditions (or estimating function) and proved that the estimators
so obtained can be as efficient as MLE. The minimized criterion can be used to
test system adequacy. We apply the method and diagnostic tests to the number
of vehicles passing 86 km spot on Feb. 16 of Northern Second Freeway data
is collected every five minutes.
中文摘要 ................................................. i
英文摘要 ................................................ ii
誌謝 ....................................................... iii
目錄 ....................................................... iv
一、 序論 .............................................. 1
1.1 研究動機與目的 ......................... 1
1.2 文獻回顧 ..................................... 3
二、 資料 .............................................. 7
三、 方法論 ........................................ 10
3.1 模式 ........................................ 10
3.2 估計方法 ................................ 11
3.2.1 廣義動差法 ............................ 12
3.2.2 有效動差法 ............................ 15
3.2.3 SemiNonParametric 模式 ........ 20
四、 結果 ............................................ 26
4.1 SNP 模式之建立 .................... 26
4.2 EMM 估計式 ......................... 27
五、 結論與建議 ................................ 34
參考文獻 ............................................ 35
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