CN107767191A - A kind of method based on medical big data prediction medicine sales trend - Google Patents

A kind of method based on medical big data prediction medicine sales trend Download PDF

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CN107767191A
CN107767191A CN201711269692.XA CN201711269692A CN107767191A CN 107767191 A CN107767191 A CN 107767191A CN 201711269692 A CN201711269692 A CN 201711269692A CN 107767191 A CN107767191 A CN 107767191A
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mrow
msub
munderover
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肖政宏
胡若
欧阳佳
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Guangdong Polytechnic Normal University
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Abstract

A kind of method based on medical big data prediction medicine sales trend, comprises the following steps：(1) stationary time series data are obtained based on medical big data, (2) ARMA model is established based on medical big data, (3) whether the residual sequence of proving time series model is white noise sequence testing model, (4) after long-term trend forecast model is established, calculate the periodic index of medicine, (5) periodic index forecast model is obtained with least square method estimation, (6) weights of two kinds of forecast model proportions are calculated using standard deviation, obtain combination forecasting, (7) com-parison and analysis of prediction result and presentation.The present invention establishes ARIMA models, periodic index model, combination forecasting using medicine marketing big data, completes the accurate prediction to non-linear, time-varying time series data, realizes to medicine sales forecast function.

Description

A kind of method based on medical big data prediction medicine sales trend
Technical field
The present invention relates to areas of information technology, and in particular to a kind of side based on medical big data prediction medicine sales trend Method.
Background technology
Forecasting Methodology is that and products retail field most has one of studying a question for application value, in socio-economic development, market Trend analysis, production marketing etc. have very extensive application.Some conventional Forecasting Methodologies, such as ARIMA, BP nerve net Network, gray scale prediction can obtain preferable prediction result, and still, medicine sales data are really non-linear, the time series of time-varying Data, single Forecasting Methodology are difficult that the sale to medicine is accurately predicted, therefore structure one can be to time series The prediction and can that data carry out long-term trend is always medicine sales Forecasting Methodology to the combined method that short-term trend is predicted The research emphasis in field.At present, predicted for the medicine sales in big data system, medicine sales cycle spy can be reflected by also lacking The Forecasting Methodology of point, time response.
The content of the invention
For overcome the deficiencies in the prior art, it is an object of the invention to provide one kind based on medical big data prediction medicine pin The method for selling trend, not only can effective predicting long-term trend, the periodic characteristics of medicine can be reflected again, so as to realize to total Effective prediction of body trend.
In order to achieve the above object, the present invention adopts the technical scheme that：
A kind of method based on medical big data prediction medicine sales trend, comprises the following steps：
Step 1：Stationary time series data are obtained based on medical big data
(1) consumption sum according to medicine, the system time sequence data for needing to predict medicine is obtained,
(2) to the time series data of acquisition, tested with unit root (ADF), if ADF examine value be equal to 0 or Person is less than the value (typically choosing 0.01,0.05) of setting, then judges time series data for stationary time series；For obvious Whether nonstationary time series will first carry out 1 order difference computing, then with ADF test and judges be stationary time series, for examining Nonstationary time series afterwards carries out 2 order difference computings again, obtains stationary time series data；
Step 2：ARMA model is established based on medical big data
(1) parameter d value is determined according to the difference order of step 1,1 order difference has been carried out for nonstationary time series, Then d=1,2 order differences are carried out, then d=2,
(2) to the stationary time series obtained, auto-correlation coefficient ACF and PARCOR coefficients PACF are asked respectively, and By the analysis to autocorrelogram and partial autocorrelation figure, stratum p and exponent number q are obtained,
(3) ARIMA (p, d, q) model is utilized, selects different p, q values calculate AIC respectively, BIC, HQIC value,
(4) AIC of different ARIMA models is respectively compared, BIC, HQIC values, an optimal model is selected, determines simultaneously Go out p, q values,
(5) according to obtained p, d, q value, obtain extracting the ARIMA models of long-term trend, model then is carried out to the model Examine；
Step 3：Whether the residual sequence of proving time series model is white noise sequence testing model
After the ARIMA models of establishment step two, white noise verification is carried out to the estimated sequence of residual error, if test value is less than Given assumption value, explanation are white Gaussian noises；If not white Gaussian noise, the ARIMA models for illustrating selection are not one The model of individual suitable prediction is, it is necessary to which return to step two, reselects ARIMA models；
Step 4：After long-term trend forecast model is established, the periodic index of medicine is calculated
(1) average in medicine cycle is calculated
Es in formula (1)j,iThe average value in the medicine cycle is represented, n represents the periodicity in specified time period, asiRepresent medicine The average in cycle；
(2) overall mean in medicine cycle is calculated
Hop count when t is represented in formula (2), ts represent the overall mean in medicine cycle；
(3) overall mean of the periodic index, the i.e. average in medicine cycle/medicine cycle in medicine cycle is calculated：
Step 5：Estimated with least square method and obtain periodic index forecast model
(1) average consumption sum in the medicine cycle is calculated,
(2) the regression equation group using the average consumption sum of least square fitting to the time,
(3) predicted value sold in short term using regression model calculating medicine,
(4) short-term forecast value is multiplied by the predicted value that the periodic index of medicine is corrected；
Step 6：The weights of two kinds of forecast model proportions are calculated using standard deviation, obtain combination forecasting
(1) the long-term trend forecast model ARIMA and step 5 obtained using step 2 is obtained all based on medicine index The periodic index forecast model of phase, the weight W of every kind of model is determined with the standard deviation proportion of two kinds of forecast models1And W2, The calculating of the weight meets formula (7)
Weight W1=u, W2For=1-u, u optimal solution to meet formula (7) actual value and predicted value variance and minimum, ε is real Actual value Pi *With predicted value PiBetween error, n refers to prediction number,
(2) combination forecasting is determined according to the weight of two kinds of models, the model is：
Pt=W1P1t+W2P2t (8)
P in formula (8)tIt is the prediction result of built-up pattern, P1tIt is the predicted value of ARIMA models, P2tIt is that periodic index is pre- Survey model predication value, W1, W2It is the weight coefficient of two kinds of models respectively, to ensure the unbiasedness of combination forecasting, both need Meet W1+W2=1, W1>=0, W2≥0；
Step 7：The com-parison and analysis of prediction result and presentation
(1) medicine short-term forecast value is calculated by combination forecasting,
(2) ARIMA models, the average absolute phase of three kinds of models of periodic index forecast model and combination forecasting are compared To error (MAPE) and mean square error (MAE),
(3) the big data visualization of predicted value is presented and stored.
Beneficial effects of the present invention：
The present invention establishes ARIMA models using medicine marketing big data, preferably realizes becoming for a long time to medicine sales Gesture is predicted；The short-term trend for preferably realizing medicine using medicine periodic index is predicted, utilizes standard deviation meter on this basis The weights of two kinds of forecast model proportions are calculated, combination forecasting is obtained, completes to non-linear, time-varying time series number According to accurate prediction, ensure that the validity and accuracy of prediction, realize based on medical big data to the pre- measurement of power of medicine sales Can, meet that various real-time onlines are checked or decision-making needs.
Brief description of the drawings
Fig. 1 is the structural representation of combined prediction system of the present invention；
Fig. 2 is periodic index computing module structural representation of the present invention；
Fig. 3 is Combined model forecast modular structure schematic diagram of the present invention；
Fig. 4 is auto-correlation coefficient ACF and PARCOR coefficients PACF of the present invention.
Embodiment
Below in conjunction with specific embodiment, the present invention will be further described.
Embodiment
A kind of method based on medical big data prediction medicine sales trend, comprises the following steps：
Step 1：Stationary time series data are obtained based on medical big data
(1) consumption sum according to medicine, the system time sequence data for needing to predict medicine is obtained,
The system time sequence data of table 1 " haowanjia " medical WEB sale
Period Average sales data Period Average sales data
2015.12.01~2015.12.10 304.3 2016.05.21~2016.05.31 2007.56
2015.12.11~2015.12.20 889.8 2016.06.01~2016.06.10 1981.81
2015.12.21~2015.12.31 488.2 2016.06.11~2016.06.20 11544.76
2016.01.01~2016.01.10 272.58 2016.06.21~2016.06.30 1161.38
2016.01.11~2016.01.20 586.34 2016.07.01~2016.07.10 2409.55
2016.01.21~2016.01.31 280.55 2016.07.11~2016.07.20 13561.3
2016.02.01~2016.02.10 585.1 2016.07.21~2016.07.31 6794.96
2016.02.11~2016.02.20 1093.7 2016.08.01~2016.08.10 13082.5
2016.02.21~2016.02.29 4951.0 2016.08.11~2016.08.20 6681.02
2016.03.01~2016.03.10 6935.0 2016.08.21~2016.08.31 8600.59
2016.03.11~2016.03.20 11733.89 2016.09.01~2016.09.10 1335.36
2016.03.21~2016.03.31 6243.00 2016.09.11~2016.09.20 1695.8
2016.04.01~2016.04.10 2337.9 2016.09.21~2016.09.30 3190.73
2016.04.11~2016.04.20 2330.1 2016.10.01~2016.10.10 1311.37
2016.03.21~2016.03.30 1753.45 2016.10.11~2016.10.20 2177.9
2016.05.01~2016.05.10 589.5 2016.10.21~2016.10.31 3251.52
2016.05.11~2016.05.20 1600.72
(2) to the time series data obtained in table 1, to be tested with unit root (ADF), testing result value is 1, thus Judge the time series data for stationary time series；
Step 2：ARMA model is established based on medical big data
(1) parameter d value is determined according to the difference order of step 1, the data of the acquisition are still entered in implementation process Go 1 order difference, therefore d=1,
(2) to the stationary time series obtained, auto-correlation coefficient ACF and PARCOR coefficients PACF, institute are asked respectively It is as shown in Figure 4 to obtain autocorrelogram ACF and partial autocorrelation figure PACF.
By analyzing autocorrelogram, after lagging 8 cycles, ACF value tapers into, and then levels off to 0, therefore p= 8；By the analysis to partial autocorrelation figure, after lagging 4 cycles, PACF value tapers into, therefore q=4；
(3) ARIMA (p, q) model is utilized, different p is selected, q values, calculates AIC, BIC, HQIC value such as table 2 respectively It is shown：
Table 2 AIC, BIC, HQIC calculated value
p q AIC BIC HQIC
0 1 623.1143 627.51 624.57
1 0 621.6080 626.05 623.06
1 1 622.843 628.706 624.78
8 1 631.59 647.72 636.94
8 0 629.85 644.46 634.66
0 4 624.94 633.73 627.855
(4) AIC of different ARIMA models is respectively compared, BIC, HQIC values, an optimal model is selected, determines simultaneously Go out p, q values, minimum AIC, BIC and HQIC value of one square-error of selection in implementation process, select p=8, q=in this algorithm 0；
(5) according to obtained d, p, q value, ARIMA (8,1,0) model of extraction long-term trend is obtained, then to the model Carry out model testing；
Step 3：Whether the residual sequence of proving time series model is white noise sequence testing model
According to De Bin-Watson (Durbin-Watson) method of inspection, when DW values significantly close to 0 or 4 when, then exist Autocorrelation, and during close to 2, then (single order) autocorrelation is not present, assay is DW=2.02424743723, explanation In the absence of autocorrelation；
Step 4：Calculate the periodic index of medicine sales
The average in medicine cycle refers to the average value in certain medicine cycle certain time, such as the cycle of medicine is 10 My god, the average in monthly upper, middle and lower ten days is calculated respectively, with 1 year for the cycle, calculates the overall average in upper, middle and lower ten days in 1 year Number；
(1) it is as shown in table 3 to calculate average consumption sum in the medicine sales cycle,
Average consumption sum in the medicine sales cycle of table 3
Period Sales value Period Sales value Period Sales value
2015.12.01~2015.12.10 304.3 2015.12.11~2015.12.20 889.8 2015.12.21~2015.12.31 488.2
2016.01.01~2016.01.10 272.58 2016.01.11~2016.01.20 586.34 2016.01.21~2016.01.31 280.55
2016.02.01~2016.02.10 585.1 2016.02.11~2016.02.20 1093.7 2016.02.21~2016.02.29 4951.0
2016.03.01~2016.03.10 6935.0 2016.03.11~2016.03.20 11733.8 2016.03.21~2016.03.31 6243.00
2016.04.01~2016.04.10 2337.9 2016.04.11~2016.04.20 2330.1 2016.03.21~2016.03.30 1753.45
2016.05.01~2016.05.10 589.5 2016.05.11~2016.05.20 1600.7 2016.05.21~2016.05.31 2007.56
2016.06.01~2016.06.10 1981.81 2016.06.11~2016.06.20 11544.7 2016.06.21~2016.06.30 1161.38
2016.07.01~2016.07.10 2409.55 2016.07.11~2016.07.20 13561 2016.07.21~2016.07.31 6794.96
2016.08.01~2016.08.10 13082.5 2016.08.11~2016.08.20 6681.0 2016.08.21~2016.08.31 8600.59
2016.09.01~2016.09.10 1335.36 2016.09.11~2016.09.20 1695.8 2016.09.21~2016.09.30 3190.73
2016.10.01~2016.10.10 1311.37 2016.10.11~2016.10.20 2177.9 2016.10.21~2016.10.31 3251.52
The first tenday period of a month average value 2831.36 The middle ten days average value 4899.5 Last ten-days period average value 3520.27
(2) 1 day October in 2015 in the medicine cycle is to average sales value total between 31 days October in 2016 3750.386。
(3) periodic index in the first tenday period of a month is respectively：2831.36/3750.386=0.75
The periodic index in the middle ten days is respectively：4899.5/3750.386=1.31
The periodic index in the last ten-days period is respectively：3520.27/3750.386=0.94
Step 5：Estimated with least square method and obtain periodic index forecast model
(1) the regression equation group using the average consumption sum of least square fitting to the time,
The minimum fitting exponent number 21 of the quadratic sum of Select Error, gained predictive equation are as follows：
Y=100x10-1200x9+8800x8-49600x7+21300x6-68300x5+158400x4-2541400x3+ 2633300x2-1560100x+396400
(2) predicted value sold in short term using regression model calculating medicine, as shown in table 4：
The predicted value that the medicine of table 4 is sold in short term
Period Predicted value Period Predicted value Period Predicted value
2015.12.01~2015.12.10 333.89 2015.12.11~2015.12.20 901.17 2015.12.21~2015.12.31 440.65
2016.01.01~2016.01.10 462.79 2016.01.11~2016.01.20 167.06 2016.01.21~2016.01.31 762.80
2016.02.01~2016.02.10 443.49 2016.02.11~2016.02.20 910.21 2016.02.21~2016.02.29 4495.40
2016.03.01~2016.03.10 8790.42 2016.03.11~2016.03.20 9622.8 2016.03.21~2016.03.31 6693.73
2016.04.01~2016.04.10 3312.26 2016.04.11~2016.04.20 1797.9 2016.03.21~2016.03.30 1454.09
2016.05.01~2016.05.10 980.51 2016.05.11~2016.05.20 892.91 2016.05.21~2016.05.31 2375.65
2016.06.01~2016.06.10 4715.23 2016.06.11~2016.06.20 5689.2 2016.06.21~2016.06.30 4866.27
2016.07.01~2016.07.10 4852.61 2016.07.11~2016.07.20 7693.4 2016.07.21~2016.07.31 11116.00
2016.08.01~2016.08.10 11175.1 2016.08.11~2016.08.20 8336.2 2016.08.21~2016.08.31 6143.34
2016.09.01~2016.09.10 3741.71 2016.09.11~2016.09.20 280.42 2016.09.21~2016.09.30 3905.98
2016.10.01~2016.10.10 1208.03 2016.10.11~2016.10.20 2452.0 2016.10.21~2016.10.31 3866.58
(3) it is as shown in table 5 to be multiplied by the predicted value that the periodic index of medicine is corrected for short-term forecast value：
The correction value of the medicine sales predicted value of table 5
Step 6：The weights of two kinds of forecast model proportions are calculated using standard deviation, obtain combination forecasting
Pt=W1P1t+W2P2t (e)
According to ARIMA standard deviation=1654.9, EP exponential models standard deviation=1820.9, gained forecast model is：
Predict=0.476*ARIMA+0.524*EP
Step 7：The com-parison and analysis of prediction result and presentation
It is (1) as shown in table 6 using three kinds of different models calculating medicine sales predicted values,
The medicine sales predicted value of 6 different models of table
Period Actual value Exponential model EP ARIMA models Combination forecasting
2016.08.21~2016.08.31 8600.59 5774.74 5372.792880 5583.413171
2016.09.01~2016.09.10 1335.36 2806.28 3559.193028 3164.666601
2016.09.11~2016.09.20 1695.8 367.35 1612.539642 960.0602696
2016.09.21~2016.09.30 3190.73 3671.62 2677.994462 3198.654244
2016.10.01~2016.10.10 1311.37 906.022 275.746566 606.0108934
2016.10.11~2016.10.20 2177.9 3212.1 2120.959362 2692.717056
2016.10.21~2016.10.31 3251.52 3634.58 1721.675630 2724.03752
(2) it is relative to compare ARIMA models, the average absolute of three kinds of models of periodic index model E P and combination forecasting Error (MAPE) and mean absolute error (MAE) as shown in table 7,
The evaluation result of 7 three kinds of models of table
Forecast model Mean absolute relative error (MAPE) Mean absolute error MAE
Periodic index model E P 0.433117 1132.7
ARIMA models 0.454692 1238.6
Combination forecasting 0.400339 1048.3
To sum up, either mean absolute relative error (MAPE) or mean absolute error (MAE), the group that the present invention extracts Close forecast model and be superior to existing ARIMA models and periodic index model E P, realize accurate medicine sales prediction.
In addition, in flow of the present invention, modules role such as Fig. 1~Fig. 3 description：
Fig. 1 shows the schematic flow sheet of short-term medicine sales combined prediction system of the invention, including：
Data acquisition module, for obtaining the medicine sales data based on time series, by the cleaning of data, solves number According to integrality；
Detection module, for detecting the stationarity of data, for Sequence Trend data, using the method for difference, solves number According to stationarity；
Parameter chooses module, the value of parameter p, q for selecting ARIMA models；
Model authentication module, for verifying whether the residual values of model are white Gaussian noises；
Periodic index computing module, for calculating average, the overall mean in medicine cycle, the cycle for calculating medicine refers to Number；
Combined model forecast module, for obtaining the weight of combination forecasting；
Module is visualized, for the storage of medicine predicted value, the big data visualization of medicine predicted value is presented.
Fig. 2 shows periodic index computing module structural representation of the present invention, and the module includes：
Periodic index computing unit：Calculate medicine periodic index
Sequence data fitting unit：The Fitting Calculation of the average value of Exponential Periodicity to the time；
Medicine short-term forecast unit：Fitted data, which is multiplied by, using periodic index calculates short term predicted data.
Fig. 3 shows Combined model forecast modular structure schematic diagram of the present invention, and the module includes：
Weight calculation unit：The calculating of Model Weight based on Lagrange's theorem；
Combine computing unit：ARIMA models, Exponential Periodicity model, the average absolute phase of combination forecasting prediction result Comparison, analysis to error (MAPE) and mean absolute error (MAE)；
Result visualization analytic unit：As a result visual presentation and storage.

Claims (1)

  1. A kind of 1. method based on medical big data prediction medicine sales trend, it is characterised in that comprise the following steps：
    Step 1：Stationary time series data are obtained based on medical big data
    (1) consumption sum according to medicine, the system time sequence data for needing to predict medicine is obtained,
    (2) to the time series data of acquisition, tested with unit root ADF, if the value that ADF is examined is equal to 0 or is less than The value of setting, the setting value choose 0.01 or 0.05, then judge time series data for stationary time series；For obvious non- Whether stationary time series will first carry out 1 order difference computing, then with ADF test and judges be stationary time series, after inspection Nonstationary time series carry out 2 order difference computings again, obtain stationary time series data；
    Step 2：ARMA model is established based on medical big data
    (1) parameter d value is determined according to the difference order of step 1, has carried out 1 order difference for nonstationary time series, then d =1,2 order differences are carried out, then d=2,
    (2) to the stationary time series obtained, auto-correlation coefficient ACF and PARCOR coefficients PACF are asked respectively, and pass through Analysis to autocorrelogram and partial autocorrelation figure, stratum p and exponent number q are obtained,
    (3) ARIMA (p, d, q) model is utilized, selects different p, q values calculate AIC respectively, BIC, HQIC value,
    (4) AIC of different ARIMA models is respectively compared, BIC, HQIC values, selects an optimal model, while determines p, q Value,
    (5) according to obtained p, d, q value, obtain extracting the ARIMA models of long-term trend, model inspection then is carried out to the model Test；
    Step 3：Whether the residual sequence of proving time series model is white noise sequence testing model
    After the ARIMA models of establishment step two, white noise verification is carried out to the estimated sequence of residual error, given if test value is less than Assumption value, explanation is white Gaussian noise；If not white Gaussian noise, the ARIMA models for illustrating selection are not one suitable The model of prediction is closed, it is necessary to which return to step two, reselects ARIMA models；
    Step 4：After long-term trend forecast model is established, the periodic index of medicine is calculated
    (1) average in medicine cycle is calculated
    <mrow> <msub> <mi>as</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>es</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Es in formula (1)j,iThe average value in the medicine cycle is represented, n represents the periodicity in specified time period, asiRepresent the medicine cycle Average；
    (2) overall mean in medicine cycle is calculated
    <mrow> <mi>t</mi> <mi>s</mi> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>t</mi> </munderover> <msub> <mi>es</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi>n</mi> <mo>*</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Hop count when t is represented in formula (2), ts represent the overall mean in medicine cycle；
    (3) overall mean of the periodic index, the i.e. average in medicine cycle/medicine cycle in medicine cycle is calculated：
    <mrow> <msub> <mi>ep</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>as</mi> <mi>i</mi> </msub> </mrow> <mrow> <mi>t</mi> <mi>s</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Step 5：Estimated with least square method and obtain periodic index forecast model
    (1) average consumption sum in the medicine cycle is calculated,
    (2) the regression equation group using the average consumption sum of least square fitting to the time,
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>n</mi> <mi>a</mi> <mo>+</mo> <mi>b</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>t</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>t</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>a</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>b</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>a</mi> <mo>=</mo> <mfrac> <mrow> <mi>&amp;Sigma;</mi> <mi>y</mi> </mrow> <mi>n</mi> </mfrac> <mo>-</mo> <mi>b</mi> <mfrac> <mrow> <mi>&amp;Sigma;</mi> <mi>t</mi> </mrow> <mi>n</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>b</mi> <mo>=</mo> <mfrac> <mrow> <mi>n</mi> <mi>&amp;Sigma;</mi> <mi>y</mi> <mi>t</mi> <mo>-</mo> <mrow> <mo>(</mo> <mi>&amp;Sigma;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>&amp;Sigma;</mi> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mi>n&amp;Sigma;t</mi> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>&amp;Sigma;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    (3) predicted value sold in short term using regression model calculating medicine,
    (4) short-term forecast value is multiplied by the predicted value that the periodic index of medicine is corrected；
    Step 6：The weights of two kinds of forecast model proportions are calculated using standard deviation, obtain combination forecasting
    (1) the long-term trend forecast model ARIMA and step 5 obtained using step 2 obtain based on medicine Exponential Periodicity Periodic index forecast model, the weight W of every kind of model is determined with the standard deviation proportion of two kinds of forecast models1And W2, it is described The calculating of weight meets formula (7)
    <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>&amp;epsiv;</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mrow> <mo>(</mo> <msubsup> <mi>p</mi> <mi>n</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mi>u</mi> <mo>(</mo> <mrow> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mi>min</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Weight W1=u, W2For=1-u, u optimal solution to meet formula (7) actual value and predicted value variance and minimum, ε is actual value Pi *With predicted value PiBetween error, n refers to prediction number,
    (2) combination forecasting is determined according to the weight of two kinds of models, the model is：
    Pt=W1P1t+W2P2t (8)
    P in formula (8)tIt is the prediction result of built-up pattern, P1tIt is the predicted value of ARIMA models, P2tIt is periodic index prediction mould Type predicted value, W1, W2It is the weight coefficient of two kinds of models respectively, to ensure the unbiasedness of combination forecasting, both need to meet W1+W2=1, W1>=0, W2≥0；
    Step 7：The com-parison and analysis of prediction result and presentation
    (1) medicine short-term forecast value is calculated by combination forecasting,
    (2) it is relative by mistake to compare ARIMA models, the average absolute of three kinds of models of periodic index forecast model and combination forecasting Poor MAPE and mean square error MAE,
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <mi>E</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>t</mi> </msub> </mrow> <msub> <mi>y</mi> <mi>t</mi> </msub> </mfrac> <mo>|</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>M</mi> <mi>A</mi> <mi>E</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>t</mi> </msub> <mo>|</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
    (3) the big data visualization of predicted value is presented and stored.
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CN112988978B (en) * 2021-04-27 2024-03-26 河南金明源信息技术有限公司 Case trend analysis system in important field of public service litigation
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