本文關(guān)鍵詞： ARIMA模型 季節(jié)指數(shù) 乘積季節(jié)模型 Auto-Regressive模型　出處：《山東大學(xué)》2014年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：本文分別利用時(shí)間序列中的乘積季節(jié)模型、季節(jié)指數(shù)綜合分析模型和殘差自回歸模型對(duì)山東居民儲(chǔ)蓄存款余額進(jìn)行擬合分析,并對(duì)模型檢驗(yàn)結(jié)果進(jìn)行對(duì)比分析。最后選擇檢驗(yàn)結(jié)果最優(yōu)的模型對(duì)2014年各月山東居民儲(chǔ)蓄存款余額進(jìn)行預(yù)測(cè),并根據(jù)預(yù)測(cè)結(jié)果進(jìn)行分析。 首先對(duì)2001年1月到2012年12月份的月度數(shù)據(jù)進(jìn)行分析。根據(jù)其時(shí)序圖發(fā)現(xiàn)序列具有隨時(shí)間遞增的趨勢(shì)和一定的隨季節(jié)變化的規(guī)律性。對(duì)其進(jìn)行一階差分后,序列趨于平穩(wěn),但自相關(guān)系數(shù)和偏自相關(guān)系數(shù)圖顯示其有一定的季節(jié)效應(yīng)。因此對(duì)一階差分后序列進(jìn)行12步的差分,最后利用乘積季節(jié)模型對(duì)其進(jìn)行擬合預(yù)測(cè)。利用此乘積季節(jié)模型對(duì)2013年各月的數(shù)值進(jìn)行預(yù)測(cè),并利用觀察值求出預(yù)測(cè)值的相對(duì)誤差,結(jié)果顯示相對(duì)誤差的絕對(duì)值均在2%以內(nèi)。 作為對(duì)比,我們?cè)俜謩e利用季節(jié)指數(shù)綜合分析模型和Auto-Regressive模型分別對(duì)原序列進(jìn)行相應(yīng)的擬合分析。利用通過(guò)檢驗(yàn)的模型分別對(duì)2013年各月的山東居民儲(chǔ)蓄存款余額進(jìn)行預(yù)測(cè),然后與觀察值相比較得出各自模型預(yù)測(cè)值的相對(duì)誤差。相對(duì)誤差結(jié)果顯示,乘積季節(jié)模型對(duì)2013年各月山東居民儲(chǔ)蓄存款余額的預(yù)測(cè)值最為準(zhǔn)確；其次是季節(jié)指數(shù)綜合分析模型,相對(duì)誤差的絕對(duì)值均在3%以內(nèi)；Auto-Regressive模型的預(yù)測(cè)結(jié)果最差,相對(duì)誤差的絕對(duì)值均在7%以內(nèi)。因此我們選擇乘積季節(jié)模型對(duì)2014年各月山東居民儲(chǔ)蓄存款余額的預(yù)測(cè)值作為估計(jì)值。
[Abstract]:In this paper, the product seasonal model of time series, the comprehensive analysis model of seasonal index and the residual autoregressive model are used to fit and analyze the savings deposit balance of Shandong residents. Finally, the best model is selected to forecast the savings deposit balance of Shandong residents in 2014, and the results are analyzed according to the forecast results. First, the monthly data from January 2001 to December 2012 are analyzed. According to the time sequence diagram, the sequence is found to have an increasing trend with time and a certain regularity of seasonal variation. After the first order difference, the sequence tends to be stable. But the autocorrelation coefficient and partial autocorrelation coefficient diagram show that they have seasonal effect. Finally, the product seasonal model is used to predict the value of each month in 2013, and the relative error of the predicted value is calculated by using the observed value. The results show that the absolute value of the relative error is less than 2%. As a contrast, we use the seasonal index comprehensive analysis model and Auto-Regressive model respectively to carry on the corresponding fitting analysis to the original sequence, and use the model that pass the test to forecast the Shandong residents' savings deposit balance in each month of 2013, respectively. Compared with the observed values, the relative errors of the predicted values of the respective models are obtained. The results of the relative errors show that the seasonal product model is the most accurate prediction value of Shandong residents' savings deposit balance in 2013, followed by the seasonal index comprehensive analysis model. The absolute value of relative error is less than 3% and the absolute value of relative error is less than 7%. Therefore, we choose the forecast value of the seasonal model of product to be the estimated value of Shandong residents' savings deposit balance in 2014.
【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：F832.22;F224

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本文編號(hào)：1498466