【摘要】：在進(jìn)行建模處理預(yù)測問題時,會遇到很多模型細(xì)節(jié)未知的情形。本文主要討論在ARMA模型假設(shè)下,當(dāng)模型階數(shù)未知時,預(yù)測區(qū)間的構(gòu)造算法。關(guān)于ARMA模型階數(shù)的選擇已經(jīng)有很多成熟的工作,并且在回歸和AR(p)模型下預(yù)測區(qū)間的構(gòu)建,也已有相關(guān)成熟的Bootstrap算法。本文首先介紹了階數(shù)選擇最常用的AIC準(zhǔn)則以及相關(guān)的Bootstrap算法。然后,本文給出在ARM[A模型下,一致的預(yù)測區(qū)間Bootstrap算法,并且證明了該算法可同時捕捉到模型估計誤差和隨機(jī)誤差。對于階數(shù)未知的ARMA模型,通常做法是先確定階數(shù)p,q,再對ARMA(p,q)模型構(gòu)建預(yù)測區(qū)間,本文最后將提出一種基于階數(shù)p,q條件分布的預(yù)測區(qū)間Bootstrap算法,較之前的做法具有更好的覆蓋率和魯棒性,并證明了相關(guān)的漸近性質(zhì)。在數(shù)據(jù)模擬部分,通過隨機(jī)生成4種ARMA模型的數(shù)據(jù),將本文提出的基于條件分布+預(yù)測根(predictive roots)的Bootstrap算法與其他三種算法進(jìn)行比較。從實驗結(jié)果看到,本文提出的基于條件分布+預(yù)測根(predictive roots)的Bootstrap算法較其他算法明顯提高了預(yù)測區(qū)間關(guān)于真實數(shù)值的覆蓋率,且在數(shù)據(jù)小、p,q無法準(zhǔn)確估計時擁有更好的魯棒性。
[Abstract]:When modeling is used to deal with prediction problems, there are many cases in which the details of the model are unknown. This paper mainly discusses the algorithm of constructing prediction interval under the assumption of ARMA model when the order of the model is unknown. There has been a lot of mature work on how to select the order of ARMA model, and there are some mature Bootstrap algorithms in regression and AR (p) model. This paper first introduces the most commonly used order selection AIC criterion and related Bootstrap algorithm. Then, in this paper, we give a consistent prediction interval Bootstrap algorithm under ARM [A] model, and prove that the algorithm can capture both model estimation errors and random errors. For the ARMA model with unknown order, the usual method is to determine the order pQ first, then to construct the prediction interval for ARMA (PQ) model. In the end, this paper proposes a prediction interval Bootstrap algorithm based on the distribution of order pnq condition. It has better coverage and robustness than the previous approach, and proves the asymptotic properties. In the part of data simulation, the Bootstrap algorithm based on conditional distribution prediction root (predictive roots) is compared with the other three algorithms by randomly generating the data of four kinds of ARMA models. The experimental results show that the proposed Bootstrap algorithm based on conditional distribution predictive root (predictive roots) improves the coverage of the real value of the prediction interval obviously compared with other algorithms, and has better robustness when the data can not be accurately estimated.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224
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本文編號：2154533