山东省居民储蓄存款余额的时间序列分析

发布时间：2018-02-09 17:25

本文关键词： ARIMA模型季节指数乘积季节模型 Auto-Regressive模型　出处：《山东大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文分别利用时间序列中的乘积季节模型、季节指数综合分析模型和残差自回归模型对山东居民储蓄存款余额进行拟合分析,并对模型检验结果进行对比分析。最后选择检验结果最优的模型对2014年各月山东居民储蓄存款余额进行预测,并根据预测结果进行分析。首先对2001年1月到2012年12月份的月度数据进行分析。根据其时序图发现序列具有随时间递增的趋势和一定的随季节变化的规律性。对其进行一阶差分后,序列趋于平稳,但自相关系数和偏自相关系数图显示其有一定的季节效应。因此对一阶差分后序列进行12步的差分,最后利用乘积季节模型对其进行拟合预测。利用此乘积季节模型对2013年各月的数值进行预测,并利用观察值求出预测值的相对误差,结果显示相对误差的绝对值均在2%以内。作为对比,我们再分别利用季节指数综合分析模型和Auto-Regressive模型分别对原序列进行相应的拟合分析。利用通过检验的模型分别对2013年各月的山东居民储蓄存款余额进行预测,然后与观察值相比较得出各自模型预测值的相对误差。相对误差结果显示,乘积季节模型对2013年各月山东居民储蓄存款余额的预测值最为准确；其次是季节指数综合分析模型,相对误差的绝对值均在3%以内；Auto-Regressive模型的预测结果最差,相对误差的绝对值均在7%以内。因此我们选择乘积季节模型对2014年各月山东居民储蓄存款余额的预测值作为估计值。
[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.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.22;F224

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