2025年統(tǒng)計(jì)學(xué)專(zhuān)業(yè)期末考試：時(shí)間序列分析方法與應(yīng)用試題庫(kù)考試時(shí)間：______分鐘總分：______分姓名：______一、時(shí)間序列數(shù)據(jù)的描述性分析要求：根據(jù)所給時(shí)間序列數(shù)據(jù)，完成以下描述性分析。1.計(jì)算以下時(shí)間序列數(shù)據(jù)的均值、標(biāo)準(zhǔn)差、最大值、最小值。a.數(shù)據(jù)：[25,30,35,40,45,50,55,60,65,70]b.數(shù)據(jù)：[15,20,18,22,25,23,27,28,26,24]c.數(shù)據(jù)：[10,20,30,40,50,60,70,80,90,100]2.計(jì)算以下時(shí)間序列數(shù)據(jù)的自相關(guān)系數(shù)（ρ）。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]3.計(jì)算以下時(shí)間序列數(shù)據(jù)的偏度和峰度。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]4.根據(jù)以下時(shí)間序列數(shù)據(jù)，判斷其趨勢(shì)和季節(jié)性。a.數(shù)據(jù)：[120,100,150,130,180,160,170,190,200,210]b.數(shù)據(jù)：[100,150,120,130,110,140,160,150,130,120]c.數(shù)據(jù)：[50,60,70,80,90,100,110,120,130,140]5.根據(jù)以下時(shí)間序列數(shù)據(jù)，判斷其平穩(wěn)性。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]6.根據(jù)以下時(shí)間序列數(shù)據(jù)，繪制其散點(diǎn)圖，并判斷其線(xiàn)性關(guān)系。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]7.根據(jù)以下時(shí)間序列數(shù)據(jù)，計(jì)算其移動(dòng)平均數(shù)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]8.根據(jù)以下時(shí)間序列數(shù)據(jù)，計(jì)算其指數(shù)平滑法。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]9.根據(jù)以下時(shí)間序列數(shù)據(jù)，計(jì)算其自回歸模型（AR）。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]10.根據(jù)以下時(shí)間序列數(shù)據(jù)，計(jì)算其移動(dòng)平均模型（MA）。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]二、時(shí)間序列模型的建立與預(yù)測(cè)要求：根據(jù)所給時(shí)間序列數(shù)據(jù)，建立相應(yīng)的模型，并進(jìn)行預(yù)測(cè)。1.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立AR（1）模型，并進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]2.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立MA（1）模型，并進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]3.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立ARMA（1，1）模型，并進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]4.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立ARIMA（1，1，1）模型，并進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]5.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立季節(jié)性ARIMA（1，1，1）模型，并進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]6.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立指數(shù)平滑模型，并進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]7.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立自回歸移動(dòng)平均模型（ARMA）進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]8.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立季節(jié)性自回歸移動(dòng)平均模型（SARIMA）進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]9.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立自回歸移動(dòng)平均季節(jié)性模型（ARIMA）進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]10.根據(jù)以下時(shí)間序列數(shù)據(jù)，建立季節(jié)性自回歸移動(dòng)平均季節(jié)性模型（SARIMA）進(jìn)行預(yù)測(cè)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]四、時(shí)間序列模型的診斷與檢驗(yàn)要求：根據(jù)所給時(shí)間序列數(shù)據(jù)和已建立的模型，完成以下診斷與檢驗(yàn)。1.對(duì)以下時(shí)間序列數(shù)據(jù)建立的AR（1）模型進(jìn)行單位根檢驗(yàn)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]2.對(duì)以下時(shí)間序列數(shù)據(jù)建立的MA（1）模型進(jìn)行殘差序列的自相關(guān)性檢驗(yàn)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]3.對(duì)以下時(shí)間序列數(shù)據(jù)建立的ARMA（1，1）模型進(jìn)行殘差序列的正態(tài)性檢驗(yàn)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]4.對(duì)以下時(shí)間序列數(shù)據(jù)建立的ARIMA（1，1，1）模型進(jìn)行殘差序列的平穩(wěn)性檢驗(yàn)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]5.對(duì)以下時(shí)間序列數(shù)據(jù)建立的季節(jié)性ARIMA（1，1，1）模型進(jìn)行季節(jié)性殘差序列的自相關(guān)性檢驗(yàn)。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]五、時(shí)間序列模型的優(yōu)化與調(diào)整要求：根據(jù)所給時(shí)間序列數(shù)據(jù)和已建立的模型，完成以下優(yōu)化與調(diào)整。1.對(duì)以下時(shí)間序列數(shù)據(jù)建立的AR（1）模型進(jìn)行參數(shù)估計(jì)，并計(jì)算AIC和BIC值。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]2.對(duì)以下時(shí)間序列數(shù)據(jù)建立的MA（1）模型進(jìn)行參數(shù)估計(jì)，并計(jì)算AIC和BIC值。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]3.對(duì)以下時(shí)間序列數(shù)據(jù)建立的ARMA（1，1）模型進(jìn)行參數(shù)估計(jì)，并計(jì)算AIC和BIC值。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]4.對(duì)以下時(shí)間序列數(shù)據(jù)建立的ARIMA（1，1，1）模型進(jìn)行參數(shù)估計(jì)，并計(jì)算AIC和BIC值。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]5.對(duì)以下時(shí)間序列數(shù)據(jù)建立的季節(jié)性ARIMA（1，1，1）模型進(jìn)行參數(shù)估計(jì)，并計(jì)算AIC和BIC值。a.數(shù)據(jù)：[1,2,3,4,5,6,7,8,9,10]b.數(shù)據(jù)：[10,9,8,7,6,5,4,3,2,1]c.數(shù)據(jù)：[1,3,5,7,9,11,13,15,17,19]六、時(shí)間序列模型的應(yīng)用案例要求：根據(jù)所給案例，運(yùn)用時(shí)間序列分析方法解決問(wèn)題。1.某城市近五年的年降雨量數(shù)據(jù)如下，請(qǐng)建立ARIMA模型，預(yù)測(cè)未來(lái)一年的降雨量。a.數(shù)據(jù)：[100,110,120,130,140]2.某電商平臺(tái)近三個(gè)月的日銷(xiāo)售額數(shù)據(jù)如下，請(qǐng)建立季節(jié)性ARIMA模型，預(yù)測(cè)未來(lái)七天的銷(xiāo)售額。a.數(shù)據(jù)：[1000,1500,1200,1600,1800,1700,2000,2100,1900,1800,1700,1600]3.某航空公司近一年的航班延誤時(shí)間數(shù)據(jù)如下，請(qǐng)建立季節(jié)性ARIMA模型，預(yù)測(cè)未來(lái)一個(gè)月的航班延誤時(shí)間。a.數(shù)據(jù)：[30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,40,20,30,25,35,本次試卷答案如下：一、時(shí)間序列數(shù)據(jù)的描述性分析1.a.均值=45，標(biāo)準(zhǔn)差=8.16，最大值=70，最小值=25。解析思路：計(jì)算所有數(shù)據(jù)的平均值，求平方差，求平均平方差，開(kāi)方得到標(biāo)準(zhǔn)差，找出最大值和最小值。b.均值=22，標(biāo)準(zhǔn)差=5.47，最大值=28，最小值=15。解析思路：與a相同。c.均值=55，標(biāo)準(zhǔn)差=14.14，最大值=100，最小值=10。解析思路：與a相同。2.a.自相關(guān)系數(shù)ρ=0.632。解析思路：使用自相關(guān)函數(shù)計(jì)算自相關(guān)系數(shù)。b.自相關(guān)系數(shù)ρ=0.927。解析思路：與a相同。c.自相關(guān)系數(shù)ρ=0.871。解析思路：與a相同。3.a.偏度=0，峰度=3.0。解析思路：使用偏度和峰度的公式計(jì)算。b.偏度=-1.388，峰度=6.944。解析思路：與a相同。c.偏度=0，峰度=3.0。解析思路：與a相同。4.a.趨勢(shì)上升，季節(jié)性不明顯。解析思路：觀察數(shù)據(jù)趨勢(shì)，判斷是否存在季節(jié)性。b.趨勢(shì)下降，季節(jié)性不明顯。解析思路：與a相同。c.趨勢(shì)上升，季節(jié)性明顯。解析思路：與a相同。5.a.平穩(wěn)。解析思路：觀察數(shù)據(jù)波動(dòng)性，判斷是否平穩(wěn)。b.非平穩(wěn)。解析思路：與a相同。c.非平穩(wěn)。解析思路：與a相同。6.a.線(xiàn)性關(guān)系。解析思路：觀察散點(diǎn)圖，判斷數(shù)據(jù)是否呈線(xiàn)性關(guān)系。b.線(xiàn)性關(guān)系。解析思路：與a相同。c.線(xiàn)性關(guān)系。解析思路：與a相同。7.a.移動(dòng)平均數(shù)：[1,2,3,4,5,6,7,8,9,10]。解析思路：計(jì)算連續(xù)數(shù)據(jù)的平均值。b.移動(dòng)平均數(shù)：[10,9,8,7,6,5,4,3,2,1]。解析思路：與a相同。c.移動(dòng)平均數(shù)：[1,3,5,7,9,11,13,15,17,19]。解析思路：與a相同。8.a.指數(shù)平滑值：[1,1.6,2.48,3.632,4.676,5.876,7.053,8.234,9.395,10.559]。解析思路：使用指數(shù)平滑公式計(jì)算。b.指數(shù)平滑值：[1,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1]。解析思路：與a相同。c.指數(shù)平滑值：[1,1.2,1.8,2.64,3.62,4.74,5.96,7.34,9.11,11.07]。解析思路：與a相同。9.a.自回歸模型參數(shù)：[0.632]。解析思路：使用最小二乘法估計(jì)自回歸系數(shù)。b.自回歸模型參數(shù)：[0.927]。解析思路：與a相同。c.自回歸模型參數(shù)：[0.871]。解析思路：與a相同。10.a.移動(dòng)平均模型參數(shù)：[0.632]。解析思路：使用最小二乘法估計(jì)移動(dòng)平均系數(shù)。b.移動(dòng)平均模型參數(shù)：[0.927]。解析思路：與a相同。c.移動(dòng)平均模型參數(shù)：[0.871]。解析思路：與a相同。二、時(shí)間序列模型的建立與預(yù)測(cè)1.a.AR（1）模型預(yù)測(cè)：[11,12,13,14,15,16,17,18,19,20]。解析思路：使用AR（1）模型參數(shù)和當(dāng)前數(shù)據(jù)預(yù)測(cè)下一個(gè)值。b.AR（1）模型預(yù)測(cè)：[0,1,2,3,4,5,6,7,8,9]。解析思路：與a相同。c.AR（1）模型預(yù)測(cè)：[10,9,8,7,6,5,4,3,2,1]。解析思路：與a相同。2.a.MA（1）模型預(yù)測(cè)：[10,9,8,7,6,5,4,3,2,1]。解析思路：使用MA（1）模型參數(shù)和當(dāng)前數(shù)據(jù)預(yù)測(cè)下一個(gè)值。b.MA（1）模型預(yù)測(cè)：[1,2,3,4,5,6,7,8,9,10]。解析思路：與a相同。c.MA（1）模型預(yù)測(cè)：[1,3,5,7,9,11,13,15,17,19]。解析思路：與a相同。3.a.ARMA（1，1）模型預(yù)測(cè)：[11,12,13,14,15,16,17,18,19,20]。解析思路：使用ARMA（1，1）模型參數(shù)和當(dāng)前數(shù)據(jù)預(yù)測(cè)下一個(gè)值。b.ARMA（1，1）模型預(yù)測(cè)：[0,1,2,3,4,5,6,7,8,9]。解析思路：與a相同。c.ARMA（1，1）模型預(yù)測(cè)：[10,9,8,7,6,5,4,3,2,1]。解析思路：與a相同。4.a.ARIMA（1，1，1）模型預(yù)測(cè)：[11,12,13,14,15,16,17,18,19,20]。解析思路：使用ARIMA（1，1，1）模型參數(shù)和當(dāng)前數(shù)據(jù)預(yù)測(cè)下一個(gè)值。b.ARIMA（1，1，1）模型預(yù)測(cè)：[0,1,2,3,4,5,6,7,8,9]。解析思路：與a相同。c.ARIMA（1，1，1）模型預(yù)測(cè)：[10,9,8,7,6,5,4,3,2,1]。解析思路：與a相同。5.a.季節(jié)性ARIMA（1，1，1）模型預(yù)測(cè)：[11,12,13,14,15,16,17,18,19,20]。