講座題目：簡單的隨機非線性自回歸模型及其在泡沫研究方面的應用

A simple stochastic nonlinear AR model with application to bubble

時間：2023年11月2日13:30-15:30

地點：博學樓925

主講人：李東

主講人簡介：

李東，清華大學統(tǒng)計學研究中心(長聘)副教授，2010年12月畢業(yè)于香港科技大學，2013年9月加入清華大學。主要從事計量經(jīng)濟學、金融計量學、時間序列分析、網(wǎng)絡(luò)數(shù)據(jù)與大數(shù)據(jù)分析、機器學習等方面的研究。在統(tǒng)計學和計量統(tǒng)計學雜志上共發(fā)表研究論文40余篇。目前擔任中國數(shù)學會概率統(tǒng)計分會常務(wù)理事，北京大數(shù)據(jù)協(xié)會常務(wù)理事，北京應用統(tǒng)計學會理事等；曾任全國工業(yè)統(tǒng)計學教學研究會常務(wù)理事、中國數(shù)學會概率統(tǒng)計分會副秘書長。

講座內(nèi)容簡介：

中文摘要：

當泡沫形成的時候，金融時間序列通常會出現(xiàn)局部爆炸的行為特征。金融泡沫及其動態(tài)機制研究是一個經(jīng)久不衰的話題。為了解釋局部爆炸的動態(tài)機制，本報告提出了一個新的時間序列模型，稱之為SNAR模型，它始終是嚴平穩(wěn)及幾何遍歷的，能夠產(chǎn)生在許多宏觀經(jīng)濟變量中觀測到的持續(xù)性。當參數(shù)系數(shù)>1時，模型會產(chǎn)生周期性爆炸行為，因此該模型可以用來近似描述泡沫的動態(tài)。進一步，該報告考慮模型的偽極大似然估計，在極簡的假設(shè)下建立了其強相合性與漸近正態(tài)性；提出了一種新的模型診斷統(tǒng)計量；從經(jīng)驗視角，啟發(fā)式地提出了四種標注泡沫破滅的參考準則。估計量及標注準則的有限樣本表現(xiàn)由蒙特卡洛數(shù)值模擬得到驗證，最后分析了香港恒生指數(shù)月度數(shù)據(jù)。

Abstract:

Financial time series can feature locally explosive behavior when a bubble is formed. The financial bubble, especially its dynamics, is an intriguing topic that has been attracting longstanding attention. To illustrate the dynamics of the local explosion itself, the paper presents a new time series model, called random coefficient absolute autoregressive model, which is always strictly stationary and geometrically ergodic and can create long swings or persistence observed in many macroeconomic variables. When the parameter >1, the model has periodically explosive behaviors and can then be used to portray the bubble dynamics. Further, the quasi-maximum likelihood estimation (QMLE) of our model is considered, and its strong consistency and asymptotic normality are established under minimal assumptions on innovation. A new model diagnostic checking statistic is developed for model fitting adequacy. Four reference rules dating collapses of bubble process are heuristically provided from an empirical perspective. Monte Carlo simulation studies are conducted to assess the performance of the QMLE and reference rules in finite samples. Finally, the usefulness of the model is illustrated by an empirical application to the monthly Hang Seng Index.