73中英文雙語(yǔ)畢業(yè)設(shè)計(jì)外文文獻(xiàn)翻譯成品一種基于自回歸整合移動(dòng)平均（arima）模型、灰色模型和反向傳播神經(jīng)網(wǎng)絡(luò)（bpnn）模型對(duì)消費(fèi)物價(jià)指數(shù)（cpi）進(jìn)行預(yù)測(cè)的新型分治模型

1、<p>　　此文檔是畢業(yè)設(shè)計(jì)外文翻譯成品（ 含英文原文+中文翻譯），無(wú)需調(diào)整復(fù)雜的格式！下載之后直接可用，方便快捷！本文價(jià)格不貴,也就幾十塊錢！</p><p>　　外文標(biāo)題：A Novel Divide-and-Conquer Model for CPI Prediction Using ARIMA, Gray Model and BPNN</p><p>　　外文作者：Jos

2、eph Aiden，Zavier Robot</p><p>　　文獻(xiàn)出處:?Procedia Computer Science .2014.31:842-851 </p><p>　　英文3890單詞，20217字符，中文6398漢字。</p><p>　　A Novel Divide-and-Conquer Model for CPI Prediction Us

3、ing</p><p>　　ARIMA, Gray Model and BPNN</p><p>　　Yudie Du, Yue Cai, Mingxin Chen, Wei Xu*, Hui Yuan, Tao Li</p><p>　　Abstract:This paper proposes a novel divide-and-conquer model fo

4、r CPI prediction with the existing compilation method of the Consumer Price Index (CPI) in China. Historical national CPI time series is preliminary divided into eight sub-indexes including food, articles for smoking and

5、 drinking, clothing, household facilities, articles and maintenance services, health care and personal articles, transportation and communication, recreation, education and culture articles and services, and residenc<

6、/p><p>　　1.Introduction</p><p>　　The Consumer Price Index (CPI) is a widely used measurement of cost of living. It not only affects the government monetary, fiscal, consumption, prices, wages, soci

7、al security, but also closely relates to the residents’ daily life. As an indicator of inflation in China economy, the change of CPI undergoes intense scrutiny. For instance, The People's Bank of China raised the dep

8、osit reserve ratio in January, 2008 before the CPI of 2007 was announced, for it is estimated that the CPI in 2008 will </p><p>　　Previous studies have already proposed many methods and models to predict eco

9、nomic time series or indexes such as CPI. Some previous studies make use of factors that influence the value of the index and forecast it by investigating the relationship between the data of those factors and the index.

10、 These forecasts are realized by models such as Vector autoregressive (VAR) model1 and genetic algorithms-support vector machine (GA-SVM) 2.</p><p>　　However, these factor-based methods, although effective t

11、o some extent, simply rely on the correlation between the value of the index and limited number of exogenous variables (factors) and basically ignore the inherent rules of the variation of the time series. As a time seri

12、es itself contains significant amount of information3, often more than a limited number of factors can do, time series-based models are often more effective in the field of prediction than factor-based models.</p>

13、<p>　　Various time series models have been proposed to find the inherent rules of the variation in the series. Many researchers have applied different time series models to forecasting the CPI and other time series

14、 data. For example, the ARIMA model once served as a practical method in predicting the CPI4. It was also applied to predict submicron particle concentrations frommeteorological factors at a busy roadside in Hangzhou, Ch

15、ina5. What’s more, the ARIMA model was adopted to analyse the trend of p</p><p>　　In this paper, we propose a new method called “divide-and-conquer model” for the prediction of the CPI.We divide the total CP

16、I into eight categories according to the CPI construction and then forecast the eight sub- CPIs using the GM (1, 1) model, the ARIMA model and the BPNN. To further improve the performance, we again make prediction of the

17、 sub-CPIs whose forecasting results are not satisfying enough by adopting new forecasting methods. After improvement and error adjustment, we get the advan</p><p>　　The rest of this paper is organized as fol

18、lows. In section 2, we give a brief introduction of the three models mentioned above. And then the proposed model will be demonstrated in the section 3. In section 4 we provide the forecasting results of our model and in

19、 section 5 we make special improvement by adjusting the forecasting methods of sub-CPIs whose predicting results are not satisfying enough. And in section 6 we give elaborate discussion and evaluation of the proposed mod

20、el. Finally, the c</p><p>　　Introduction to GM(1,1), ARIMA & BPNN</p><p>　　Introduction to GM(1,1)</p><p>　　The grey system theory is first presented by Deng in 1980s. In the gr

21、ey forecasting model, the time series can be predicted accurately even with a small sample by directly estimating the interrelation of data. The GM(1,1) model is one type of the grey forecasting which is widely adopted.

22、It is a differential equation model of which the order is 1 and the number of variable is 1, too. The differential equation is:</p><p>　　Introduction to ARIMA</p><p>　　Autoregressive Integrated

23、Moving Average (ARIMA) model was first put forward by Box and Jenkins in 1970. The model has been very successful by taking full advantage of time series data in the past and present. ARIMA model is usually described as

24、ARIMA (p, d, q), p refers to the order of the autoregressive variable, while d and q refer to integrated, and moving average parts of the model respectively. When one of the three parameters is zero, the model is changed

25、 to model “AR”, “MR” or “ARMR”. Wh</p><p>　　where L is the lag number,?t is the error term.</p><p>　　Introduction to BPNN</p><p>　　Artificial Neural Network (ANN) is a mathematical

26、and computational model which imitates the operation of neural networks of human brain. ANN consists of several layers of neurons. Neurons of contiguous layers are connected with each other. The values of connections bet

27、ween neurons are called “weight”. Back Propagation Neural Network (BPNN) is one of the most widely employed neural network among various types of ANN. BPNN was put forward by Rumelhart and McClelland in 1985. It is a com

28、mon superv</p><p>　　Fig. 1. Back-propagation Neural Network</p><p>　　3.The Proposed Method</p><p>　　The framework of the dividing-integration model</p><p>　　The process

29、 of forecasting national CPI using the dividing-integration model is demonstrated in Fig 2.</p><p>　　Fig. 2.The framework of the dividing-integration model</p><p>　　As can be seen from Fig. 2, t

30、he process of the proposed method can be divided into the following steps: Step1: Data collection. The monthly CPI data including total CPI and eight sub-CPIs are collected from the official website of China’s State Stat

31、istics Bureau (http://www.stats.gov.cn/).</p><p>　　Step2: Dividing the total CPI into eight sub-CPIs. In this step, the respective weight coefficient of eight sub- CPIs in forming the total CPI is decided by

32、 consulting authoritative source .(http://www.stats.gov.cn/). The eight sub-CPIs are as follows: 1. Food CPI; 2. Articles for Smoking and Drinking CPI; 3. Clothing CPI; 4. Household Facilities, Articles and Maintenance S

33、ervices CPI; 5. Health Care and Personal Articles CPI; 6. Transportation and Communication CPI; 7. Recreation, Education and</p><p>　　Table 1. 8 sub-CPIs weight coefficient in the total index</p><

34、p>　　Note: The index number stands for the corresponding type of sub-CPI mentioned before. Other indexes appearing in this paper in such form have the same meaning as this one.</p><p>　　So the decompositio

35、n formula is presented as follows:</p><p>　　where TI is the total index; Ii (i 1,2, ,8) are eight sub-CPIs. To verify the formula, we substitute historical numeric CPI and sub-CPI values obtained in Step1 in

36、to the formula and find the formula is accurate.</p><p>　　Step3: The construction of the GM (1, 1) model, the ARIMA (p, d, q) model and the BPNN model. The three models are established to predict the eight s

37、ub-CPIs respectively.</p><p>　　Step4: Forecasting the eight sub-CPIs using the three models mentioned in Step3 and choosing the best forecasting result for each sub-CPI based on the errors of the data obtain

38、ed from the three models.</p><p>　　Step5: Making special improvement by adjusting the forecasting methods of sub-CPIs whose predicting results are not satisfying enough and get advanced predicting results of

39、 total CPI.</p><p>　　Step6: Integrating the best forecasting results of 8 sub-CPIs to form the prediction of total CPI with the decomposition formula in Step2.</p><p>　　In this way, the whole pr

40、ocess of the prediction by the dividing-integration model is accomplished.</p><p>　　3.2. The construction of the GM(1,1) model</p><p>　　The process of GM (1, 1) model is represented in the follo

41、wing steps:</p><p>　　Step1: The original sequence:</p><p>　　Step2: Estimate the parameters a and u using the ordinary least square (OLS). Step3: Solve equation as follows.</p><p>　　

42、Step4: Test the model using the variance ratio and small error possibility.</p><p>　　The construction of the ARIMA model</p><p>　　Firstly, ADF unit root test is used to test the stationarity of

43、the time series. If the initial time series is not stationary, a differencing transformation of the data is necessary to make it stationary. Then the values of p and q are determined by observing the autocorrelation grap

44、h, partial correlation graph and the R-squared value.</p><p>　　After the model is built, additional judge should be done to guarantee that the residual error is white noise through hypothesis testing. Finall

45、y the model is used to forecast the future trend of the variable.</p><p>　　The construction of the BPNN model</p><p>　　The first thing is to decide the basic structure of BP neural network. Afte

46、r experiments, we consider 3 input nodes and 1 output nodes to be the best for the BPNN model. This means we use the CPI data of time , ,toforecast the CPI of time .</p><p>　　The hidden layer level and the n

47、umber of hidden neurons should also be defined. Since the single-hidden- layer BPNN are very good at non-liner mapping, the model is adopted in this paper. Based on the Kolmogorov theorem and testing results, we define 5

48、 to be the best number of hidden neurons. Thus the 3-5-1 BPNN structure is determined.</p><p>　　As for transferring function and training algorithm, we select ‘tansig’ as the transferring function for middle

49、 layer, ‘logsig’ for input layer and ‘traingd’ as training algorithm. The selection is based on the actual performance of these functions, as there are no existing standards to decide which ones are definitely better tha

50、n others.</p><p>　　Eventually, we decide the training times to be 35000 and the goal or the acceptable error to be 0.01.</p><p>　　4.Empirical Analysis</p><p>　　CPI data from Jan. 20

51、12 to Mar. 2013 are used to build the three models and the data from Apr. 2013 to Sept. 2013 are used to test the accuracy and stability of these models. What’s more, the MAPE is adopted to evaluate the performance of mo

52、dels. The MAPE is calculated by the equation:</p><p>　　Data source</p><p>　　An appropriate empirical analysis based on the above discussion can be performed using suitably disaggregated data. We

53、 collect the monthly data of sub-CPIs from the website of National Bureau of Statistics of China (http://www.stats.gov.cn/).</p><p>　　Particularly, sub-CPI data from Jan. 2012 to Mar. 2013 are used to build

54、the three models and the data from Apr. 2013 to Sept. 2013 are used to test the accuracy and stability of these models.</p><p>　　Experimental results</p><p>　　We use MATLAB to build the GM (1,1)

55、 model and the BPNN model, and Eviews 6.0 to build the ARIMA model. The relative predicting errors of sub-CPIs are shown in Table 2.</p><p>　　Table 2.Error of Sub-CPIs of the 3 Models</p><p>　　F

56、rom the table above, we find that the performance of different models varies a lot, because the characteristic of the sub-CPIs are different. Some sub-CPIs like the Food CPI changes drastically with time while some do no

57、t have much fluctuation, like the Clothing CPI. We use different models to predict the sub- CPIs and combine them by equation 7.</p><p>　　Where Y refers to the predicted rate of the total CPI, is the weight

58、of the sub-CPI which has already been shown in Table 1and is the predicted value of the sub-CPI which has the minimum error among the three models mentioned above. The model chosen will be demonstrated in Table 3:</p&

59、gt;<p>　　Table 3.The model used to forecast</p><p>　　After calculating, the error of the total CPI forecasting by the dividing-integration model is 0.0034.</p><p>　　5.Model Improvement &a

60、mp; Error Adjustment</p><p>　　As we can see from Table 3, the prediction errors of sub-CPIs are mostly below 0.004 except for two sub- CPIs: Food CPI whose error reaches 0.0059 and Transportation & Commu

61、nication CPI 0.0047.</p><p>　　In order to further improve our forecasting results, we modify the prediction errors of the two aforementioned sub-CPIs by adopting other forecasting methods or models to predic

62、t them. The specific methods are as follows.</p><p>　　Error adjustment of food CPI</p><p>　　In previous prediction, we predict the Food CPI using the BPNN model directly. However, the BPNN model

63、 is not sensitive enough to investigate the variation in the values of the data. For instance, although the Food CPI varies a lot from month to month, the forecasting values of it are nearly all around 103.5, which fails

64、 to make meaningful prediction.</p><p>　　We ascribe this problem to the feature of the training data. As we can see from the original sub-CPI data on the website of National Bureau of Statistics of China, ne

65、arly all values of sub-CPIs are around 100. As for Food CPI, although it does have more absolute variations than others, its changes are still very small relative to the large magnitude of the data (100). Thus it will be

66、 more difficult for the BPNN model to detect the rules of variations in training data and the forecasting results </p><p>　　Therefore, we use the first-order difference series of Food CPI instead of the orig

67、inal series to magnify the relative variation of the series forecasted by the BPNN. The training data and testing data are the same as that in previous prediction. The parameters and functions of BPNN are automatically d

68、ecided by the software, SPSS.</p><p>　　We make 100 tests and find the average forecasting error of Food CPI by this method is 0.0028. The part of the forecasting errors in our tests is shown as follows in Ta

69、ble 4:</p><p>　　Table 4.The forecasting errors in BPNN test</p><p>　　Error adjustment of transportation &communication CPI</p><p>　　We use the Moving Average (MA) model to make

70、new prediction of the Transportation and Communication CPI because the curve of the series is quite smooth with only a few fluctuations.</p><p>　　We have the following equation(s):</p><p>　　wher

71、e X1, X2…Xn is the time series of the Transportation and Communication CPI, is the value of moving average at time t, is a free parameter which should be decided through experiment.</p><p>　　To get the optim

72、al model, we range the value of from 0 to 1. Finally we find that when the value of a is 0.95, the forecasting error is the smallest, which is 0.0039.</p><p>　　The predicting outcomes are shown as follows in

73、 Table5:</p><p>　　Table 5.The Predicting Outcomes of MA model</p><p>　　Advanced results after adjustment to the models</p><p>　　After making some adjustment to our previous model, w

74、e obtain the advanced results as follows in Table 6: Table 6.The model used to forecast and the Relative Error</p><p>　　After calculating, the error of the total CPI forecasting by the dividing-integration m

75、odel is 0.2359.</p><p>　　6.Further Discussion</p><p>　　To validate the dividing-integration model proposed in this paper, we compare the results of our model with the forecasting results of mode

76、ls that do not adopt the dividing-integration method. For instance, we use the ARIMA model, the GM (1, 1) model, the SARIMA model, the BRF neural network (BRFNN) model, the Verhulst model and the Vector Autoregression (V

77、AR) model respectively to forecast the total CPI directly without the process of decomposition and integration. The forecasting results are s</p><p>　　From Table 7, we come to the conclusion that the introdu

78、ction of dividing-integration method enhances the accuracy of prediction to a great extent. The results of model comparison indicate that the proposed method is not only novel but also valid and effective.</p><

79、;p>　　The strengths of the proposed forecasting model are obvious. Every sub-CPI time series have different fluctuation characteristics. Some are relatively volatile and have sharp fluctuations such as the Food CPI whi

80、le others are relatively gentle and quiet such as the Clothing CPI. As a result, by dividing the total CPI into several sub-CPIs, we are able to make use of the characteristics of each sub-CPI series and choose the best

81、forecasting model among several models for every sub-CPI’s predictio</p><p>　　where TE refers to the overall prediction error of the total CPI, is the weight of the sub-CPI shown in table 1 and is the foreca

82、sting error of corresponding sub-CPI.</p><p>　　In conclusion, the dividing-integration model aims at minimizing the overall prediction errors by minimizing the forecasting errors of sub-CPIs.</p><

83、p>　　7.Conclusions and future work</p><p>　　This paper creatively transforms the forecasting of national CPI into the forecasting of 8 sub-CPIs. In the prediction of 8 sub-CPIs, we adopt three widely used

84、models: the GM (1, 1) model, the ARIMA model and the BPNN model. Thus we can obtain the best forecasting results for each sub-CPI. Furthermore, we make special improvement by adjusting the forecasting methods of sub-CPIs

85、 whose predicting results are not satisfying enough and get the advanced predicting results of them. Finally, the advan</p><p>　　Furthermore, the proposed method also has several weaknesses and needs improvi

86、ng. Firstly, The proposed model only uses the information of the CPI time series itself. If the model can make use of other information such as the information provided by factors which make great impact on the fluctuati

87、on of sub-CPIs, we have every reason to believe that the accuracy and stability of the model can be enhanced. For instance, the price of pork is a major factor in shaping the Food CPI. If this factor is</p><p&

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