CN106354995A - Predicting method based on Lagrange interpolation and time sequence - Google Patents
Predicting method based on Lagrange interpolation and time sequence Download PDFInfo
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Abstract
The invention belongs to the technical field of data mining, and particularly relates to a data predicting method based on Lagrange interpolation and time sequence analysis. On the technological basis of data preprocessing, data predicting and data mining, a missing value and an abnormal value are preprocessed by means of a Lagrange interpolation method and are completely filled, historical data is kept, and a data basis is provided for subsequent data mining. On the basis of preprocessed data, a future value is predicted by means of the time sequence analysis method. Compared with an existing model, the problems that when the time sequence predicting method is directly applied to incomplete original data, the prediction result is deviated and accuracy is reduced are solved, the data prediction accuracy is improved, and the prediction requirement of enterprises is well met.
Description
Technical field
The invention belongs to data mining technology field is and in particular to one kind is pre- with seasonal effect in time series based on Lagrange's interpolation
Survey method.
Background technology
Along with the fast development of computer science and technology data, the big data epoch already arrive.Quantity of information occurs quick-fried
The phenomenon increasing, the difficulty therefrom finding useful information also increasingly increases, and leads to every profession and trade more next to the wish of data mining technology
Stronger.Data prediction is an extremely important problem of Data Mining, by being carried out to mass data, repairs
The data of incompleteness, the data correcting mistake and the data that removal is unnecessary, ignorant relation before excavating, and use these relations
Predict unknown result.In gathered data, sometimes because the reason such as problem of the fault of instrument or operation, lead to observe
To data failed fill in strictly according to the facts.When there being missing values, just destroy the succession of data, destroy the continuous of system
Property, the analysis to result causes significant impact.The method processing missing values can be divided three classes: deletion record, data interpolation and not
Process.Concrete condition also will be made a concrete analysis of, if be analyzed by simply deleting the record of disappearance, and also can obtain pre-
Phase effect, then this method that records containing missing values of deletion is to be certainly maximally effective.But, this method is being permitted
Have the shortcomings that very big in the case of many.It is to reduce historical data as cost, to lead to some possible relations in data to fail to dig
Excavate.Especially in the case that data set natively comprises seldom to record, delete a small amount of record and may badly influence point
The objectivity of analysis result and correctness.Indivedual values in sample are away from the extreme large of sequence mean level and extreme small.?
During data prediction, whether exceptional value is rejected, and need to be determined on a case-by-case basis, because some exceptional values may contain useful letter
Breath.Under many circumstances, to first analyze the possible cause of exceptional value appearance, then judge whether exceptional value should be given up, if
Correct data, can directly carry out excavating modeling on the data set have exceptional value.Will be direct for the record containing exceptional value
Delete this method simple, but shortcoming is also apparent from.In the case that observation is little, deletion can cause sample size not
Foot, may change original distribution of variable, thus causing the inaccurate of analysis result.The advantage that exceptional value is regarded as missing values
It is to expand historical data, make the analysis result to sequence more accurate.
Time series forecasting, as one of Forecasting Methodology in data mining, occupies in scientific research, business data analysis
Critically important status.Traditional Time Series Forecasting Methods have only done simple process for some missing values and exceptional value
Or do not process, the accuracy predicted below so may be led to reduce.The present invention is on studying above-mentioned technical foundation, carries
Go out the novel method combining using Lagrange's interpolation with time series analysis, before this on the basis of time series analysis
Using the missing values in Lagrange's interpolation more convenient processing data cleaning process, exceptional value, reapply time sequence
Arima model is set up in row analysis, and future value is relatively accurately predicted, achieves good effect.
Content of the invention
The present invention seeks to proposing a kind of data predication method based on Lagrange's interpolation and time series analysis, letter
During title, drawknot is legal, solves and leads to because of direct Time Series Analysis Forecasting method is applied on incomplete initial data
Predict the outcome deviation, accuracy the problems such as reduce, improves data prediction accuracy.
The technical scheme is that on the basis of data prediction, data prediction data digging technology, using glug
Bright day, interpolation method carried out pretreatment to missing values and exceptional value, missing values and exceptional value is filled up complete, remains historical data,
Provide data basis for follow-up data mining, on the basis of preprocessed data, applied time series analysis method is predicted not
To be worth, that is, one kind, based on Lagrange's interpolation and seasonal effect in time series data predication method, specifically comprises the following steps that
Step 1: initial data is analyzed, shortage of data value has been checked whether using progressive scan mode scarce
Mistake value, and rejecting outliers are taken and sets normal span and compare one by one, the value outside scope is labeled as exceptional value,
The missing values and exceptional value detecting are marked.
Step 2: to detecting in step 1 that problematic data separate Lagrange's interpolation carries out pretreatment, obtain clear
Reason, reduced data.
Step 3: pure randomness test (white noise verification) is carried out for the data after clearing up in step 2, if pure random
Sequence then terminates, if not pure random sequences then enter step 4.
Step 4: sequence stationary inspection is carried out for the data after clearing up in step 3, if not stationary sequence then enters
Step 5 carries out difference till steady, if then entering step 6.
Step 5: for sequence in step 4 be non-stationary series, carry out non-stationary time series.
Step 6: stable time rank analysis are carried out to the data in step 4.
Step 7: the data sequence meeting step 3 and step 4 is carried out to the matching of arima model.
Step 8: the data after drawknot legal processes during application is stored in data base, draws predictive value.
Brief description
Fig. 1 is based on Lagrange's interpolation and seasonal effect in time series Forecasting Methodology flow chart
Fig. 2 stationary time series arma model modeling step
The modeling procedure of Fig. 3 difference stationary time series
Specific embodiment
It is based on Lagrange's interpolation and seasonal effect in time series Forecasting Methodology flow chart with reference to Fig. 1.The present invention is directed to because directly
Time Series Analysis Forecasting method is applied on incomplete initial data and leads to predict the outcome deviation, accuracy reduction etc.
Problem, proposes a kind of data predication method based on Lagrange's interpolation and time series analysis, during abbreviation, drawknot is legal, carries
High data prediction accuracy.This model mainly divides two parts: carries out data prediction using Lagrange's interpolation, locates to pre-
Data separate Time series analysis method after reason is predicted.
Specifically comprise the following steps that
Step 1: initial data is analyzed, shortage of data value has been checked whether using progressive scan mode scarce
Mistake value, and rejecting outliers are taken and sets normal span and compare one by one, the value outside scope is labeled as exceptional value,
The missing values and exceptional value detecting are marked.
Step 2: to detecting in step 1 that problematic data separate Lagrange's interpolation carries out pretreatment, obtain clear
Reason, reduced data.
According to mathematical knowledge, one can be found for n point known in plane (point-blank) at no 2 points
Individual n-1 order polynomial y=a0+a1x+a2x2+…+an-1xn-1, make this polynomial curve cross n point.
(1) seek the known n-1 order polynomial crossing n point:
Y=a0+a1x+a2x2+…+an-1xn-1
Coordinate (x by n point1, y1), (x2, y2) ..., (xn, yn) substitute into multinomial, and it is many to solve Lagrange's interpolation
Xiang Shiwei:
(2) corresponding for the functional value of disappearance point x substitution interpolation polynomial is obtained approximation l (x) of missing values.
Missing values are processed into for data problematic in step 1, application Lagrange's interpolation is processed, process cores
Heart code is as follows:
Step 3: pure randomness test (white noise verification) is carried out for the data after clearing up in step 2, if pure random
Sequence then terminates, if not pure random sequences then enter step 4.
If a sequence is pure random sequences, then refer to that this sequence is a useless sequence, its sequential value it
Between should there is no any contact, that is, meet γ (k)=0, k ≠ 0, certainly this situation will not really occur, because auto-correlation
Coefficient will not be 0, only can be close to 0.
Pure randomness test (white noise verification) method therefor usually constructs statistic of test, and wherein conventional inspection is united
Metering has q statistic, lb statistic, can be calculated statistic of test by the autocorrelation coefficient that sample respectively postpones issue, so
After calculate corresponding p value, if p value be noticeably greater than significance level a then it represents that this sequence can not refuse purely random former vacation
If the analysis to this sequence can be stopped.
Step 4: sequence stationary inspection is carried out for the data after clearing up in step 3, if not stationary sequence then enters
Step 5 carries out difference till steady, if then entering step 6.
For stochastic variable x, its average (mathematic expectaion) μ, variances sigma can be calculated2；For two stochastic variable x and y,
X, covariance cov (x, y)=e [(x- μ of y can be calculatedx)(y-μy)] and correlation coefficientThey have measured two
The degree that influences each other between individual different event.
If time serieses { xt, t ∈ t } near a certain constant fluctuation and fluctuation range is limited, that is, have constant mean and
Constant variance, and postpone the auto-covariance of the sequence variables of k phase and autocorrelation coefficient is the equal sequence postponing the k phase in other words
Influence degree between row variable is the same, then claim { xt, t ∈ t } and it is stationary sequence.
Inspection to the stationarity of sequence has two kinds of methods of inspection, and a kind of is according to the real spy of sequential chart and autocorrelogram
Levy the method judging, the method very simple is quick, but shortcoming seeks to oneself to judge, subjectivity is too strong；Another
The method of kind is that construction statistic of test is tested, the main method of inspection of current unit root test method.
(1) datagram inspection
Average according to stationary time series and variance are all the property of constant, and the datagram obtaining stationary sequence should show
Show that the value of sequence carries out random fluctuation near a constant value, and scope bounded, no visible trend and the cycle fluctuated
Property.
(2) autocorrelogram inspection
Stationary sequence generally all has short-term correlation, that is only recent in the stationary sequence data of this property
Impact to certain data is larger, and dependency is larger.The stationarity of distinguishing sequence for how, refers to the increasing postponing issue k
Plus, the autocorrelation coefficient of sequence postpones the k phase and decay the speed difference going to zero, smoothly comparatively fast.
(3) unit root test
Whether checking sequence has unit root, and stationary sequence does not have unit root.
Step 5: for sequence in step 4 be non-stationary series, carry out non-stationary time series.
But in real life, most time sequence is all non-stable sequence.Therefore to nonstationary time series
The processing method that analysis is very vital, required also gets more and more.Permissible to the analysis method of nonstationary time series
Be divided into certainty factor decompose Time-Series analyses and random opportunity sequential two big class:
The method that certainty factor decomposes all is attributed to four factors the change of all sequences, and (long-term trend, season become
Change, circulation change and change at random) combined influence, wherein long-term trend and seasonal variations also have its rule at last, easily catch
Catch, but change at random is to be difficult to catch and analysis.
Based on a determination that the deficiency of sexual factor decomposition method, random sequence analysis application and give birth to.According to the different characteristics of sequence,
The model that random sequence analysis can be set up has arima model, residual auto-regression model, seaconal model, heteroscedastic model etc..Under
Face introduces arima model and nonstationary time series is modeled.
1) calculus of differences
P order difference: the subtraction between two sequential values of 1 phase is referred to as 1 order difference computing.
2) arima model
For the nonstationary time series that in life, we are run into, if becoming stationary sequence to after their difference,
Then this sequence is called difference stationary sequence, and to this, we set up arima model and process.Arima model is exactly poor in fact
Partite transport calculation is combined with arima model.
Step 6: stable time rank analysis are carried out to the data in step 4.
Process for stationary time series is generally processed using arma model (ARMA model), tool
Body ground it be divided into ar model, ma model and arma tri- class again, this three class is all multivariate linear model.
(1) model meeting below equation is referred to as p rank autoregression model, is abbreviated as ar (p):
xt=φ0+φ1xt-1+φ2xt-2+…+φpxt-p+εt
I.e. in the stochastic variable x of ttValue xtIt is front p phase xt-1, xt-2..., xt-pMultiple linear regression it is believed that
xtMainly affected by p phase sequential value in the past.Error term is current random disturbances εt, it is zero-mean white noise sequence.
(2) model meeting below equation is referred to as q rank autoregression model, is abbreviated as ma (q):
xt=μ+εt-θ1εt-1-θ2εt-2-…-θqεt-q
I.e. in the stochastic variable x of ttValue xtIt is the random disturbance ε of front q phaset-1, εt-2..., εt-qMultiple linear
Function, error term is current random disturbances εt, it is zero-mean white noise sequence, and μ is sequence { xtAverage.Think xtMain
If the error term by the q phase in the past is affected.
(3) model meeting below equation is referred to as ARMA model, is abbreviated as arma (p, q):
xt=φ0+φ1xt-1+φ2xt-2+…+φpxt-p+εt-θ1εt-1-θ2εt-2-…-θqεt-q
I.e. in the stochastic variable x of ttValue xtIt is front p phase xt-1, xt-2..., xt-pWith front q phase εt-1, εt-2...,
εt-qMultiple linear function, error term is current random disturbances ε1, it is zero-mean white noise sequence.Think xtMainly receive
Remove the sequential value of p phase and the joint effect of the error term of q phase in past.
It is to be particularly noted that as q=0, being that ar returns model；As p=0, it is ma (q) model.
When certain time series is after pretreatment, it has been judged as steadily and non-white noise sequence is it is possible to utilize
Arma model is modeled.Calculate steady non-white noise sequence { x firsttAutocorrelation coefficient and PARCOR coefficients, then
By model ar (p), ma (q) and the autocorrelation coefficient of arma (p, q) and the property of PARCOR coefficients, select optimum model.
The step that Fig. 2 models for stationary time series.
(1) calculate acf and pacf
First calculate autocorrelation coefficient (acf) and the PARCOR coefficients (pacf) of non-stationary white noise sequence.
(2) arma Model Identification
For the identification of model, that is, determine rank, we are by ar (p) model, ma (q) model and arma (p, q) model
Autocorrelation coefficient and the property of PARCOR coefficients, select optimum model.Identification principle for each model is similar.
(3) estimate model in unknown parameter value go forward side by side line parameter inspection.
(4) model testing
(5) model optimization
(6) model application: short-term forecast
Step 7: the data sequence meeting step 3 and step 4 is carried out to the matching of arima model, Fig. 3 is that difference is steady
Seasonal effect in time series modeling procedure.
For the rank of determining of model, the present invention adopts criterion bic method, relatively has pattern recognition most: calculate arima (p,
Q) when p and q is respectively less than the bic quantity of information of all combinations being equal to 5, wherein bic quantity of information is taken to reach the model order of minimum.
Part false code is as follows:
Step 8: the data after drawknot legal processes during application is stored in data base, draws predictive value.
Claims (3)
1. a kind of based on Lagrange's interpolation with seasonal effect in time series Forecasting Methodology it is characterised in that: comprise the following steps:
Step 1: initial data is analyzed, using progressive scan mode, disappearance has been checked whether for shortage of data value
Value, and rejecting outliers are taken and sets normal span and compare one by one, the value outside scope is labeled as exceptional value, right
It is marked in the missing values detecting and exceptional value.
Step 2: to detecting in step 1 that problematic data separate Lagrange's interpolation carries out pretreatment, cleared up, whole
Data after reason.
Step 3: pure randomness test (white noise verification) is carried out for the data after clearing up in step 2, if pure random sequences
Then terminate, if not pure random sequences then enter step 4.
Step 4: sequence stationary inspection is carried out for the data after clearing up in step 3, if not stationary sequence then enters step 5
Carry out difference till steady, if then entering step 6.
Step 5: for sequence in step 4 be non-stationary series, carry out non-stationary time series.
Step 6: stable time rank analysis are carried out to the data in step 4.
Step 7: the data sequence meeting step 3 and step 4 is carried out to the matching of arima model.
Step 8: the data after drawknot legal processes during application is stored in data base, draws predictive value.
2. be based on as claimed in claim 1 Lagrange's interpolation with seasonal effect in time series Forecasting Methodology it is characterised in that: described step
1st, in 2, propose to carry out pretreatment using Lagrange's interpolation to the missing values detecting and exceptional value.
3. be based on as claimed in claim 1 Lagrange's interpolation with seasonal effect in time series Forecasting Methodology it is characterised in that: described step
In rapid 3,4,5,6,7, on the basis of Lagrange's interpolation data prediction, complete data using Time series analysis method
Prediction, improves data prediction accuracy.
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