CN107358311A - A kind of Time Series Forecasting Methods - Google Patents

A kind of Time Series Forecasting Methods Download PDF

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Publication number
CN107358311A
CN107358311A CN201710423923.1A CN201710423923A CN107358311A CN 107358311 A CN107358311 A CN 107358311A CN 201710423923 A CN201710423923 A CN 201710423923A CN 107358311 A CN107358311 A CN 107358311A
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time series
training data
series forecasting
calculated
gur
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CN201710423923.1A
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肖秦琨
司阳
高嵩
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Xian Technological University
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Xian Technological University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G06F18/232—Non-hierarchical techniques
    • G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
    • G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering

Abstract

The invention discloses a kind of Time Series Forecasting Methods, including input training data and test data, Takens theorems are then based on, calculate Parameters for Phase Space Reconstruction；Training data is rebuild, the training data rebuild, and calculate the parameter of GUR models, and estimated probability density, and calculate reconstruct test data；Prior distribution is set based on prior information, the next step prediction of prior distribution is calculated based on bayesian theory method, it is optimal to estimate optimum prediction value again, and export the optimum prediction value.This method ensure that the accuracy and speed of time series forecasting, greatly reduces the complexity of algorithm, has saved calculating cost.

Description

A kind of Time Series Forecasting Methods
Technical field
The invention belongs to identification technology field, is related to a kind of Time Series Forecasting Methods, and in particular to one kind is based on The Time Series Forecasting Methods of long short-term memory and dynamic bayesian network.
Background technology
Time series forecasting is the hot issue in System Discrimination field, is with a wide range of applications, by many scholars With the concern of researcher.Simultaneously as probabilistic increase, multi-step prediction encounters huge challenge.Multi-step prediction is frequent Some elementary tactics are used, such as iterative method and direct method.
In the strategy based on iterative method, a step advanced prediction is calculated first, is then based on a step advanced prediction value and is come in advance Survey other data.On the other hand, in the strategy based on direct method, can be estimated according to identical forecast model a step it is advanced or Multistep advance value.Generally, an important factor for accumulated error is precision of prediction in influence iterative method, and it is then direct method to calculate cost In need consider an important factor for.
In addition some other algorithms, such as multiple-input and multiple-output (MIMO) method and DirRec strategies are also proposed, And multiple-input and multiple-output (MISMO) forecast model etc..In MIMO and MISMO algorithms, main thought be obtain it is higher pre- Survey precision.Meanwhile these methods all have higher calculating cost.In MISMO algorithms, initial predicted task is generally changed For subtask, and then output is calculated using optimal solution, wherein algorithm complex is a key issue.
At present in document disclosed in foreign countries, document [1] .A.Sorjamaa and A.Lendasse, " Time series prediction using DirRec strategy,"European Symposium on Artificial Neural Networks Bruges (Belgium), 26-28April2006. propose DirRec strategies；Document [2] .G.Bontempi, " Long term time series prediction with multi-input multi-output local learning,"European Symposium on Time Series Prediction,Helsinki,Finland,2008, Pp.145-154. multiple-input and multiple-output (MIMO) method is proposed；Document [3] .S.Ben Taieb, G.Bontempi, A.Sorjamaa,and A.Lendasse,"Long-term prediction of time series by combining direct and MIMO strategies,"IEEE International Joint Conference on Neural Networks, Atlanta, U.S.A., 2009, pp.3054-3061. propose multiple-input and multiple-output (MISMO) forecast model； Document [4] .S.Ben Taieb, A.Sorjamaa, and G.Bontempi, " Multiple-output modeling for multi-step-ahead time series forecasting,"Neurocomputing,vol.73,pp.1950-1957, 2010. have used optimal solution output algorithm.
But the prediction effect of above-mentioned document has some deficiency：
(1) document [1] [2] [3] main thought is to obtain higher precision of prediction, but these methods have higher calculating Cost；
(2) multiple-input and multiple-output (MIMO) method and multiple-input and multiple-output (MISMO) prediction proposed in document [2] [3] For model in order to reach higher precision of prediction, general sample data requires the complexity for as far as possible greatly, considerably increasing algorithm, Also improve computing cost simultaneously；
(3) the optimal solution output algorithm that document [4] proposes, algorithm realization is very simple, but is easily trapped into locally optimal solution, and Differ and surely search globally optimal solution；
(4) in the elementary tactics of multi-step prediction involved in document [2], accumulated error is to influence to predict in iterative method An important factor for precision, and it is then an important factor for needing to consider in direct method to calculate cost.
The content of the invention
The invention provides a kind of Time Series Forecasting Methods, this method ensure that the precision and speed of time series forecasting Degree, greatly reduces the complexity of algorithm, has saved calculating cost.
The technical scheme is that：A kind of Time Series Forecasting Methods, comprise the following steps：
Step 1, training data and test data are inputted；
Step 2, based on Takens theorems, Parameters for Phase Space Reconstruction is calculated；
Step 3, training data is rebuild, the training data rebuild；
Step 4, using the training data of reconstruction, GUR parameters, and GUR parameter Gaussian distributeds is calculated, is then estimated Probability density；
Step 5, by test data, reconstruct test data is calculated by system equation；
Step 6, prior distribution is set based on prior information；
Step 7, the next step prediction of prior distribution is calculated based on bayesian theory method；
Step 8, measurement updaue is calculated based on Bayes rule, and estimates optimum prediction value, then export optimum prediction Value.
Further, the features of the present invention also resides in：
Wherein it is to the process of reconstruction of training data in step 3：Time series forecasting mould based on long memory network in short-term Type, build the nonlinear model of a multiple input single output.
Wherein the detailed process of estimated probability density is in step 4：It is primarily based on gradient descent algorithm and calculates GUR parameters, It is then based on maximum likelihood method estimated probability Density Density.
The process of prior distribution is set wherein in step 6 is：GUR parameters are divided into multiple sections, calculate each section Decision subjective probability, then the subjective probability according to all sections obtain prior distribution.
Subjective probability wherein according to all sections obtains probability histogram, and the curve obtained according to probability histogram is Prior distribution.
Wherein subjective probability is to meet nonnegativity axiom, axiom of regularity, and countable additivity axiom.
Compared with prior art, the beneficial effects of the invention are as follows：This method by using the length based on iconic model in short-term Memory time series model, the model combine the long prediction of Memory Neural Networks in short-term and Bayes's graphical inference, significantly Reduce the complexity of algorithm, and higher precision of prediction is obtained using optimal estimation principle and recursive algorithm.Pass through simultaneously Recursive operation structure is proposed using based on probability theory and Bayes rule, to obtain more preferable estimated performance, the structure is than existing Model better performance.
Further, the problem of obtaining validity for information of forecasting in prediction algorithm in conventional art, using will be short When pre- geodesic structure be combined with long-term sequence signal model.All previous valid data are used during Sequence Operation Theory, are protected The integrality of acquisition of information and the validity of information of forecasting are demonstrate,proved.
Further, the time series being combined using the long short-term memory based on graph model with dynamic bayesian network Forecasting Methodology, precision of prediction is improved, while reduce the complexity of algorithm.
Further, recursive operation structure is proposed by using based on probability theory and Bayes rule, it is more preferable to obtain Estimated performance；The new multistep forecasting method based on graph model combined using most there is estimation to predict with recursive operation, While prediction cost is reduced, the validity of prediction is also improved.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the present invention；
Fig. 2 is GUR model schematics in the present invention.
Embodiment
Technical scheme is further illustrated with specific embodiment below in conjunction with the accompanying drawings.
The invention provides a kind of Time Series Forecasting Methods, as shown in figure 1, comprising the following steps：
Step 1, training data and test data are inputted.
Step 2, based on Takens theorems, Parameters for Phase Space Reconstruction is calculated.
Step 3, training data is rebuild, the training data rebuild；Time wherein based on long memory network in short-term Sequential forecasting models, build the nonlinear model of a multiple input single output.
Step 4, using the training data of reconstruction, GUR parameters, and GUR parameter Gaussian distributeds is calculated, is then estimated Probability density；It is primarily based on gradient descent algorithm and calculates GUR parameters, is then based on maximum likelihood method estimated probability Density Density.
Step 5, by test data, reconstruct test data is calculated by system equation.
Step 6, prior distribution is set based on prior information；GUR parameters are wherein divided into multiple sections, calculate each area Between decision subjective probability, then the subjective probability according to all sections obtain prior distribution.
Step 7, the next step prediction of prior distribution is calculated based on bayesian theory method.
Step 8, measurement updaue is calculated based on Bayes rule, and estimates optimum prediction value, then export optimum prediction Value.
The specific embodiment of the invention concretely comprises the following steps：
Step 1, training data { a is inputted1,…,atAnd test data { at+1,…,aT}。
Step 2, Parameters for Phase Space Reconstruction is calculated based on Takens theorems：D,τ.Restructuring procedure is specially：It is non-for one Linear system S, one group of measured value x (n), n=1,2 ... N is obtained by observation.Using this measured value can construct one group of m tie up to Amount
X (n)=(x (n), x (n- τ) ..., x (n- (D-1) τ)) (1)
If parameter τ, D selection is appropriate, then X (n) can describe original system.τ is referred to as time delay, and D is referred to as Embedded dimensions.By X (n) construction X (n) are referred to as phase space reconfiguration.
Made in the present embodiment (x (1), x (2) ..., x (N))=(a1,…,at) be system S observation sequence, can pass through Takens theorems find suitable parameters τ, D, complete reconstruct.
Step 3, training data is redeveloped into [xi,hi]I=1:t；Detailed process is：Time based on long memory network in short-term Sequential forecasting models, build the nonlinear system model of a multiple input single outputThe model is used for h step predictions, The model is expressed as:
Wherein t is time delay coefficient, and the precondition of time series data reconstruct is D >=2d1+ 1, wherein, d1It is related Dimension.
The process description is training data process of reconstruction, i.e., is inputted n-th to n- (D-1) τ time datas as system Data, using n+h step datas as system output data, so as to establish input and the data pair of output data.These data are to inciting somebody to action Training for system.
Step 4, using the training data [x of reconstructioni,hi]I=1:t, calculate GUR parameters Wz, Wr, W, and the parameter obeys height This is distributed, then estimated probability density；GUR parameters W is specifically calculated based on gradient descent algorithmz, Wr, W；Pass through priori With big data count, then by maximize study ML algorithms or maximum-likelihood method carry out parameter Estimation obtain probability density P (x, h)；Leave out original P (ht, zt) etc..
As shown in Fig. 2 being GUR model schematics, i.e. this Recurrent neural network neuronal structures of GUR, wherein W is represented Weight matrix in core cell Cell internal memories, W (r) are the network weight matrix of input block, and W (z) weighs for output unit networking Value matrix.Specific neural network weight is calculated and can calculated by neural network BP training algorithm, can be according to training data pair Using error back propagation algorithm.
Step 5, for test data { at+1,…,aT, use system equation
Calculate and obtain reconstruct data { xt+1,…,xT}。
According to the formula, xt and ht-1 is inputted, is calculated by data flow in Fig. 2 and formula, that is, obtains ht.
Step 6, prior distribution is set based on prior information；GUR parameter spaces are specifically divided into multiple minizones first； It is then determined that the decision subjective probability of each minizone, determines that subjective probability need to meet nonnegativity axiom, i.e., to any one occurrence A, 0 ≤ P (A)≤1, the probability of axiom of regularity, i.e. necessary event are 1, countable additivity axiom, pair can arrange a mutual exclusive thing Part A1, A2, A3 ..., is obtainedOr determine subjective probability according to historical data；Then according to subjective frequency Rate obtains frequency histogram, in the smoothed curve obtained according to the histogram, as prior distribution P (ht)。
Step 7, based on bayesian theory method according to its integral formula：
P(h1)=∫hP(h1|h0)P(h0) dh, (4)
The next step prediction P (h of prior distribution are calculatedt+1)：
P(ht+1)=∫hP(ht+1|ht)P(ht)dh (5)
Step 8, P (h are calculated based on Bayes rule1|z1) measurement updaue, and estimate optimum prediction
Then optimum prediction value is exportedIt is specific to calculate P (hi|zi), when α ∈ [0,1 ,], filtering equations are：
Pass through P (h1t:Instead of P (ht|z1:t), calculate maxP (ht+1:i|zt+1:i), calculation formula is：
Calculate optimum predictionWherein：
Then optimum prediction is exported
The invention provides a kind of time forecasting methods, time series forecasting mould of this method based on long memory network in short-term Type, and the mode combined based on histogram graphical model, reduce the complexity of algorithm, and using optimal estimation principle and pass Reduction method obtains higher precision of prediction.

Claims (6)

1. a kind of Time Series Forecasting Methods, it is characterised in that comprise the following steps：
Step 1, training data and test data are inputted；
Step 2, based on Takens theorems, Parameters for Phase Space Reconstruction is calculated；
Step 3, training data is rebuild, the training data rebuild；
Step 4, using the training data of reconstruction, GUR parameters, and GUR parameter Gaussian distributeds are calculated, then estimated probability Density；
Step 5, by test data, reconstruct test data is calculated by system equation；
Step 6, prior distribution is set based on prior information；
Step 7, the next step prediction of prior distribution is calculated based on bayesian theory method；
Step 8, measurement updaue is calculated based on Bayes rule, and estimates optimum prediction value, then export optimum prediction value.
2. Time Series Forecasting Methods according to claim 1, it is characterised in that to training data in the step 3 Process of reconstruction is：Based on the time series predicting model of long memory network in short-term, the non-linear of multiple input single output is built Model.
3. Time Series Forecasting Methods according to claim 1, it is characterised in that estimated probability density in the step 4 Detailed process be：It is primarily based on gradient descent algorithm and calculates GUR parameters, it is close is then based on maximum likelihood method estimated probability density Degree.
4. Time Series Forecasting Methods according to claim 1, it is characterised in that prior distribution is set in the step 6 Process be：GUR parameters are divided into multiple sections, the decision subjective probability in each section are calculated, then according to all sections Subjective probability obtain prior distribution.
5. Time Series Forecasting Methods according to claim 5, it is characterised in that the subjectivity according to all sections is general Rate obtains probability histogram, and the curve obtained according to probability histogram is prior distribution.
6. the Time Series Forecasting Methods according to claim 4 or 5, it is characterised in that the subjective probability is non-to meet Negativity axiom, axiom of regularity, and countable additivity axiom.
CN201710423923.1A 2017-06-07 2017-06-07 A kind of Time Series Forecasting Methods Pending CN107358311A (en)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110727553A (en) * 2019-10-15 2020-01-24 上海交通大学 Method and device for predicting and diagnosing faults of processor system
CN111913887A (en) * 2020-08-19 2020-11-10 中国人民解放军军事科学院国防科技创新研究院 Software behavior prediction method based on beta distribution and Bayesian estimation
CN112862004A (en) * 2021-03-19 2021-05-28 三峡大学 Power grid engineering cost control index prediction method based on variational Bayesian deep learning
CN113341919A (en) * 2021-05-31 2021-09-03 中国科学院重庆绿色智能技术研究院 Computing system fault prediction method based on time sequence data length optimization

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110727553A (en) * 2019-10-15 2020-01-24 上海交通大学 Method and device for predicting and diagnosing faults of processor system
CN111913887A (en) * 2020-08-19 2020-11-10 中国人民解放军军事科学院国防科技创新研究院 Software behavior prediction method based on beta distribution and Bayesian estimation
CN111913887B (en) * 2020-08-19 2022-11-11 中国人民解放军军事科学院国防科技创新研究院 Software behavior prediction method based on beta distribution and Bayesian estimation
CN112862004A (en) * 2021-03-19 2021-05-28 三峡大学 Power grid engineering cost control index prediction method based on variational Bayesian deep learning
CN113341919A (en) * 2021-05-31 2021-09-03 中国科学院重庆绿色智能技术研究院 Computing system fault prediction method based on time sequence data length optimization

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