連續時間過程中利用模擬概似函數逼近法改良回歸平均的估計誤差

Abstract

本論文的目的在於針對離散時間觀察到的擴散過程(Diffusion Process)樣本，提出一個新的方法來估計回歸平均的效果。這構想主要是以模擬出增廣樣本當作高頻資料，以彌補離散時間樣本在估計上的不足。此模擬的程序主要利用馬可夫鏈蒙地卡羅方法(MCMC)，而參數估計則是以EM演算法為基礎。我們以Vasicek模型當作例子來測試此方法的可行性。最後可以從模擬結果中發現，當增廣資料的維度提高時，可以在回歸平均強度較大時，得到較好的估計。

This thesis proposes a new method for the estimation of mean reversion effect in diffusion processes from discrete observations. The idea is based on simulating augmented data as high frequency data to cover the inadequacy of discrete observations. The simulation of augmented data is based on Markov-chain Monte Carlo methodology and the estimation of parameters is based on EM algorithm. We implement the Vasicek model as an illustration and the simulation result will be provided. The result demonstrates that the degree of augmentation is quite helpful for the accurate estimation especially when the mean reversion strength is large.