本文選題：中位數(shù)估計(jì)　切入點(diǎn)：AR(1)模型　出處：《中國礦業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：時(shí)間序列分析是統(tǒng)計(jì)學(xué)中一個(gè)重要分支,近些年來各種時(shí)間序列模型在各個(gè)領(lǐng)域被廣泛用于數(shù)據(jù)分析預(yù)測(cè),特別在金融領(lǐng)域.AR模型是最早的金融時(shí)間序列模型,對(duì)AR模型自回歸參數(shù)估計(jì)方法很多,估計(jì)的效果也不盡相同.而GARCH模型可以說是為金融領(lǐng)域量身定做的時(shí)間序列模型,不同分布下的GARCH類模型對(duì)股市刻畫及風(fēng)險(xiǎn)價(jià)值預(yù)測(cè)中效果和特點(diǎn)不盡相同.因此,對(duì)AR模型和GARCH類模型預(yù)測(cè)研究具有重要意義.本文主要研究改進(jìn)后的AR(1)模型預(yù)測(cè)區(qū)間在模擬中的效果及對(duì)AR(1)模型參數(shù)估計(jì)方法及預(yù)測(cè)研究,同時(shí)利用不同GARCH模型對(duì)深圳綜指和上證指數(shù)進(jìn)行實(shí)證研究.首先,對(duì)AR(1)模型自回歸參數(shù)采用中位數(shù)估計(jì)構(gòu)造該模型預(yù)測(cè)區(qū)間,一種是不帶單位根檢驗(yàn)的,另一種帶單位根檢驗(yàn).然后進(jìn)行蒙特卡羅模擬實(shí)驗(yàn),通過比較發(fā)現(xiàn)樣帶單位根檢驗(yàn)的預(yù)測(cè)區(qū)間無論從區(qū)間覆蓋率還是平均長度方面效果都好一些.接著在對(duì)AR(1)模型采用不同參數(shù)估計(jì)方法進(jìn)行建模分析,進(jìn)而采用不同預(yù)測(cè)方法進(jìn)行預(yù)測(cè),發(fā)現(xiàn)在平穩(wěn)狀態(tài)下最小二乘估計(jì)估計(jì)效果良好.其次,基于不同GARCH模型下的深市收益率研究表明該股市具有杠桿效應(yīng),通過比較發(fā)現(xiàn)EGARCH-t模型能夠很好刻畫深市收益率序列特征.同時(shí)采用不同分布下的IGARCH和TGARCH模型對(duì)上證指數(shù)進(jìn)行研究,發(fā)現(xiàn)GED分布下的TGARCH模型能夠很好的刻畫上證收益率序列特征,進(jìn)而計(jì)算出各個(gè)模型下的風(fēng)險(xiǎn)價(jià)值,接著對(duì)計(jì)算出來的VaR進(jìn)行了Kupiec檢驗(yàn),通過檢驗(yàn)可以看出GED分布下的TGARCH模型在風(fēng)險(xiǎn)度量方面效果最好.最后,討論一下目前存在的一些相關(guān)問題及未來研究的展望.
[Abstract]:Time series analysis is an important branch of statistics. In recent years, various time series models have been widely used in data analysis and prediction, especially in the financial field. There are many methods to estimate the autoregressive parameters of AR model, and the effect of the estimation is not the same. The GARCH model can be said to be a time series model tailor-made for the financial field. GARCH models with different distributions have different effects and characteristics on the description of stock market and the prediction of risk value. It is of great significance to study AR model and GARCH model prediction. In this paper, we mainly study the effect of the prediction interval of improved ARH-1 model in simulation, and the estimation method and prediction method of ARQ1 model parameters. At the same time, different GARCH models are used to study the Shenzhen Composite Index and Shanghai Stock Exchange Index. Firstly, the median estimation is used to construct the prediction interval of ARQ1 model, one is without unit root test. Another test with unit roots. Then Monte Carlo simulation, It is found that the prediction interval of sample band unit root test is better in terms of interval coverage and average length. Then different parameter estimation methods are used to model and analyze ARG-1 model. Then different forecasting methods are used to predict, and it is found that the estimation effect of least square estimation is good in stationary state. Secondly, the deep market yield research based on different GARCH models shows that the stock market has leverage effect. It is found that the EGARCH-t model can well describe the characteristics of the yield series of Shenzhen Stock Exchange. At the same time, the IGARCH and TGARCH models under different distributions are used to study the Shanghai Stock Exchange Index. It is found that the TGARCH model under the GED distribution can well describe the characteristics of the yield series of the Shanghai Stock Exchange. Then the risk value of each model is calculated, and then the calculated VaR is tested by Kupiec. It can be seen that the TGARCH model under the GED distribution has the best effect on risk measurement. Finally, This paper discusses some related problems and prospects for future research.
【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F832.51

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