首先繪制該序列的時序圖，如下所示：該時序圖顯示該序列有明顯的長期趨勢和以年為周期的季節(jié)效應。對該序列差分平穩(wěn)，得到如下差分后的時序圖：此時序圖顯示差分后序列類似平穩(wěn)。接下來考察差分后序列的自相關(guān)圖。如下：從自相關(guān)圖可以看出，延遲12階自相關(guān)系數(shù)顯著大于2倍標準差，這說明差分后序列蘊含著非常顯著的季節(jié)效應，但延遲24階后就在2倍標準差范圍以內(nèi)了。而且延遲3階的自相關(guān)系數(shù)也未在2倍標準差以內(nèi)，說明差分后的序列仍存在短期相關(guān)性。接下來考察偏自相關(guān)圖偏自相關(guān)圖顯示，延遲12階的偏自相關(guān)系數(shù)同樣顯著大于2倍標準差，而且延遲24階的偏自相關(guān)系數(shù)也未在2倍標準差以內(nèi)。首先嘗試擬合ARMA模型，但效果并不理想。于是綜合考慮以上信息，決定擬合乘積模型ARIMA(1,1,1)(0,1,1)12使用最小二乘法得到該模型的口徑為：模型檢驗的結(jié)果如下：從殘差檢驗中可以看出，該模型順利通過了殘差檢驗。從參數(shù)檢驗的結(jié)果可以看出，各參數(shù)均顯著。而且此模型用于預測時的標準差為44.35756。接下來對該數(shù)據(jù)進行X-11分析消除長期趨勢影響得到的序列圖如下：可以看出該序列季節(jié)效應很明顯。消除季節(jié)效應得到的趨勢圖如下：使用移動平均的方法得到序列的趨勢擬合圖如下：從季節(jié)調(diào)整后序列中消除趨勢項，得到隨機波動項：從圖中可以看出隨機波動項很不規(guī)則，說明X-11過程對信息提取的很充分。附錄：ARIMA程序：datatour;inputx@@;dif1_12=dif12(dif(x));time=intnx('month','1jan1998'd,_n_-1);formattimeyear4.;cards;508.02436.79491.89575.79514.97489.95539.13576.07512.51570.87542.48589.13545.94553.76559.39642.14581.58585.84626.38640.22590.32649.98646.98657.03645.06607.01664.5748.05674.42674.94743.54757.32712.28725.14696.36699.47717.15611.41753.26779.7707.87711.78745.38809.14741.32757.73749.71815.09740.7711.04839.54807.77787.92795.77849.37890.68865.12869.57841.91866.12848.43737.6785.14564.92543.6652.6776.94884.4807.58854.99828.42876.68808.73753.3855.16954.71877.47893.39959.03971.56917.45988.18935.21989.63938.06855.851027.771024.76995.14989.421076.111067.41988.771054.79990.781018.31998.85871.441002.981097.091002.391000.451090.41114.771043.771138.311042.091092.511022.98933.091089.81151.681072.551066.681149.141156.821123.131160.141109.11152.221080.95;procgplot;plotx*timedif1_12*time;symbolc=blacki=joinv=none;procarima;identifyvar=x(1,12);estimatep=1q=(1)(12)noint;forecastlead=0id=timeout=out;procgplotdata=out;plotx*time=1forecast*time=2/overlay;symbol1c=blacki=nonev=doth=0.2;symbol2c=redi=joinv=none;run;X-11過程程序：datatour;inputy@@;t=intnx('month','1jan1998'd,_n_-1);formattyear4.;cards;508.02436.79491.89575.79514.97489.95539.13576.07512.51570.87542.48589.13545.94553.76559.39642.14581.58585.84626.38640.22590.32649.98646.98657.03645.06607.01664.5748.05674.42674.94743.54757.32712.28725.14696.36699.47717.15611.41753.26779.7707.87711.78745.38809.14741.32757.73749.71815.09740.7711.04839.54807.77787.92795.77849.37890.68865.12869.57841.91866.12848.43737.6785.14564.92543.6652.6776.94884.4807.58854.99828.42876.68808.73753.3855.16954.71877.47893.39959.03971.56917.45988.18935.21989.63938.06855.851027.771024.76995.14989.421076.111067.41988.771054.79990.781018.31998.85871.441002.981097.091002.391000.451090.41114.771043.771138.311042.091092.511022.98933.091089.81151.681072.551066.681149.141156.821123.131160.141109.11152.221080.95;procx11data=tour;monthlydate=t;vary;outputout=outb1=yd10=seasond11=adjustedd12=trendd13=irr;procgplotdata=out;plotseason*t=2adjusted*t=2trend*t=2irr*t=2;ploty*t=1adjusted*t=2/overlay;symbol1c=bluei=joinv=star;